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The mechanic-electro coupling overlapping finite element method (OFEM) is proposed to improve the accuracy in solving the mechanical characteristics of piezoelectric structures. Based on the basic equations and boundary conditions of piezoelectric materials, overlapping triangle elements are used to discretize the solution domain of piezoelectric structures, and the displacement function and potential function of the mechanic-electro coupling OFEM are constructed through local interpolation. The control equation of the mechanic-electro coupling OFEM is derived using the variation principle. The accuracy and validity of this method are verified by comparing with the reference solution and analytical solution in patch test and piezoelectric patch bending test. The static characteristics of the cantilever-typed piezoelectric sensor model, the rectangular plate with one-sided piezoelectric patch configuration, and the hole-containing piezoelectric energy harvester model are analyzed. The mechanic-electro coupling OFEM has high engineering value and broad application prospects in analyzing the structural mechanical properties of intelligent piezoelectric components. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) enables the production of complex geometries that are not accessible by conventional processes. Fused deposition modeling (FDM) 3D printing is an important choice for many industries, particularly for additive manufacturing of microelectronic systems. The various physical properties of printing polymer materials, such as geometry, rheological behavior, and others, need to be taken into account in the printing process. In our study, a semi-crystalline polypropylene polymer PP is used in the FDM process, as it is characterized by deformability due to crystallization. We investigate the thermomechanical behavior of a semi-crystalline polymer PP (polypropylene) with different material deposition geometries ranging from a parallelepiped filament to a cylindrical filament in a numerical model developed. A coupling (to temperature vs. time evolution during printing) of solid mechanics, heat transfer, and crystallization kinetics equations was considered to build the Multiphysics numerical model capable of predicting temperature profiles, residual stresses, and degree of crystallization during the FDM process. The results obtained with the numerical model provide a reliable approach to predicting and adjusting the actual thermomechanical behavior of a printed electronics package. The values are calculated and compared to the six points in the two samples. The results show that the change in deposit shape resulted in a maximum deviation of 3.3 MPa for residual stress and 0.376 for the degree of crystallization, while a decrease was observed in the selected points with an average deviation of 1.81 MPa and 0.193 for residual stress and the degree of crystallization, respectively. This is due to the effects of the modification of the shape model on the temperature profile model, with the change in the 3D structures of the printed polymer material; the methodology presented in this paper allows the numerical model to be validated with an experimental study of the literature. The paper proposes future work and an experimental study to validate the results of the numerical model. [ABSTRACT FROM AUTHOR]

Two-dimensional (plane) elasticity equations in solid mechanics are solved numerically with the use of an ensemble of physics-informed neural networks (PINNs). The system of equations consists of the kinematic definitions, i.e. the strain–displacement relations, the equilibrium equations connecting a stress tensor with external loading forces and the isotropic constitutive relations for stress and strain tensors. Different boundary conditions for the strain tensor and displacements are considered. The proposed computational approach is based on principles of artificial intelligence and uses a developed open-source machine learning platform, scientific software Tensorflow, written in Python and Keras library, an application programming interface, intended for a deep learning. A deep learning is performed through training the physics-informed neural network model in order to fit the plain elasticity equations and given boundary conditions at collocation points. The numerical technique is tested on an example, where the exact solution is given. Two examples with plane stress problems are calculated with the proposed multi-PINN model. The numerical solution is compared with results obtained after using commercial finite element software. The numerical results have shown that an application of a multi-network approach is more beneficial in comparison with using a single PINN with many outputs. The derived results confirmed the efficiency of the introduced methodology. The proposed technique can be extended and applied to the structures with nonlinear material properties. [ABSTRACT FROM AUTHOR]

Material parameter identification within the field of mechanics of materials is driven by different issues: experiments affecting the parameters, constitutive models describing the physical behavior of a material, discretization schemes for solving the initial boundary‐value problem of the underlying tests, as well as schemes calibrating the parameters at experimental observations. Furthermore, the question of the quality of the parameters must be addressed. The result concerns the issue of which influence parameter uncertainties have on the uncertainty of simulation results and can be addressed during validation. In this contribution, we provide a short overview of concurrent approaches to identify the parameters, where most of the methods can be distinguished into the reduced formulation, which is based on the implicit function theorem, and a particular form of the all‐at‐once approach. The latter represents the weighted sum of two contributions, first, the distances between physical state equations and zero, and, second, the distance between model response (simulation result) and experimental data. Since the formulation of the all‐at‐once approach is not well‐known in computational solid mechanics, it is investigated for the simple example of linear elasticity employing artificially noised data. It turns out that the all‐at‐once approach is not as robust as the well‐established reduced approach, especially for problems considering full‐field data. Moreover, a strong sensitivity to the noise and the initialization of the optimized parameters are observed indicating a pronounced ill‐posedness of the all‐at‐once formulation for specific applications. [ABSTRACT FROM AUTHOR]

