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The deformation behavior of an artificial heart valve was analyzed using the explicit dynamic finite element method. Time variations of the left ventricle and the aortic pressure were considered as the mechanical boundary conditions in order to reproduce the opening and closing movements of the valve under the full cardiac cycle. The valve was assumed to be made from a medical polymer and hence, a hyperelastic Mooney–Rivlin model was assigned as the material model. A simple formula of the damage mechanics was also introduced into the theoretical material model to express the hysteresis response under the unloading state. Effects of the hysteresis on the valve deformation were characterized by the delay of response and the enlargement of displacement. Most importantly, the elastic vibration observed in the pure elastic response under the full close state was dramatically reduced by the conversion of a part of elastic energy to the dissipated energy due to hysteresis.

Ateroskleroza je jedna od najčešćih kardiovaskularnih bolesti, a tijekom njezinog razvoja dolazi do zadebljanja i oštećenja stijenke krvnih žila stvaranjem različitih aterosklerotskih promjena, najčešće plaka. Liječenje se može provesti kirurškim ili endovaskularnim pristupom. Endovaskularni pristup često uključuje ugradnju stenta. Stentovi se, prema načinu ugradnje, dijele na one koje se šire balonom (npr. metalni stentovi) i samoekspandirajuće (izrađeni od legura ili polimera s memorijom oblika). Samoekspandirajući stentovi uzrokuju manje oštećenja stijenke prilikom ugradnje, ali je s druge strane poznato da polimerni stentovi imaju lošija mehanička svojstva od metalnih. Međutim, razvoj novih i unapređenje postojećih materijala i tehnologija izrade omogućuje izradu složenijih geometrija stentova, pa tako i prilagođavanje oblika stenta svakom pacijentu posebno. Primjerice, da bi se osigurala dovoljna radijalna čvrstoća polimernog stenta, moguće je izraditi stent koji ima promjenjiv promjer, umjesto često korištene ravne mrežaste cjevčice. U sklopu ovog diplomskog rada definirana je pojednostavljena geometrija karotide s aterosklerotskim plakom kako bi se procijenila upotrebljivost stentova izrađenih od polimera s memorijom oblika i promjenjivim promjerom stenta. Razvijen je numerički postupak ugradnje stenta u karotidnu arteriju, koristeći hiperelastične modele za opisivanje materijala stijenke i stenta. Analizirana je upotrebljivost stentova s promjenjivim promjerom koristeći naprezanja u stentu kao kriterij, te je ocijenjena učinkovitost predloženih stentova s obzirom na smanjenje stenoze nakon ugradnje. Atherosclerosis is one of the most common cardiovascular diseases, characterized by thickening and damage to the blood vessel walls due to the formation of various atherosclerotic changes, most commonly plaques. Treatment can be performed through surgical or endovascular approaches. The endovascular approach often involves the implantation of a stent. Stents are divided based on the method of implantation, into those that expand with a balloon (e.g., metal stents) and self-expanding stents (made of shape memory alloys or polymers). Self-expanding stents cause less damage to the vessel wall during implantation, but it is known that polymer stents have inferior mechanical properties compared to metal stents. However, the development of new and improved materials and manufacturing technologies allows for the production of more complex stent geometries, including customized stent shapes for individual patients. For example, to ensure sufficient radial strength of a polymer stent, it is possible to create a stent with a variable diameter instead of the commonly used straight mesh tube. In this thesis, a simplified geometry of the carotid artery with an atherosclerotic plaque was defined to assess the usability of shape memory polymer stents with a variable diameter. A numerical procedure for stent implantation in the carotid artery was developed using hyperelastic models to describe the material behavior of the vessel wall and stent. The usability of stents with a variable diameter was analyzed using stress in the stent as a criterion, and the effectiveness of the proposed stents in reducing stenosis after implantation was evaluated.

Cilj naloge je zasnovati preprosto simulacijo streljanja s fračo, ki odraža obnašanje frače in izstrelka med strelom. Frača ima dva rogla, elastična nit pa je narejena iz gumijastega materiala, ki ga je možno dobro opisati s hiperelastičnim materialnim modelom. Pred obravnavo gibanja izstrelka smo s pomočjo nateznega preizkusa določili potrebne materialne lastnosti elastične niti. Za teoretično analizo mehanske karakteristike elastike smo uporabili dva reološka hiperelastična modela materiala, Mooney-Rivlinovega in Neo-Hookeovega. S primerjavo teoretično dobljene krivulje z eksperimentalno smo določili materialne parametre elastike, s pomočjo katerih smo nato izračunali količino potencialne energije, ki se med napenjanjem frače shrani v njej. Ob predpostavki, da se vsa potencialna energija, shranjena v frači med strelom pretvori v kinetično energijo, smo izračunali izstrelitveno hitrost in nato preko preproste simulacije analizirali kakšen vpliv na gibanje izstrelka imajo izstrelitvena hitrost, naklonski kot izstrelitve in aerodinamični upor. Prišli smo do ugotovitve, da izbira hiperelastičnega materialnega modela vpliva na količino energije, ki se med napenjanjem shrani v frači, kar posledično vpliva na izstrelitveno hitrost in gibanje izstrelka. The goal of the thesis assignment is to design a simple slingshot shooting simulation that reflects the behavior of the slingshot and projectile during the shot. The classic Y-shaped frame sling has the elastic tube/thread made of a rubber material that can be well described with a hyperelastic material model. Before considering the movement of the projectile, we determined the necessary material properties of the elastic thread with the help of a tensile testing. For the theoretical analysis of the mechanical characteristics of elastic, we used two rheological hyperelastic material models, Mooney-Rivlin and Neo-Hooke. By comparing the theoretically obtained curve with the experimental one, we determined the material parameters of the elastic, with the help of which we then calculated the amount of potential energy that is stored in it during pulling back the elastic of the slingshot. Assuming that during the shot all the potential energy stored in the slingshot is converted into kinetic energy, we calculated the launch speed/initial velocity of the projectile and then through a simple simulation analyzed the influence of the initial velocity, launch angle and aerodynamic resistance on the movement of the projectile. We have concluded that the choice of hyperelastic material model affects the amount of energy that is stored in the sling during tensioning, which in turn affects the launch speed and the movement of the projectile.

Nonlinear finite element analysis is widely used for structural optimization of the design and the reliability analysis of complex elastomeric components. However, high-precision numerical results cannot be achieved without reliable strain energy functions (SEFs) of the rubber or rubber nanocomposite material. Although hyperelastic constitutive models have been studied for nearly 80 years, selecting one that accurately describes rubber's mechanical response is still a challenge. This work reviews 85 isotropic SEFs based on both the phenomenological theory and the micromechanical network theory proposed from the 1940s to 2019. A fitting algorithm which can realize the automatic fitting optimization and determination of the parameters of all SEFs reviewed is developed. The ability of each SEF to reproduce the experimental data of both the unfilled and highly filled rubber nanocomposite is quantitatively assessed based on a new proposed evaluation index. The top 30 SEFs for the unfilled rubber and the top 14 SEFs for the highly filled rubber nanocomposite are presented in the ranking lists. Finally, some suggestions on how to select an appropriate hyperelastic constitutive model are given, and the perspective on the future progress of constitutive models is summarized.

A wide variety of hyperelastic rubber-like materials, exhibiting strong nonlinear stress–strain relations under large deformations, is applied in various industrial mechanical systems and engineering applications involving shock and vibration absorbers. An optimal design procedure of an elevator chassis crashing on a hyperelastic shock absorber in a fail scenario, applicable in large-scale mechanical systems or industrial structures of high importance under strong nonlinear dynamic excitation, is presented in this work. For the characterization of the hyperelastic absorber, a Mooney–Rivlin material model was adopted, and a series of in-lab compression quasi-static tests were conducted. Applying a fully parallelizable state-of-the-art stochastic model updating methodology, coupled with robust, accurate and efficient Finite Element Analysis (FEA) software, the hyperelastic behavior of the shock absorber was validated under uniaxial large deformation, in order to tune all material parameters and develop a high-fidelity FE model of the shock absorber system. Next, a series of in situ full-scale experimental trials were carried out using a test-case elevator chassis, representing the crash scenario on the buffer absorber system, after a controlled free fall. A limited number of sensors, i.e., triaxial accelerometers and strain gauges, were placed at characteristic points of the real structure of the elevator chassis recording experimental data. A discrete Finite Element (FE) model of the experimentally tested arrangement involving the elevator chassis and updated buffer absorber system along with all boundary conditions was developed and used in explicit nonlinear analysis of the crash scenario. Steel material properties and the characterized updated Mooney–Rivlin material model were assigned to the elevator chassis and buffer, respectively. A direct comparison of the numerical and experimental data validated the reliability and accuracy of the methodology applied, whereas results of the analysis were used in order to redesign and optimize a new-design elevator chassis, achieving minimum design stresses and satisfying serviceability limit states.

Objective: This study develops a biomedical ultrasound imaging method to infer microstructural information (i.e., tissue level) from imaging mechanical behavior of skeletal muscle (i.e., organ level). Methods: We first reviewed the constitutive model of skeletal muscle by regarding it as a transversely isotropic (TI) hyperelastic composite material, for which a theoretical formula was established among shear wave speed, deformation, and material parameters (MPs) using the acoustoelasticity theory. The formula was evaluated by finite element (FE) simulations and experimentally examined using ultrasound shear wave imaging (SWI) and strain imaging (SI) on in vivo passive biceps brachii muscles of two healthy volunteers. The imaging sequence included 1) generation of SW in multiple propagation directions while resting the muscle at an elbow angle of 90; 2) generation of SW propagating along the myofiber direction during continuous uniaxial muscle extension by passively changing the elbow angle from 90 to 120. Ultrasound-quantified SW speeds and muscle deformations were fitted by the theoretical formula to estimate MPs of in vivo passive muscle. Results: Estimated myofiber stiffness, stiffness ratio of myofiber to extracellular matrix (ECM), ECM volume ratio all agreed with literature findings. Conclusion: The proposed mathematical formula together with our in-house ultrasound imaging method enabled assessing microstructural material properties of in vivo passive skeletal muscle from organ-level mechanical behavior in an entirely noninvasive way. Significance: Noninvasive assessment of both micro and macro properties of in vivo skeletal muscle will advance our understanding of complex muscle dynamics and facilitate treatment and rehabilitation planning.

In this article we obtain a 1-dimensional asymptotic model for a junction of thin hyperelastic rods as the thickness goes to zero. We show, under appropriate hypotheses on the loads, that the deformations that minimize the total energy weakly converge in a Sobolev space towards the minimum of a 1 D-dimensional energy for elastic strings by using techniques from Γ-convergence.

We use a three-dimensional (3D) microvascular platform to measure the elasticity and membrane permeability of the endothelial cell layer. The microfluidic platform is connected with a pneumatic pressure controller to apply hydrostatic pressure. The deformation is measured by tracking the mean vessel diameter under varying pressures up to 300 Pa. We obtain a value for the Young's modulus of the cell layer in low strain where a linear elastic response is observed and use a hyperelastic model that describes the strain hardening observed at larger strains (pressure). A fluorescent dye is used to track the flow through the cell layer to determine the membrane flow resistance as a function of applied pressure. Finally, we track the 3D positions of cell nuclei while the vessel is pressurized to observe local deformation and correlate inter-cell deformation with the local structure of the cell layer. This approach is able to probe the mechanical properties of blood vessels in vitro and provides a methodology for investigating microvascular related diseases.

The human annulus fibrosus (HAF) is the major component in response to external forces for the intervertebral disk (IVD), which maintains the stability and flexibility of human spine. It can be assumed to be an anisotropic nearly incompressible hyperelastic composite consisting of collagen fibers and matrix in the numerical simulations of biomechanics. However, due to the geometric complexity and material nonlinearity of HAF, the conventional Finite Element Method (FEM) often gets into difficulties in mesh generation and uncertainty of accuracy control. In this paper, a modified composite-based constitutive model, which considers the slight compressibility of ground substance and the shear interaction between collagen fibers and matrix, is developed to describe the mechanical behavior of HAF. In addition, based on the gradient smoothing techniques, the selective 3D-edge-based and node-based smoothed finite element method (Selective 3D-ES/NS-FEM) is developed to alleviate volume locking and improve the accuracy of linear four-node tetrahedral (TET4) elements. Combined with the modified constitutive model, the Selective 3D-ES/NS-FEM is applied into the explicit dynamic analysis of HAF undergoing large deformation. By comparing with the experiment data in the literatures and the numerical results produced by conventional FEM, the presented approach is proved to possess excellent accuracy and efficiency in predicting the nonlinear mechanical behavior of HAF, as well as the orientation change of the collagen fibers. Moreover, the Selective 3D-ES/NS-FEM is demonstrated to have robust capability in handling element distortion, even with the simplest TET4 mesh. This study is significant to the biomechanical research of HAF, and has potential value for guiding the prevention and treatment of low back pain.