Since the fundamental works of Kachanov and Rabotnov, creep damage mechanics is an established field of research in solid mechanics. The starting point is the creep behavior of materials under moderate loads but elevated temperatures. The final stage of creep behavior is accompanied by damage and other microstructural changes such as embrittlement. In the present paper a detailed analysis of literature is given. A special focus is made on the different types of representation of damage by scalar, vectorial and tensorial variables. In addition, some Russian sources are presented which are not widely known yet. The survey is representative, but not complete - due to the large number of sources, it is not possible to provide a complete overview. Considering the huge number of parameters of tensorial damage variables which should be established experimentally in the second part of the paper a simple model for the high temperature creep and embrittlement in metals and alloys under conditions of the long-term usage is introduced. The model is an extension of R. Arutunyan's model developed in the 90th of the last century. The extension includes the consideration of a compressible medium, the introduction of the mass conservation law and true stress, and definition of the damage parameter as a relative change in the density of the material. The parameters are experimentally estimated and the comparison of simulations and experiments is given. [ABSTRACT FROM AUTHOR]

This technical document discusses the development of elastic-viscoplastic deformation models for salt rocks. The study focuses on the behavior of salt specimens under compression and analyzes fracture criteria and plastic flow rules. Creep tests were conducted to study transient effects, and a mathematical model was constructed and calibrated using experimental data. The document provides equations, parameters, and results for different viscoplastic models and numerical simulations. The research was funded by the Ministry of Science and Higher Education of the Russian Federation. [Extracted from the article]

Bi-quadratic programming over unit spheres is a fundamental problem in quantum mechanics introduced by pioneer work of Einstein, Schrödinger, and others. It has been shown to be NP-hard; so it must be solve by efficient heuristic algorithms such as the block improvement method (BIM). This paper focuses on the maximization of bi-quadratic forms with nonnegative coefficient tensors, which leads to a rank-one approximation problem that is equivalent to computing the M-spectral radius and its corresponding eigenvectors. Specifically, we propose a tight upper bound of the M-spectral radius for nonnegative fourth-order partially symmetric (PS) tensors. This bound, serving as an improved shift parameter, significantly enhances the convergence speed of BIM while maintaining computational complexity aligned with the initial shift parameter of BIM. Moreover, we elucidate that the computation cost of such upper bound can be further simplified for certain sets and delve into the nature of these sets. Building on the insights gained from the proposed bounds, we derive the exact solutions of the M-spectral radius and its corresponding M-eigenvectors for certain classes of fourth-order PS-tensors and discuss the nature of this specific category. Lastly, as a practical application, we introduce a testable sufficient condition for the strong ellipticity in the field of solid mechanics. Numerical experiments demonstrate the utility of the proposed results. [ABSTRACT FROM AUTHOR]

Machine learning methods are progressively investigated for a large amount of applications. Recently, the solution of partial differential equations (PDE) describing problems in elastostatics came into focus. The current work investigates two neural network-based classes of methods for their solution, namely the neural finite element method (FEM) and neural operator methods. The analysis of these approaches is carried out by means of numerical experiments with linear and nonlinear material behavior where the conventional FEM serves as a benchmark. The formulation of neural FEM allows for elegant integration of finite deformation hyperelasticity at medium training effort. Here, training data are replaced by the evaluation of the equilibrium PDE at sample points. In contrast, most neural operator methods require expensive training with large data sets, but then allow for solving multiple boundary value problems with the same machine learning model. For the comparative analysis, the maximal relative error values over the whole domain and over all components of the strain tensor are evaluated as accuracy measure. The current state of research shows that none of the methods investigated reaches the accuracy and computational performance of the conventional FEM. In many standard applications, the FEM achieves an accuracy of 10 - 6 , whereas the numerical tests in the present work report a relative error of order of magnitude of 10 - 4 for the neural FEM and 10 - 2 to 10 - 3 for neural operator methods. [ABSTRACT FROM AUTHOR]

Smoothed particle hydrodynamics (SPH) is a state-of-the-art numerical simulation method in fluid mechanics. It is a novel approach for modeling and comprehending complex fluid behaviors. In contrast to traditional grid-dependent techniques like finite element and finite difference methods, SPH utilizes a meshless, purely Lagrangian approach, offering significant advantages in fluid simulations. By leveraging a set of arbitrarily distributed particles to represent the continuous fluid medium, SPH enables the precise estimation of partial differential equations. This grid-free methodology effectively addresses many challenges associated with conventional methods, providing a more adaptable and efficient solution framework. SPH's versatility is evident across a broad spectrum of applications, ranging from advanced computational fluid dynamics (CFD) to complex computational solid mechanics (CSM), and proves effective across various scales—from micro to macro and even astronomical phenomena. Although SPH excels in tackling problems involving multiple degrees of freedom, complex boundaries, and large discontinuous deformations, it is still in its developmental phase and has not yet been widely adopted. As such, a thorough understanding and systematic analysis of SPH's foundational theories are critical. This paper offers a comprehensive review of the defining characteristics and theoretical foundations of the SPH method, supported by practical examples derived from the Navier–Stokes (N-S) equations. It also provides a critical examination of successful SPH applications across various fields. Additionally, the paper presents case studies of SPH's application in tunnel and underground engineering based on practical engineering experiences and long-term on-site monitoring, highlighting SPH's alignment with real-world conditions. The theory and application of SPH have thus emerged as highly dynamic and rapidly evolving research areas. The detailed theoretical analysis and case studies presented in this paper offer valuable insights and practical guidance for scholars and practitioners alike. [ABSTRACT FROM AUTHOR]

Predicting failure initiation in nonlinear composite materials, often referred to as metamaterials, is a fundamental challenge in nonlinear solid mechanics. Microstructural failure mechanisms encompass fracture, decohesion, cavitation, compression-induced contact and instabilities, affecting their unconventional static and dynamic performances. To fully take advantage of these materials, especially in extreme applications, it is imperative to predict their nonlinear behaviour using reliable, accurate and computationally efficient numerical methodologies. This study presents an innovative nonlinear homogenization-based theoretical framework for characterizing the failure behaviour of periodic reinforced hyperelastic composites induced by reinforcement/matrix decohesion and interaction between contact mechanisms and microscopic instabilities. Debonding and unilateral contact between different phases are incorporated by employing an enhanced cohesive/contact model, which features a special nonlinear interface constitutive law and an accurate contact formulation within the context of finite strain continuum mechanics. The theoretical formulation is demonstrated using periodically layered composites subjected to macroscopic compressive loading conditions along the lamination direction. Numerical results illustrate the ways in which debonding phenomena, in conjunction with fibre microbuckling, may influence the critical loads of the examined composite solid. The sensitivity of the results obtained through the proposed contact–cohesive model at finite strain with respect to its implementation is also explored. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'. [ABSTRACT FROM AUTHOR]

• A coupled electromagnetic-mechanical model is built to calculate the coupling behaviors of superconducting coils. • Mechanical deformation impacts the motion of magnetic flux and changes the critical current of superconductors. • The roles of contact conditions in the superconducting coils are derived theoretically. • A mechanical homogenization model is proposed to simplify the model containing hundreds of contact pairs. Rare-earth based barium copper oxide (REBCO) superconducting coated conductors are promising candidates for the design of high field magnets. In a high magnetic field, these conductors have to withstand huge Lorentz force, which would threaten the safety of superconducting devices. Recently, researchers have found that the electromagnetic-mechanical coupling has a significant impact on the overall response of the magnet system. It has been demonstrated that mechanical deformation can lead to the movement of magnetic flux in superconductors and changes in the critical current of superconductors. To take into account the electromagnetic-mechanical coupling effects, REBCO coated conductors are modeled as deformable conductors based on continuum mechanics of electromagnetic solids. Then, a fully coupled electromagnetic-mechanical model is developed in this paper, which is verified with the experimental results. Furthermore, during the electromagnetic-mechanical coupling simulation, contact separation occurs in REBCO pancake coils. To characterize the global mechanical performance of the REBCO pancake coils (containing hundreds of contact conditions), the concept of flexural rigidity in elastic shell theory is employed. Then, a mechanical homogeneous model is proposed to simplify the model containing hundreds of contact pairs and enable the effective simulation of large-scale HTS systems. This framework can provide theoretical support to the mechanical research of high field magnets. [ABSTRACT FROM AUTHOR]

A physics-informed neural network (PINN) is a powerful tool for solving differential equations in solid and fluid mechanics. However, it suffers from singularly perturbed boundary-layer problems in which there exist sharp changes caused by a small perturbation parameter multiplying the highest-order derivatives. In this paper, we introduce Chien's composite expansion method into PINNs, and propose a novel architecture for the PINNs, namely, the Chien-PINN (C-PINN) method. This novel PINN method is validated by singularly perturbed differential equations, and successfully solves the well-known thin plate bending problems. In particular, no cumbersome matching conditions are needed for the C-PINN method, compared with the previous studies based on matched asymptotic expansions. [ABSTRACT FROM AUTHOR]