This study describes the basic design, material selection, fabrication, and evaluation of soft pneumatic actuators (SPA) for lower-limb rehabilitation compression therapy. SPAs can be a promising technology in proactive pressure delivery, with a wide range of dosages for treating venous-related diseases. However, the most effective design and material selection of SPAs for dynamic pressure delivery have not been fully explored. Therefore, a SPA chamber with two elastomeric layers was developed for this study, with single-side inflation. The 3D deformation profiles of the SPA chamber using three different elastomeric rubbers were analyzed using the finite element method (FEM). The best SPA-compliant behavior was displayed by food-grade silicone A10 Shore with a maximum deformation value of 25.34 mm. Next, the SPA chamber was fabricated using A10 Shore silicone and experimentally validated. During the simulation in FEM, the air pressure was applied on the inner wall of the chamber (i.e., the affected area). This is to ensure the applied pressure was evenly distributed in the inner wall while the outer wall of the chamber remained undeformed for all compression levels. During the inflation process, pressure will be applied to the SPA chamber, causing exerted pressure on the skin which is then measured for comparison. The simulation and experimental results show an excellent agreement of pressure transmission on the skin for the pressure range of 0–120 mmHg, as depicted in the Bland–Altman plots. The findings exhibited promising results in the development of the SPA chamber using low-cost and biocompatible food-grade silicone.

Primarna svrha ovog diplomskog rada je razvoj numeričke procedure za modeliranje ugradnje stenta izrađenog od polimera s memorijom oblika u karotidnu arteriju te analiza učinkovitosti bionički nadahnutih modela stentova s osvrtom na zaostalu stenozu i naprezanja u stijenci arterije. Pri tome je potrebno modelirati stijenku arterije što realnije. Budući da stvarno ponašanje stijenke arterije karakterizira anizotropija, uzrokovana rasporedom kolagenih vlakana, stijenci je dodijeljen anizotropni hiperelastični materijal opisan Holzapfel-Gasser-Ogden (HGO) modelom, a aterosklerotskom plaku i stentu izotropni hiperelastični materijal opisan Neo-Hooke modelom. Pri tome je korištena korisnička rutina UMAT za implementaciju HGO modela s predistezanjem elastina i kolagena u programski paket Abaqus 6.14-4. U programskom paketu SOLIDWORKS Premium 2022 SP2.0. je izrađen model konvencionalnog modela stenta, kao i niz prijedloga bionički nadahnutih modela stentova. Simulacijom ugradnje stentova u stijenku s 50 % stenoze je analizirana njihova učinkovitost. Rezultati su uspoređeni za slučaj krutog, hipocelularnog aterosklerotskog plaka čiji sastav i mehanička svojstva uzrokuju najopasniji slučaj bolesti, najniži stupanj redukcije stenoze. Evaluacijom rezultata je utvrđeno da predloženi Favus-O model nadahnut strukturom pčelinjeg saća osigurava povoljnije uvjete ugradnje stenta u odnosu na konvencionalni i druge predložene modele redukcijom stenoze s 50 % na 31 % uz očekivano povećanje naprezanja u stijenci uzrokovano većim radijalnim pomacima. The primary purpose of this master’s thesis is the development of a numerical procedure for modelling of a shape memory polymer carotid stent implementation and efficiency analysis of bionic-inspired stent models. The stenting efficiency is defined by the residual stenosis and arterial wall stress. To achieve that, it is necessary to model the arterial wall as realistically as possible. Since the real arterial wall behaviour is characterized by anisotropy due to the arrangement of collagen fibres, the arterial wall was modelled as an anisotropic hyperelastic material described by the Holzapfel-Gasser-Ogden (HGO) model, while isotropic hyperelastic material described by the Neo-Hooke model was used for both atherosclerotic plaque and stent. User material subroutine (UMAT) was used for the implementation of HGO model that takes into account pre-stretches in elastin and collagen in Abaqus 6.14-4 software. A model of a conventional stent and various proposed bionic-inspired stents were created in SOLIDWORKS Premium 2022 SP2.0 software. Their efficiency was analysed by simulating the stent implantation into an artery with 50 % degree of stenosis. The obtained results were compared for the case of the stiff hypocellular atherosclerotic plaque, whose composition and mechanical properties generate the most threatening case of the disease, and result in the least reduction of stenosis. The numerical results show that the suggested Favus-O model inspired by the honeycomb structure provides more favourable lumen expansion after stent implementation in comparison to the conventional, but also to the other proposed models, by reducing the stenosis from 50 % to 31 % with the expected increase in wall stress caused by larger radial displacements.

The choice of an appropriate strain energy function W is key to accurate modeling and computational finite element analysis of the mechanical behavior of unfilled non-crystalizing rubberlike materials. Despite the existing variety of models, finding a suitable model that can capture many deformation modes of a rubber specimen with a single set of parameter values and satisfy the a priori mathematical and structural requirements remains a formidable task. Previous work proposed a new generalized neo-Hookean W (I1) function (doi: 10.1016/j.ijnonlinmec.2020.103626), showing a promising fitting capability and enjoying a structural basis. In this work we use two extended forms of that model which include an I2 term adjunct, W(I1,I2), for application to various boundary value problems commonly encountered in rubber mechanics applications. Specifically, two functional forms of the I2 invariant are considered: a linear function and a logarithmic function. The boundary value problems of interest include the in-plane uniaxial, equi-biaxial, and pure shear deformations and simple shear, inflation, and nonhomogeneous deformations such as torsion. By simultaneous fitting of each model to various deformation modes of rubber specimens, it is demonstrated that a single set of model parameter values favorably captures the mechanical response for all the considered deformations of each specimen. It is further shown that the model with a logarithmic I2 function provides better fits than the linear function. Given the functional simplicity of the considered W (I1, I2) models, the low number of model parameters (three in total), the structurally motivated bases of the models, and their capability to capture the mechanical response for various deformations of rubber specimens, the considered models are recommended as a powerful tool for practical applications and analysis of rubber elasticity.

The dynamic mechanical properties of rubber spring have great influence on the vehicle dynamic performance, so the accurate description of the mechanical properties of rubber spring has always been the focus of the train dynamics. Among the mechanical properties of rubber springs, the study of non-hyperelastic properties are the most difficult and complex. Therefore, this paper mainly studies non-hyperelastic forces. Based on the experimental data of rubber springs, an elliptic analysis model is derived to describe the non-hyperelastic properties of rubber springs. On the basis of this model, a modified model based on time change and a modified model based on displacement change are also proposed. The results show that the ellipse analysis model is simple, but the error of calculation is large; the calculation precision of time correction model is high, but the calculation process is complex; the displacement correction model is between the previous two models, with both accuracy and convenience. Compared with other models, the displacement correction model has great advantages, which can improve the accuracy of the calculation of train dynamics. It is suggested to adopt the rubber spring displacement correction model in engineering application.