[Display omitted] Brain disorders represent an ever-increasing health challenge worldwide. While conventional drug therapies are less effective due to the presence of the blood-brain barrier, infusion-based methods of drug delivery to the brain represent a promising option. Since these methods are mechanically controlled and involve multiple physical phases ranging from the neural and molecular scales to the brain scale, highly efficient and precise delivery procedures can significantly benefit from a comprehensive understanding of drug-brain and device-brain interactions. Behind these interactions are principles of biophysics and biomechanics that can be described and captured using mathematical models. Although biomechanics and biophysics have received considerable attention, a comprehensive mechanistic model for modeling infusion-based drug delivery in the brain has yet to be developed. Therefore, this article reviews the state-of-the-art mechanistic studies that can support the development of next-generation models for infusion-based brain drug delivery from the perspective of fluid mechanics, solid mechanics, and mathematical modeling. The supporting techniques and database are also summarized to provide further insights. Finally, the challenges are highlighted and perspectives on future research directions are provided. Despite the immense potential of infusion-based drug delivery methods for bypassing the blood-brain barrier and efficiently delivering drugs to the brain, achieving optimal drug distribution remains a significant challenge. This is primarily due to our limited understanding of the complex interactions between drugs and the brain that are governed by principles of biophysics and biomechanics, and can be described using mathematical models. This article provides a comprehensive review of state-of-the-art mechanistic studies that can help to unravel the mechanism of drug transport in the brain across the scales, which underpins the development of next-generation models for infusion-based brain drug delivery. More broadly, this review will serve as a starting point for developing more effective treatments for brain diseases and mechanistic models that can be used to study other soft tissue and biomaterials. [ABSTRACT FROM AUTHOR]

This study investigated student's knowledge and understanding of mechanical stress including strain, and the relation between mechanical stress and strain, using material created by the authors of this text. It also investigated what the students perceived helpful for learning. The material was a complete laboratory setup and was intended to be simple and visual, including a digital part. During the studies in a Swedish upper secondary school, students enrolled in the technology programme took a general introductory course in solid mechanics. The students' participation in our study was composed of four classes. The study was implemented by answering a questionnaire prior to laboratory and a similar one after the laboratory, 85 out of 107 students answered both questionnaires. A thematic analysis was applied on the material, resulting in six thematic groups based on the students' previous knowledge and how much they have learned from the laboratory. To find correlations between the thematic groups, classes, and what the students perceived important for learning, a One-way Analysis of Variance (ANOVA) with multiple comparison post hoc test was performed. A significant difference between the class and the thematic groups was found (p<0.05). Another significant difference was found between the teacher and the class the students were in (p<0.001). This study showed that the teacher was important for the students' perception of solid mechanics during this laboratory and that the interactive lab description played less roll. The teacher's importance depended on what class the students were in. [ABSTRACT FROM AUTHOR]

This article discusses the use of non-smooth variational methods in a wide range of applications, particularly in fields that involve partial differential equations. The authors focus on nonlinear problems in solid and fluid mechanics, as well as inverse and optimal control problems. They aim to develop non-standard analysis and effective numerical methods for solving these problems. The article also highlights the contributions of various authors from different countries and discusses the physical applications of non-smooth variational methods in areas such as elastic and inelastic solids, heat transfer, and fracture mechanics. [Extracted from the article]

This study examines a class of time-dependent constitutive equations used to describe viscoelastic materials under creep in solid mechanics. In nonlinear elasticity, the strain response to the applied stress is expressed via an implicit graph allowing multi-valued functions. For coercive and maximal monotone graphs, the existence of a solution to the quasi-static viscoelastic problem is proven by applying the Browder–Minty fixed point theorem. Moreover, for quasi-linear viscoelastic problems, the solution is constructed as a semi-analytic formula. The inverse viscoelastic problem is represented by identification of a design variable from non-smooth measurements. A non-empty set of optimal variables is obtained based on the compactness argument by applying Tikhonov regularization in the space of bounded measures and deformations. Furthermore, an illustrative example is given for the inverse problem of isotropic kernel identification. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'. [ABSTRACT FROM AUTHOR]

Nonlinear evolution equations appear in various branches of physics, including fluid dynamics, solid mechanics, quantum mechanics, and other fields. They are essential for describing systems where interactions and nonlinearity play a significant role, providing a more accurate representation of real-world phenomena than linear equations in certain cases. The study of nonlinear evolution equations involves exploring their solutions, stability properties, and the behavior of the systems they describe over time. In this study, we provide plenty of analytical solutions to a very recently proposed water wave model using the modified generalized exponential rational function, modified extended tanh-function, and the exp(−φ(ξ))-expansion methods. To examine the dynamic characteristics of these results, we displayed three-dimensional (3D), contour, and two-dimensional (2D) visual representations of specific solutions. The outcomes reveal a multitude of novel solutions, emphasizing the robustness and effectiveness of the applied methodologies. It is important to note that all the solutions derived in this study are original and have not been previously documented in the existing literature. These novel solutions hold significant value for researchers in the realms of fluids and plasma physics, providing insights into the dynamics of nonlinear waves within various physical systems. Furthermore, this research contributes to a deeper understanding of the nature of nonlinear waves prevalent in seas and oceans, offering valuable knowledge for the broader study of such phenomena. [ABSTRACT FROM AUTHOR]