The performance of a structurally dissipating rock-shed (SDR) depends largely on the capacity of its energy dissipators. At present, most energy dissipators are made of metals, which dissipate energy by unrecoverable plastic deformation. Therefore, they are not able to recover their energy-dissipation capacity after deformation under rockfall impact. However, a rockfall usually disintegrates into pieces when it rolls down from a higher position and results in multiple rockfall impacts. An energy dissipator with self-recovery capability is therefore more suitable for ensuring the safety of SDRs. Replacing metal with polyurethane (a hyperelastic material with remarkable self-recovery capability) can provide self-recovery capability for energy dissipators, making them more suitable for resisting multiple rockfall impacts. In this work, polyurethane was manufactured into two types of energy dissipators: cylindrical and cubical. Full-scale falling rock impact tests and dynamic numerical simulations were conducted to study the mechanical response of the energy dissipators. In addition, in order to ensure the accuracy of the simulation, the dynamic mechanical properties of the polyurethane were tested and its dynamic constitutive model was established. The experimental and simulation tests have clarified the advantages of the polyurethane energy dissipator. We also summarized the practical considerations in the design of energy dissipators.

In order to develop optimum microneedle designs, researchers must first develop robust, repeatable and adaptable test methods which are representative of in vivo conditions. However, there is a lack of experimental tools which can accurately comparatively interrogate functional microneedle penetration of tissue. In this study, we seek to develop a state of the art finite element model of microneedle insertion into and penetration of human skin. The developed model employs a 3D hyperelastic, anisotropic pre-stressed multi-layered material which more accurately reflects in vivo skin conditions, while the microneedle is modeled as an array, which can capture the influence of adjacent microneedles on the overall response. Using the developed finite element model, we highlight the importance of accurate computational modeling which can decipher the mechanics of microneedle insertion, including the influence of its position within an array and how it correlates well with experimental observations. In particular, we have concluded that, for our model microneedle array, increasing skin pretension from 0 to 10% strain reduces the penetration force by 13%, ultimate local deformation about the microneedle by 22% and the ultimate penetration efficiency by 15%. We have also concluded that the presence of a base plate limits the penetration efficiency by up to 24%, while the penetration efficiency across a 5 × 1 microneedle array may vary by 27%. This model elucidates, for the first time, the combined effects of skin tension and needle geometry on accurately predicting microneedle penetration efficiency. Statement of Significance Microneedles arrays (MNAs) are medical devices with microscale protrusions, typically designed to penetrate the outermost layer of the skin, that upon optimisation, could lead to disruptive minimally-invasive disease management. However, the mechanics of MNA insertion are complex, due in part to a ‘bed of nails’ effect, and difficult to elucidate experimentally. Therefore, comparisons between designs, functional assessment of production batches and ultimately the likelihood of clinical translation are challenging to predict. Here, we have develop the most sophisticated in silico model of MNA insertion into pre-tensioned human skin to predict the extent of MNA penetration and therefore the likelihood of successful therapeutic delivery. Researchers can customise this model to predict the penetration efficiency of any MNA design.

A nonlinear viscoelastic contact interphase is modeled using a Cosserat rod-like string. This Cosserat model is a rod with a deformable cross-section, but with no constitutive resistance to bending. The model allows for axial extension, tangential shear deformation and normal extension of the cross-section which are determined by finite deformations of the interphase. Moreover, the constitutive response of this string model can be determined directly by three-dimensional constitutive equations for a hyperelastic component and a Maxwell elastic-viscoplastic component that together produce viscoelastic response of the interphase. The example of vibrations of a rigid outer ring connected to a fixed inner disk by a nonlinear viscoelastic interphase is used to show that the Cosserat string model of the interface predicts torque and force applied to the outer ring which include nonlinear coupling that is not present in simple uncoupled models of Maxwell components for torque and force applied to the outer ring by the interphase.

Moving boundaries and interfaces are commonly encountered in fluid flow simulations. For instance, fluid-structure interaction simulations require the formulation of the problem in moving domains, making the mesh distortion an issue of concern towards ensuring the accuracy of numerical model predictions. In this work, we propose a technique for the simultaneous mesh optimization and motion characterization. The mesh optimization/motion method introduced here is inspired by the mechanobiology of soft tissues, particularly those present in arterial walls, which feature an incredible capability to adapt to altered mechanical stimuli through adaptive mechanisms such as growth and remodeling. The proposed approach is in the framework of a low-distortion mesh moving method that is based on fiber-reinforced hyperelasticity and optimized zero-stress state. We adopt different reference configurations for the different constituents, namely ground substance and fibers. Hypothetical reference configurations are postulated for the different pieces of pseudo-material (the elements) as target shapes. Also, we modify the equilibrium equations using a volume-invariant strategy. Through the introduction of growth and remodeling adaptive processes we build an optimization algorithm which can attain an optimal configuration through a series of consecutive nonlinear optimizations steps. The remodeling mechanism allows to adapt the fiber deposition orientations, which become the driving force towards an homeostatic state, that is the optimal configuration. Also, a recruitment mechanism is introduced to selectively deal with initial highly distorted elements where high stresses develop due to the departure from the ideal configuration. We report 2D and 3D numerical experiments to show the application of this biologically-inspired mesh optimizer (BIMO) to simplicial finite element meshes. We also present additional numerical tests using BIMO as a mesh moving method. The results show that the proposed method performs satisfactorily, either as mesh optimizer and/or mesh motion strategy.

The inverse motion concept is used to optimize thermo-hyperelastic structures using an exact description of the deformed geometry. This method prescribes the shape of the structure in the deformed ...

Herein, an artificial neural network (ANN)-based approach for the efficient automated modeling and simulation of isotropic hyperelastic solids is presented. Starting from a large data set comprising deformations and corresponding stresses, a simple, physically based reduction of the problem’s dimensionality is performed in a data processing step. More specifically, three deformation type invariants serve as the input instead of the deformation tensor itself. In the same way, three corresponding stress coefficients replace the stress tensor in the output layer. These initially unknown values are calculated from a linear least square optimization problem for each data tuple. Using the reduced data set, an ANN-based constitutive model is trained by using standard machine learning methods. Furthermore, in order to ensure thermodynamic consistency, the previously trained network is modified by constructing a pseudo-potential within an integration step and a subsequent derivation which leads to a further ANN-based model. In the second part of this work, the proposed method is exemplarily used for the description of a highly nonlinear Ogden type material. Thereby, the necessary data set is collected from virtual experiments of discs with holes in pure plane stress modes, where influences of different loading types and specimen geometries on the resulting data sets are investigated. Afterwards, the collected data are used for the ANN training within the reduced data space, whereby an excellent approximation quality could be achieved with only one hidden layer comprising a low number of neurons. Finally, the application of the trained constitutive ANN for the simulation of two three-dimensional samples is shown. Thereby, a rather high accuracy could be achieved, although the occurring stresses are fully three-dimensional whereas the training data are taken from pure two-dimensional plane stress states.

Objectives The objective of this study is to demonstrate that computational finite element models can be used to reliably simulate dynamic interaction between a pacifier, the palate, and the tongue during nonnutritive sucking (NNS). The interactions can be quantified by the results of finite element analyses which include deformation, strain, stress, contact force, and contact area. Materials and Methods A finite element model was created based upon CAD solid models of an infant pacifier and palate. The silicone pacifier bulb is represented by a hyperelastic constitutive law. Contact surfaces are defined between the pacifier and palate. A time and spatially varying pressure load is applied to the bulb representing peristaltic interaction with the tongue. A second time‐varying, periodic pressure representing NNS is applied to the model simultaneously. A large displacement, nonlinear transient dynamic analysis is run over two NNS cycles. Results Results from the finite element analysis show the deformed shape of the bulb with maximum principal elastic strain of 0.23 and a range of maximum principal stress on the palate from 0.60 MPa (tensile) to −0.27 MPa (compressive) over the NNS cycles. The areas of contact between the pacifier and the palate are shown in surface contour plots. Conclusions A nonlinear transient dynamic finite element model can simulate the mechanical behavior of a pacifier and its interaction with the tongue and contact with the palate subject to NNS. Quantitative results predicting deformation, strain, stress, contact force, and contact area can be used in comparative studies to provide insight on how pacifiers cause changes in dental, orthognathic, and facial development.

In this paper, the nonlinear dynamic behaviors of a hyperelastic cylindrical membrane composed of the incompressible Ogden material are examined, where the membrane is subjected to uniformly distributed radial periodic loads at the internal surface and surrounded by a thermal field. A second-order nonlinear differential equation describing the radially symmetric motion of the membrane is obtained. Then, the dynamic characteristics of the system are qualitatively analyzed in terms of different material parameter spaces and ambient temperatures. Particularly, for a given constant load, the bifurcation phenomenon of equilibrium points is examined. It is shown that there exists a critical load, and the phase orbits may be the asymmetric homoclinic orbits of the “ $$\infty $$ ” type. Moreover, for the system with two centers and one saddle point, the dynamic behaviors of the system show softening phenomena at both centers, but the temperature has opposite effects on the stiffness of the structure. For a given periodically perturbed load superposed on the constant term, some complex dynamic behaviors such as quasiperiodic and chaotic oscillations are analyzed. With the Poincare section and the maximum Lyapunov characteristic exponent, it is found that the ambient temperature could lead to the irregularity and unpredictability of the nonlinear system, and also changes the threshold of chaos.

Cornea transplant involving applanation results in a deformation of the cornea. This deformation combined with a mismatch of dimensional and mechanical properties between donor and recipient corneas gives rise to tension on the transplanted cornea, astigmatism and vision difficulties. Therefore, accurate prediction of deformation of the incision plant during such operations is necessary to minimize complications. In this work, we employed a finite element simulation on a cornea with measured geometry and hyperelastic Mooney–Rivlin mechanical properties to analyze the intended incision plane’s change during corneal applanation. A simulation of the cornea transplant procedure assuming two different geometries to be the same was performed, and the transplanted cornea showed a 5.1% change in the exterior radius. When the proposed method was applied, no change in the radius after transplant was observed. Moreover, a precise matching of the incision plane can be selected for the corneas, and the corneal deformation after an IntraLase-Enabled Keratoplasty (ILEK) corneal transplant procedure is expected to be minimal.

In this paper, the physical and mechanical properties of products with the geometry of a triply periodic minimal energy surfaces (TPMES) are studied by computer simulation. The calculations are performed by the FEN method (hyperelastic viscoplastic fracture with a finite deformation) for typical samples of polyamide-12 material obtained by selective laser sintering (SLS). As a result of the study using the Comsol Multiphysics program, the distribution of mechanical stresses and the appearance of deformed products at various values of the applied mechanical stress, as well as the deformation curves, were obtained. The convergence of the calculations on the mesh size of the model under study is shown. The simulation results are in close agreement with the experimental data. As a result of the study, excellent physical and mechanical characteristics of the samples with the proposed geometry are found.

We propose a new methodology to estimate the 3D displacement field of deformable objects from video sequences using standard monocular cameras. We solve in real time the complete (possibly visco-)hyperelasticity problem to properly describe the strain and stress fields that are consistent with the displacements captured by the images, constrained by real physics. We do not impose any ad-hoc prior or energy minimization in the external surface, since the real and complete mechanics problem is solved. This means that we can also estimate the internal state of the objects, even in occluded areas, just by observing the external surface and the knowledge of material properties and geometry. Solving this problem in real time using a realistic constitutive law, usually non-linear, is out of reach for current systems. To overcome this difficulty, we solve off-line a parametrized problem that considers each source of variability in the problem as a new parameter and, consequently, as a new dimension in the formulation. Model Order Reduction methods allow us to reduce the dimensionality of the problem, and therefore, its computational cost, while preserving the visualization of the solution in the high-dimensionality space. This allows an accurate estimation of the object deformations, improving also the robustness in the 3D points estimation.

In this paper, we present a computationally efficient cellular mathematical model that accounts for the boundary collective behavior of a cell group by hepatocyte growth factor. The large cell group is modeled using continuum-based finite elements with incompressible hyperelastic materials for the nonlinear elastic behaviors. The total Lagrangian formulation is used enabling for large deformations, and the explicit time integration scheme without the Newton-Raphson iterative solution required for a time step is adopted to model the dynamics of the collective cell migration. With the explicit time integration and low order finite elements under the total Lagrangian framework, the proposed model is much computationally efficient for modeling the dynamic mechanical behavior of a cell colony. Detailed comparison to the experimental data shows that the proposed mathematical model provides a quantitatively accurate description of the collective cell motion in three different concentrations of hepatocyte growth factor.

Modeling the mechanical behavior of soft tissue probe insertion remains a challenging endeavor due to involved interdependent phenomena comprising tissue nonlinear deformation, contact between the probe and the tissue, crack propagation, and viscoelastic effects. To that matter, cohesive elements allow simulating crack formation and propagation, which provides a promising path to modeling the mechanical behavior of probe insertion in soft tissues. As such, the aim of the present study was to investigate the feasibility of devising and integrating an algorithm in a finite element (FE) case study in efforts of reverse engineering the material properties of non-homogeneous soft tissues. A layered nonlinear tissue model with a cohesive zone was created in the commercial software ABAQUS. Material properties were iteratively modified via a hybrid gradient descent optimization algorithm: minimizing the resultant error to first find optimum Ogden’s hyperelastic parameters, followed by obtaining the damage parameters. Perceived material properties were then compared to those obtained via experimental human cadaver testing. Under the investigated four-layered muscle model, numerical results overlapped, to a great extent, with six different force-insertion experimental profiles with an average error of $$\pm$$ 15%. The best profile fit was realized when the highest sudden force drop was less than 60% of the peak force. Lastly, the FE analysis revealed an increase in stiffness as the probe advanced inside the tissue. The optimization algorithm demonstrated its capability to reverse engineer the material parameters required for the FE analysis of real, non-homogeneous, soft tissues. The significance of this procedure lies within its ability to extract tissue material parameters, in real time, with little to no intervention or invasive experimental tests. This could potentially further serve as a database for different muscle layers and force-insertion profiles, used for surgeon and physician clinical training purposes.