The human stomach is a complex organ. Its role is to degrade food particles by using mechanical forces and chemical reactions in order to release nutrients. All ingested items, including our nutrition, should first pass through the stomach, making it arguably the most crucial segment in the gastrointestinal tract. Computational and mathematical modeling of the stomach is an emerging field of biomechanics where several complex phenomena, such as solid mechanics of the gastric wall, gastric electrophysiology, and fluid mechanics of the digesta need to be addressed. Developing a meshfree comprehensive algorithm for solving the nervous stomach model that enables analysing the relationships between these phenomena remains one of the most significant challenges in biomechanics. This research dedicates to study the dynamics of nervous stomach model governed by a mathematical representation depending on three categories viz. Tension (T), Food (F) and Medicine (M), i.e. TFM model. In this regard, a machine learning paradigm, namely POLYnomial WinOwed with Gaussian (PolyWOG) Wavelet Neural Network (PWNN) model has been implemented for handling the non-linear TFM models. We compared the obtained outcomes of present work with results of a well-known numerical computing paradigm and an existing wavelet neural algorithm. Also, we have done statistical assessment studies at different testing points, which reveal that the proposed architecture is effective and accurate. [ABSTRACT FROM AUTHOR]

In this paper, the freezing and strengthening project of the Sanya estuary tunnel is analyzed, which is facilitated by the use of the partial differential equation (PDE) module in COMSOL Multiphysics software. The solid–liquid ratio is utilized as the water–heat coupling term, and the solid mechanics module is introduced to achieve three-field coupling. Numerical simulations are conducted to study changes in the temperature field, moisture field, and vertical displacement due to freezing and expansion in the most unfavorable soil layer during the freezing process. The results indicate that a complete freezing curtain forms around the 30th day. The distribution of freezing pipes significantly influences the freezing effect. The strong freezing zone is characterized by a high cooling rate and rapid water content reduction with the opposite trends being observed in the weak freezing zone. Upon completion of the freezing process, a large uplift of the ground surface is observed with more pronounced vertical displacement changes in areas affected by temperature and phase changes. The maximum vertical displacement of the ground surface deviates from the center position. While the frozen soil curtain meets the design requirements for freezing, the effects of freezing and expansion should be taken into account. These findings could be instrumental in elaborating the most effective freezing and expansion control measures for areas with powdery clay-based layers in AGF-based projects. [ABSTRACT FROM AUTHOR]

The virtual element method (VEM) allows discretization of elasticity and plasticity problems with polygons in 2D and polyhedrals in 3D. The polygons (and polyhedrals) can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing complex geometries. However, to the author's knowledge axisymmetric virtual elements have not appeared before in the literature. Hence, in this work a novel first order consistent axisymmetric VEM is applied to problems of elasticity and plasticity. The VEM specific implementation details and adjustments needed to solve axisymmetric simulations are presented. Representative benchmark problems including pressure vessels and circular plates are illustrated. Examples also show that problems of near incompressibility are solved successfully. Consequently, this research demonstrates that the axisymmetric VEM formulation successfully solves certain classes of solid mechanics problems. The work concludes with a discussion of results for the current formulation and future research directions. [ABSTRACT FROM AUTHOR]

The calibration of constitutive models using experimental observations is a well‐established task in computational solid mechanics. Especially for complex constitutive models, multistep calibrations are regularly applied. While this approach is advantageous for reducing the complexity of the calibration problem, the quantification of parameter uncertainties becomes more challenging. In this study, we perform two‐step statistical parameter inference for an elasto‐plastic constitutive model utilizing a frequentist approach and Bayesian inference. The uncertainties are quantified by different methods, in particular, we compare an asymptotic normality analysis and Gaussian error propagation in the frequentist setting with sampling‐based Bayesian inference. Although frequentist and Bayesian parameter inference differ significantly in the way parameters are calibrated, both methods yield similar estimates. Additionally, the uncertainties quantified by asymptotic normality considerations and Gaussian error propagation are quite similar. However, the uncertainties of the elasticity parameters in the frequentist approach are found to be significantly smaller compared to Bayesian inference, due to the underlying approximations in the frequentist setting. Thus, uncertainties can be estimated in both settings, but it is crucial to be aware of the inherent assumptions and simplifications when interpreting the results. [ABSTRACT FROM AUTHOR]

Multiscale problems are widely observed across diverse domains in physics and engineering. Translating these problems into numerical simulations and solving them using numerical schemes, for example, the finite element method, is costly due to the demand of solving initial boundary‐value problems at multiple scales. On the other hand, multiscale finite element computations are commended for their ability to integrate micro‐structural properties into macroscopic computational analyses using homogenization techniques. Recently, neural operator‐based surrogate models have shown trustworthy performance for solving a wide range of partial differential equations. In this work, we propose a hybrid method in which we utilize deep operator networks for surrogate modeling of the microscale physics. This allows us to embed the constitutive relations of the microscale into the model architecture and to predict microscale strains and stresses based on the prescribed macroscale strain inputs. Furthermore, numerical homogenization is carried out to obtain the macroscale quantities of interest. We apply the proposed approach to quasi‐static problems of solid mechanics. The results demonstrate that our constitutive relations‐aware DeepONet can yield accurate solutions even when being confronted with a restricted dataset during model development. [ABSTRACT FROM AUTHOR]