This paper demonstrates how a strain energy transition approach can be used to remove artificial buckling modes that often occur in stability constrained topology optimization problems. To simulate the structural response, a nonlinear large deformation hyperelastic simulation is performed, wherein the fundamental load path is traversed using Newton’s method and the critical buckling load levels are estimated by an eigenvalue analysis. The goal of the optimization is to minimize displacement, subject to constraints on the lowest critical buckling loads and maximum volume. The topology optimization problem is regularized via the Helmholtz PDE-filter and the method of moving asymptotes is used to update the design. The stability and sensitivity analyses are outlined in detail. The effectiveness of the energy transition scheme is demonstrated in numerical examples.

Abstract Additive Manufacturing provides the opportunity to produce tailored and complex structures economically. The use of lattice structures in combination with a thermoplastic elastomer enables the generation of structures with configurable properties by varying the cell parameters. Since there is only little knowledge about the producibility of lattice structures made of TPE in the laser sintering process and the resulting mechanical properties, different kinds of lattice structures are investigated within this work. The cell type, cell size and strut thickness of these structures are varied and analyzed. Within the experimental characterization of Dodecahedron-cell static and cyclic compression tests of sandwich structures are focused. The material exhibits hyperelastic and plastic properties and also the Mullins-Effect. For the later design of real TPE structures, the use of numerical methods helps to reduce time and costs. The preceding experimental investigations are used to develop a concept for the numerical modeling of TPE lattice structures. Graphic abstract

This article presents an analytical model for soft pneumatic network actuators (PneuNets) consisting of a series of chambers made of elastomeric material and an inextensible bottom layer. The model links the input pressure with the bending angle in free space and the tip force of the PneuNets. The bending principle of the PneuNets is comprehensively analyzed through the analytical model. The bending angle of PneuNets is analyzed considering the deflection of the gap layer. The tip force of PneuNets is analyzed considering the equilibrium moment of the PneuNets at the applied pressure. This article focuses on the deformation of the gap layer of the PneuNets and the effect of gap length on the bending angle. The proposed model considers the deformation of the lateral wall of the chamber as the deformation of the nonlinear hyperelastic membrane. Futhermore, the contact moment is included considering the Hertzian contact between the adjacent chambers. Finite element analysis and physical experiments are carried out and the results show that the bending angle and tip force of the PneuNets can be effectively predicted by the analytical model with an error of less than 10%.

A sequential nonlinear multiscale method for the simulation of elastic metamaterials subject to large deformations and instabilities is proposed. For the finite strain homogenization of cubic beam lattice unit cells, a stochastic perturbation approach is applied to induce buckling. Then, three variants of anisotropic effective constitutive models built upon artificial neural networks are trained on the homogenization data and investigated: one is hyperelastic and fulfills the material symmetry conditions by construction, while the other two are hyperelastic and elastic, respectively, and approximate the material symmetry through data augmentation based on strain energy densities and stresses. Finally, macroscopic nonlinear finite element simulations are conducted and compared to fully resolved simulations of a lattice structure. The good agreement between both approaches in tension and compression scenarios shows that the sequential multiscale approach based on anisotropic constitutive models can accurately reproduce the highly nonlinear behavior of buckling-driven 3D metamaterials at lesser computational effort.

This paper presents a novel direct Jacobian total Lagrangian explicit dynamics (DJ-TLED) finite element algorithm for real-time nonlinear mechanics simulation. The nodal force contributions are expressed using only the Jacobian operator, instead of the deformation gradient tensor and finite deformation tensor, for fewer computational operations at run-time. Owing to this proposed Jacobian formulation, novel expressions are developed for strain invariants and constant components, which are also based on the Jacobian operator. Results show that the proposed DJ-TLED consumed between 0.70x and 0.88x CPU solution times compared to state-of-the-art TLED and achieved up to 121.72x and 94.26x speed improvements in tetrahedral and hexahedral meshes, respectively, using GPU acceleration. Compared to TLED, the most notable difference is that the notions of stress and strain are not explicitly visible in the proposed DJ-TLED but embedded implicitly in the formulation of nodal forces. Such a force formulation can be beneficial for fast deformation computation and can be particularly useful if the displacement field is of primary interest, which is demonstrated using a neurosurgical simulation of brain deformations for image-guided neurosurgery. The present work contributes towards a comprehensive DJ-TLED algorithm concerning isotropic and anisotropic hyperelastic constitutive models and GPU implementation. The source code is available at https://github.com/jinaojakezhang/DJTLED., Comment: Published in International Journal for Numerical Methods in Engineering

International audience; In this study, the Finite-Element Model Updating (FEMU) technique is used to identify hyperelastic parameters from only one heterogeneous test. A residual considering measured and identified stretches as well as the global reaction force of the specimen is built. The originality of this paper is to investigate the feasibility of the resolution of this minimisation problem using the Inverse-PageRank-particle swarm optimisation (PSO) for identifying hyperelastic parameters. For that purpose, the so-called PSO technique has been enriched with a PageRank algorithm to adapt iteratively the PSO parameters. As the paper examines whether Inverse-PageRank-PSO is adapted or not to the minimisation of the objective function in the present case, only two basic hyperelastic models have been considered.

The rubber-cord layers in passenger car tires are usually calculated assuming that deformations in them are small. However, rubber-cord layers can experience deformations of up to 15%. In calculations, the rubber-cordis usually replaced by an effective material. In this work, a phenomenological approach is used to construct a model of the effective material, where the inhomogeneous rubber-cord layer is replaced by an equivalent homogeneous anisotropic hyperelastic material. To describe the averaged properties of rubber-cord, the elastic potential of a transversely isotropic or orthotropic material can be used. However, in the case of a thin inhomogeneous layer, the traditional definition of averaging needs a modification. In this work, it is proposed to use the 3D averaged elastic properties of the layer surrounded by a homogeneous material. To determine constants of the elastic potential, nonlinear local problems on the periodicity cell has to be solved. In the case of a transversely isotropic potential, a set of local problems sufficient to determine the constants is proposed. It is shown that the procedure for determining the constants is stable relative to perturbations of the parameters of periodicity cell. To differentiate the potential, the symbolic calculations from the Octave package were used. The numerical calculations performed showed that the structure of the potential proposed and the scheme for determining material parameters are suitable.

Corrections to the harmonic approximation are obtained for the first order of the theory of hyperelasticity in the relaxation approximation for a cubic crystal. The Vlasov equation is constructed for a collisionless gas of phonons in a self-consistent deformation field. Collisions of phonons are considered in the relaxation approximation to the equilibrium distribution. It is shown that the thermoelasticity equations are valid for the hydrodynamics of a phonon gas in the thermodynamic limit. The relationship between the kinetic model of a phonon gas and the equations of Cattaneo and Guyer-Crumhansl, as well as Biot’s thermoelasticity, is considered.

In order to improve the printing quality, this study focused on the thermo-fluid-solid coupling process of ink roller-ink. One of the highlights of this study is to consider the influence of temperature on the rubber hyperelastic parameters, viscoelastic parameters, and ink viscosity. The other highlight is to improve the elastohydrodynamic lubrication theory and Hertz contact theory through the rubber elastic modulus, which is determined by the relaxation curve considering the temperature and working conditions. Furthermore, based on the improved theory, the thermo-fluid-solid coupling model of ink roller-ink was established. Finally, the effect of temperature on the coupling process was analyzed. The results show that under the working conditions, with increasing temperature from 20 °C to 40 °C, the contact half-width increases from 4.2335 mm to 4.4701 mm, and the minimum ink film thickness decreases from 0.5097 mm to 0.1410 mm, and the maximum ink pressure decreases from 0.6802 MPa to 0.6618 MPa.

This contribution aims at developing a formulation for the large viscoelastic deformation of hyperelastic beams and frames under various loading and boundary conditions. To do so, the kinematics of deformation in two-dimensional space is formulated and basic kinematics and kinetic quantities are introduced. The quasi-linear viscoelasticity theory is employed to capture the time-dependent behavior of the underlying material. The corresponding time integration scheme and the consistent tangent moduli are then presented. Because of the highly nonlinear nature of governing equations at the large regime of deformations including time dependency, a nonlinear finite element formulation in the total Lagrangian framework is developed. Several numerical examples are provided to investigate the applicability of derived formulations. It is observed that the formulation can successfully capture the relaxation and creep phenomena in visco-hyperelastic beams and frames.

An improved mathematical model of soft heart tissue has been developed here. Nonlinear material equations were derived from the fundamental principles of nonequilibrium thermodynamics. The passive ...

pH-sensitive hydrogels are classified as soft materials that can be employed for future imaginative applications due to their interesting characteristics. Smart hydrogels undergo large deformation under exterior stimuli. However, the swelling behaviors of hydrogels that can be harnessed for microfluidic applications are not well perceived. In this paper, the functionality of an assortment of micro-valves which are composed of pH-sensitive cylindrical hydrogel jackets coated on rigid pillars is inspected considering fully coupled fluid–solid interaction analysis. Therefore, in order to introduce the theory of transient swelling of a pH-sensitive micro-check valve, a transient constitutive model capturing electrical, chemical, and mechanical fields for the hydrogel domain is utilized with fluid fields passing around the micro-valve. In this regard, the Nernst–Planck equation is employed to describe the ions’ diffusion, and Gent hyperelastic model is used to account for the large deformation of the hydrogel. Implementing this nonlinear finite element framework, we examine the performance of one cylindrical jacket and also three patterns of multiple cylindrical valves considering transient 3D FSI behavior of the hydrogel micro-valve. The foremost emphasized novelty of this paper is considering three-dimensional geometry, new designs of micro-valves, and time-dependent swelling of hydrogels by coupling ions diffusion and their large deformation.

For finite-strain plasticity with anisotropic yield functions and anisotropic hyperelasticity, we use the Kroner-Lee decomposition of the deformation gradient combined with a yield function written in terms of the Mandel stress. The source is here the right Cauchy-Green tensor provided by a FE discretization. For the integration of the flow law we adopt a scaled/squared series approximation of the matrix exponential, which is compared with a classical backward-Euler method. The exact Jacobian of the second Piola-Kirchhoff stress is determined with respect to this source, consistent with the approximation. The resulting system is produced by symbolic source-code generation for each yield function and hyperelastic strain-energy density function. The constitutive system is solved by a damped Newton-Raphson algorithm for the plastic multiplier and the elastic right Cauchy-Green tensor $$\varvec{C}_{e}$$ . To ensure power-consistency, we make use of the elastic Mandel stress construction. Two numerical examples exhibit the comparative effectiveness of the Algorithm for very large elastic and plastic deformations. The elasto-plastic pinched cylinder makes use of as few as 2 steps for the total radius displacement of 300 mm and only 25 steps are required for the cup drawing problem.

Blood clots play a diametric role in our bodies as they are both vital as a wound sealant, as well as the source for many devastating diseases. In blood clots' physiological and pathological roles, their mechanics play a critical part. These mechanics are non-trivial owing to blood clots' complex nonlinear, viscoelastic behavior. Casting this behavior into mathematical form is a fundamental step toward a better basic scientific understanding of blood clots, as well as toward diagnostic and prognostic computational models. Here, we identify a hyper-viscoelastic damage model that we fit to original data on the nonlinear, viscoelastic behavior of blood clots. Our model combines the classic Ogden hyperelastic constitutive law, a finite viscoelastic model for large deformations, and a non-local, gradient-enhanced damage formulation. By fitting our model to cyclic tensile test data and extension-to-failure data, we inform the model's nine unknown material parameters. We demonstrate the predictability of our model by validating it against unseen cyclic tensile test and stress-relaxation data. Our original data, model formulation, and the identified constitutive parameters of this model are openly available for others to use, which will aid in developing accurate, quantitative simulations of blood clot mechanics.

A mathematical modeling is employed to investigate the axisymmetric nonlinear low-frequency vibrations of a class of hyperelastic thin-walled cylindrical shells subjected to axial harmonic excitations. A modified frequency domain method is presented to determine the stability of periodic solutions. Based on the variational method, the system of nonlinear governing differential equations describing the coupled axial-radial vibrations of simply supported shells is derived. Then, the harmonic balance method and the arc length method with two-point prediction are adopted to obtain the complicated steady-state solutions effectively, and the stability is discussed with the modified sorting method. Significantly, numerical results manifest that the length-diameter ratio serves a critical role in the nonlinear low-frequency vibrations, its variation should give rise to abundant nonlinear phenomena, such as the typical softening and hardening, the resonance peak shift and the isolated bubble shaped response.