Drip irrigation using a high-performance pressure-compensating (PC) emitter is one of the essential components for precision agriculture, and it is necessary to accurately predict its performance prior to design. In this study, an efficient two-way fluid–structure interaction (FSI) simulation model was developed and verified through an enlarged model experiment. The computational fluid dynamics (CFD) and computational solid mechanics (CSM) models of the FSI simulation were systematically verified, and a calibration method for the overestimated flow rate in the re-rising range was applied. The CFD model was determined to be the shear stress transport turbulence model, and the CSM model was determined to be the Ogden hyperelastic model for the PC emitter. The minimum prediction error for the flow rate was 7.93%, which was within 10% for all cases. The simulation model demonstrated its efficiency by analysing the performance of a single PC emitter with an average total analysis time of 18.6 h. In addition, by comparing various cases according to the design parameters, it is considered that the hardness of the diaphragm has a significant impact on the design of low-pressure PC emitters. The simulation model of this study can accurately predict the performance of PC emitter under specific conditions, yet improvement of simulation model is required to be applied in design optimisation. Future studies may benefit from combining an improved FSI simulation with a surrogate model to further enhance optimisation efforts. • The performance experiment of a pressure-compensating (PC) emitter was modelled. • The accuracy of two-way FSI simulation suggested was within 10% in all the cases. • Hardness of diaphragm was considered as design parameter along with groove size. • Hardness of a diaphragm played a key role in the design of low-pressure PC emitters. [ABSTRACT FROM AUTHOR]

High‐voltage electric pulse drilling technology has the advantages of high rock‐breaking efficiency, and low rock‐breaking energy consumption, which is one of the most promising rock‐breaking methods in geothermal drilling. However, there is insufficient understanding of the mechanism of high‐voltage electric pulse breaking of HDR under high‐temperature and high‐pressure environments (HTHP). In this paper, a numerical simulation model of electric breakdown under HTHP is constructed, and the whole process of high voltage electric pulse rock‐breaking and plasma channel generation is realized from the seven‐field coupling of circuit field, current field, magnetic field, breakdown field, heat transfer field, solid mechanics field and flow field. The temperature changes in the rock during the electric pulse rock‐breaking process were comprehensively analyzed, and the effects of different initial rock temperatures (200°C, 300°C, 400°C) and surrounding pressure conditions (30, 60, 90 MPa) on the high‐voltage electric pulse rock breaking law were considered. It is found that the thermal conductivity of the rock shows an increasing and then decreasing trend as the initial temperature of the rock increases, and that the thermal conductivity has a tendency to guide the development of plasma channels, and the radius of the plasma channels increases with the increase of the initial temperature of the rock. The heat transfer generated by high‐voltage electric pulse rock breaking is mainly in conduction, and the distribution shape of conduction heat is similar to the shape of the breakdown channel. The research in this paper can provide theoretical and technical guidance for developing electric pulse rock‐breaking technology. [ABSTRACT FROM AUTHOR]

In the realm of high-pressure vessel simulation, conventional finite element method (FEM) approaches, as per ASME standards, may inadequately predict the behavior of flat surfaces under elevated temperatures. This study challenges the efficacy of shell-type mesh modeling for high-temperature flat plates, demonstrating that the thermal conditions within such high-pressure vessels can induce thermal instability and buckling, not accounted for by traditional FEM methods recommended by ASME. Through comprehensive analytical investigations, we reveal that traditional shell-type meshing techniques, while suitable for certain applications, fail to capture the intricate thermal stresses and deformation patterns inherent in high-temperature flat plate configurations. Our analysis delineates distinct stability regimes governed by key design parameters, including plate thickness, operating temperature, and geometric dimensions, profoundly impacting the structural integrity of heating plates under thermal loading. Specifically, we found that increasing the plate thickness enhances resistance to thermal buckling, clamping the plate edges raises the critical buckling temperature, and selecting materials with lower thermal expansion coefficients improves stability. These findings provide engineers with critical insights necessary for optimizing the design and performance of high-temperature equipment. This includes the design of high-pressure vessels with flat surfaces for heating materials, flanges in high-temperature environments, and fins in heat exchangers across various industries such as oil and gas, pyrolysis, and power plants. The findings presented herein serve as a valuable reference for engineers seeking to comprehend and mitigate instability phenomena in solid mechanics, offering practical guidance for developing robust and reliable high-temperature structures in demanding industrial environments. [ABSTRACT FROM AUTHOR]

The optical properties of an off-axis integrated cavity system are influenced by both structural deformation and thermal deformation. In this paper, the finite element simulation and analysis software COMSOL multiphysics was used to numerically simulate the optical system. By coupling geometric optics, solid mechanics, and solid heat transfer and conducting parametric temperature scanning, a multiphysics simulation of the off-axis integrated cavity optical sensing system was achieved. The effects of different temperature conditions on the stress field, displacement field, and optical mirrors were analyzed, and changes in optical properties were assessed using ray trajectories and point diagrams. Additionally, optical simulation software was used to simulate and optimize the experimental optical path, obtaining the distribution of light spots on the detector surface. This provides a theoretical basis for the subsequent optimization of the off-axis integrated cavity optical system. [ABSTRACT FROM AUTHOR]