We describe the behavior of a deformable porous material by means of a poro-hyperelastic model that has been previously proposed in Chapelle and Moireau (2014) under general assumptions for mass and momentum balance and isothermal conditions for a two-component mixture of fluid and solid phases. In particular, we address here a linearized version of the model, based on the assumption of small displacements. We consider the mathematical analysis and the numerical approximation of the problem. More precisely, we carry out firstly the well-posedness analysis of the model. Then, we propose a numerical discretization scheme based on finite differences in time and finite elements for the spatial approximation; stability and numerical error estimates are proved. Particular attention is dedicated to the study of the saddle-point structure of the problem, that turns out to be interesting because velocities of the fluid phase and of the solid phase are combined into a single quasi-incompressibility constraint. Our analysis provides guidelines to select the componentwise polynomial degree of approximation of fluid velocity, solid displacement and pressure, to obtain a stable and robust discretization based on Taylor–Hood type finite element spaces. Interestingly, we show how this choice depends on the porosity of the mixture, i.e. the volume fraction of the fluid phase.

This article introduces a computational approach for routing thin artificial muscle actuators through hyperelastic soft robots, in order to achieve a desired deformation behavior. Provided with a robot design and a set of example deformations, we continuously co-optimize the routing of actuators, and their actuation, to approximate example deformations as closely as possible. We introduce a data-driven model for McKibben muscles, modeling their contraction behavior when embedded in a silicone elastomer matrix. To enable the automated routing, a differentiable hyperelastic material simulation is presented. Because standard finite elements are not differentiable at element boundaries, we implement a moving least squares formulation, making the deformation gradient twice differentiable. Our robots are fabricated in a two-step molding process, with the complex mold design steps automated. While most soft robotic designs utilize bending, we study the use of our technique in approximating twisting deformations on a bar example. To demonstrate the efficacy of our technique in soft robotic design, we show a continuum robot, a tentacle, and a four-legged walking robot.

Za procjenu mehaničkih svojstava anizotropnih materijala potrebno je koristiti dvoosno vlačno ispitivanje prilikom kojeg se mjere podaci o naprezanju i deformacijama u dva smjera. Dvoosno vlačno ispitivanje se provodi na uređajima koji se nazivaju kidalice. U praksi se ova vrsta ispitivanja najčešće koristi za ispitivanje svojstava biomaterijala, poput arterijskog tkiva, ili za ispitivanje različitih kompozitnih materijala. S obzirom da su uzorci biomaterijala jako malih dimezija, treba obratiti pozornost na odabir vrste prihvata uzorka s ciljem ostvarenja što veće homogenosti polja naprezanja i deformacije. Najčešće se koristi prihvat u obliku steznih čeljusti čiji se kontakt s uzorkom zasniva na faktoru trenja. U ovom radu je eksperimentalno određeno pet faktora trenja na dodiru čeljusti i pet različitih vrsta uzoraka. Uz poznatu maksimalnu silu razvlačenja i faktor trenja, određena je vrijednost normalne sile koja se koristila kao ulazni podatak za numeričku simulaciju koja se provodila pomoću metode konačnih elemenata. Cilj ove simulacije je bio provjeriti čvrstoću i krutost stezne čeljusti prilikom maksimalnog opterećenja. Također, prikazana je numeriča analiza pet različitih hiperelastičnih materijala u teorijskom i realnom slučaju. U teorijskom slučaju uzorak je opterećen samo vlačnim silama, dok je u realnom slučaju u obzir uzeto i djelovanje sile pritezanja stezne čeljusti te dodirna površina između uzorka i čeljusti. Cilj ove simulacije je bio analizirati utjecaj sile pritezanja na homogenost polja naprezanja te odrediti približno potreban moment pritezanja. Ako je moment pritezanja prevelik, uzorak se nepotrebno deformira pri postavljanju na uređaj i povećava se koncentracija naprezanja. S druge strane, ako je moment pritezanja premali, uzorak tijekom eksperimenta može iskliznuti i eksperiment je tad neuspješan. Za izradu modela korišten je programski paket SolidWorks, dok su numeričke analize provedene u programskom paketu Abaqus. To evaluate the mechanical properties of anisotropic materials it is necessary to use biaxial testing test during which data on stress and deformations are measured in two directions. Biaxial tensile testing is performed on devices called tensile testing machines. In practice, this type of testing is most often used to test the properties of biomaterials such as arterial tissue or to test different composite materials. Since the samples of biomaterials are small in size, we should pay attention to the choice of the type of sample acceptance with the aim of achieving greater homogeneity of the stress and deformation field. The most commonly used sample acceptance is in the form of clamping jaws whose contact with the specimen is based on the coefficient of friction. In this paper, five coefficients of friction at contact between clamping jaws and five different types of samples were experimentally determined. With the known maximum stretching force and coefficient of friction, the value of normal force was determined which was used as input data for the numerical simulation, which was carried out using finite element method. The aim of this simulation was to verify the strength and stiffness of the clamping jaws during maximum load. Also, a numerical analysis of five different hyperelastic materials in theoretical and real case is presented. In the theoretical case, the sample is loaded only by tensile forces, while in the real case, the action of force of tightening the clamping jaws is also taken into account. The aim of this simulation was to analyze the influence of the tightening force on the homogeneity of the stress field and to determine the approximately required tightening torque. If the tightening torque is too high, the sample is unnecessarily deformed when placed on the device and the stress concentration increases. On the other hand, if the tightening torque is too small, the sample may slip during the experiment and the experiment is then unsuccessful. The SolidWorks software package was used to create the model, while numerical analyzes were performed in the Abaqus software package.

Cilj ovog rada je izgradnja razumijevanja metode materijalne točke. Na početku je predstavljena osnovna teorijska podloga iza metode materijalne točke. Dana je formulacija algoritma za simulaciju koraka metode materijalne točke koji koristi eksplicitnu integraciju. Objašnjena je i jednostavna tehnika adaptivnog vremenskog koraka. Definirano je više modela materijala - voda, hiperelastični materijal, snijeg i pijesak. Objašnjen je jednostavan način za definiranje i interakciju s krutim objektima u sceni, korištenjem funkcija udaljenosti s predznakom. Pokazani su različiti uvjeti na granici. Izneseni su pseudokodovi potrebni za implementaciju opisanih koncepata. Izrađen je simulacijski model unutar programskog alata Unity. Vizualni rezultati dobiveni su korištenjem tehnike praćenja zrake nad rezultatima simulacije unutar alata Blender. The goal of this paper is building the understanding of the material point method. The basic theoretical background required for understanding the material point method is presented. Formulation of an algorithm for explicit time integration is given. A simple technique to implement an adaptive time step is presented. Various material models are defined - water, hyperelastic material, snow and sand material models. A simple way to define and interact with rigid objects is explained, based on signed distance functions. Different border conditions are explained. Pseudocode required for the implementation of discussed topics is given. A simulation model is made using the Unity engine. Visual results are made by raytracing the simulation results using Blender.