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Machine learning (ML) and Deep learning (DL) are increasingly pivotal in the design of advanced metamaterials, seamlessly integrated with material or topology optimization. Their intrinsic capability to predict and interconnect material properties across vast design spaces, often computationally prohibitive for conventional methods, has led to groundbreaking possibilities. This paper introduces an innovative machine learning approach for the optimization of acoustic metamaterials, focusing on Multiresonant Layered Acoustic Metamaterial (MLAM), designed for targeted noise attenuation at low frequencies (below 1000 Hz). This method leverages ML to create a continuous model of the Representative Volume Element (RVE) effective properties essential for evaluating sound transmission loss (STL), and subsequently used to optimize the overall topology configuration for maximum sound attenuation using a Genetic Algorithm (GA). The significance of this methodology lies in its ability to deliver rapid results without compromising accuracy, significantly reducing the computational overhead of complete topology optimization by several orders of magnitude. To demonstrate the versatility and scalability of this approach, it is extended to a more intricate RVE model, characterized by a higher number of parameters, and is optimized using the same strategy. In addition, to underscore the potential of ML techniques in synergy with traditional topology optimization, a comparative analysis is conducted, comparing the outcomes of the proposed method with those obtained through direct numerical simulation (DNS) of the corresponding full 3D MLAM model. This comparative analysis highlights the transformative potential of this combination, particularly when addressing complex topological challenges with significant computational demands, ushering in a new era of metamaterial and component design. [ABSTRACT FROM AUTHOR]

The Meager Mountain Geothermal Project stands as one of the pioneering geothermal energy initiatives in its early stages of resource development. Despite its abundant geothermal heat resources, no prior studies have systematically evaluated the potential of implementing coaxial borehole heat exchangers on site. This study addresses this research gap by presenting a comprehensive heat transfer model for an underground closed-loop geothermal system utilizing a single coaxial well. Finite element analysis incorporated fluid and solid heat transfer, as well as solid mechanics. The results obtained facilitated the construction of the temperature and thermal stress profiles induced by the cooling effects resulting from years of heat extraction. After 25 years of operation, the outlet temperature has reached approximately 74 °C, and the maximum radial tensile thermal stress amounts to ~47 MPa. Furthermore, the analysis demonstrates that higher fluid velocities contribute to more perturbed temperature and stress distributions. The study attained maximum thermal and electric power outputs of 208 kW and 17 kW, respectively. This research also underscores the significant impact of geothermal gradient and well length on BHE design, with longer wells yielding more power, especially at higher injection velocities. [ABSTRACT FROM AUTHOR]

A heat and mass transfer and stress model in Camellia oleifera fruit was built based on the theory of heat and mass transfer and solid mechanics. The splitting process by hot-air drying was simulated using COMSOL Multiphysical software. The simulation results showed that the moisture diffusion in the splitting process by hot-air drying of Camellia oleifera fruit gradually promoted from the center to the surface, moisture near the surface first migrated and moisture far away from the surface lagged. The internal and external moisture did not move outward simultaneously with different diffusion rates, and the temperature promoted the moisture diffusion. The moisture gradient in the peel caused the stress difference, which shrank and cracked under the action of stress, and its shape gradually changed from arch to flat. With the continuous moisture loss from the peel under the effect of temperature, the shrinkage and deformation of the peel become more severe, increasing the distance between the peels continuously; finally, the peel was removed. The peel's arc length and width directions were contracted during the splitting process by hot-air drying of Camellia oleifera fruit. The maximum deviation between the simulated and experimental values in the arc width direction was 8.9%, and the average deviation was 5.7%. The maximum deviation of the arc length between the simulated and experimental values was 7.4%, and the average deviation was 4.2%. The results showed that the simulation was consistent with the actual splitting law of Camellia oleifera fruit, which could be used to optimize the splitting process by the hot-air drying of Camellia oleifera fruit. [ABSTRACT FROM AUTHOR]

In this paper, a new multidimensional Takagi–Sugeno (T-S) identification technique is proposed for multivariable nonlinear systems. In this technique, multidimensional membership functions are designed using concepts from solid mechanics. The design of membership functions is carried out in multidimensional space, defining the principal axes from the eigenvectors of the inertia matrix, and it has the characteristic of dividing the space into regions with the same inertia. These regions are analyzed to define the center of gravity for each rule. Illustrative examples of multivariable nonlinear systems, such as a thermal mixing process and a binary distillation column, are selected to evaluate the effectiveness of the proposed method. The proposed method is compared with traditional T-S identification that uses one-dimensional membership functions and shows a reduction in the relative identification error and the algorithm execution time. Additionally, the proposed method prevents rules from being positioned outside the system's range, thereby avoiding the generation of unnecessary rules. [ABSTRACT FROM AUTHOR]

We present a family of fast explicit time integration schemes of first, second and third order accuracy for parabolic problems in mechanics solved via standard numerical methods that have considerable higher computational efficiency versus existing explicit methods of the same order. The derivation of the new explicit schemes is inspired on the finite increment calculus (FIC) procedure used for obtaining stabilized numerical schemes in fluid and solid mechanics. The new (so‐called) explicit FIC‐Time (EFT) schemes allow considerable larger time steps than the standard first order forward Euler (FE) scheme and the second and third order Adams–Bashforth schemes. The comparison with Runge–Kutta schemes also favors the FIC‐Time schemes in terms of the limit time step size (for second order schemes) and the total number of matrix‐vector multiplications per time step (for second and third order schemes). The new first order explicit schemes have a faster convergence to steady‐state than the FE scheme. The accuracy and efficiency of the new EFT schemes are verified in examples of application to the transient heat conduction equation using the finite element method. [ABSTRACT FROM AUTHOR]

The complex vibration phenomenon occurs in the downhole environment of the gas-liquid hydrocyclone, which affects the flow field in the hydrocyclone. In order to study the influence of vibration on hydrocyclone separation, the characteristics of the flow field in the downhole gas-liquid hydrocyclone were analyzed and studied under the condition of vibration coupling. Based on Computational Fluid Dynamics (CFD), Computational Solid Mechanics Method (CSM) and fluid-solid coupling method, a fluid-solid coupling mechanical model of a gas-liquid cyclone is established. It is found that under the condition of vibration coupling, the velocity components in the three directions of the hydrocyclone flow field change obviously. The peak values of tangential velocity and axial velocity decrease, and the asymmetry of radial velocity increases. The distribution regularity of vorticity and turbulence intensity in the overflow pipe becomes worse. Among them, the vorticity intensity of the overflow pipe is obviously enhanced, and the higher turbulence intensity near the wall occupies more area distribution range. The gas-liquid separation efficiency of the hydrocyclone will decrease with the increase of the rotational speed of the screw pump, and the degree of reduction can reach more than 10%. However, this effect will decrease with the increase of the rotational speed of the screw pump, so the excitation effect caused by the rotational speed has a maximum limit on the flow field. [ABSTRACT FROM AUTHOR]

Physics‐Informed Neural Networks (PINNs) have solved numerous mechanics problems by training to minimize the loss functions of governing partial differential equations (PDEs). Despite successful development of PINNs in various systems, computational efficiency and fidelity prediction have remained profound challenges. To fill such gaps, this study proposed a Physics‐Informed Neural Operator Solver (PINOS) to achieve accurate and fast simulations without any required data set. The training of PINOS adopts a weak form based on the principle of least work for static simulations and a storng form for dynamic systems in solid mechanics. Results from numerical examples indicated that PINOS is capable of approximating solutions notably faster than the benchmarks of PINNs in both static an dynamic systems. The comparisons also showed that PINOS reached a convergence speed of over 20 times faster than finite element software in two‐dimensional and three‐dimensional static problems. Furthermore, this study examined the zero‐shot super‐resolution capability by developing Super‐Resolution PINOS (SR‐PINOS) that was trained on a coarse mesh and validated on fine mesh. The numerical results demonstrate the great performance of the model to obtain accurate solutions with a speed up, suggesting effectiveness in increasing sampling points and scaling a simulation. This study also discusses the differentiation methods of PINOS and SR‐PINOS and suggests potential implementations related to forward applications for promising machine learning methods for structural designs and optimization. [ABSTRACT FROM AUTHOR]

Cancer engineering is an interdisciplinary approach that promises to confront the complexities of cancer and accelerate transformative discoveries by integrating innovative fields across engineering and the physical sciences with a focus on cancer. We offer a conceptual framework for the hallmarks of cancer engineering, integrating 12 fields: system dynamics; imaging, radiation, and spectroscopy; robotics and controls; solid mechanics; fluid mechanics; chemistry and nanomaterials; mathematics and simulation; cellular and protein engineering; kinetics and thermodynamics; materials science; manufacturing and biofabrication; and microsystems. [ABSTRACT FROM AUTHOR]

The technological process of vegetable oil production requires significant energy costs, while the introduction of new technologies requires investment, which is a challenge for small and medium-sized enterprises in the current environment. This makes it important to introduce energy-efficient equipment in the conditions of these enterprises, which does not require significant investments. The article was concerned with improving the technological process of pressing oilseeds by introducing an energy-efficient oil press into the technological process and studying its structural and kinematic characteristics. In the context of the study, the determination of the physical and mechanical properties of raw materials, methods of theoretical mechanics and solid mechanics, calculation of structural elements of technological equipment for processing oilseeds were used. The necessity and expediency of theoretical analysis and experimental research are substantiated. The main regularities of oil separation from the crushed mass are determined. The study of physical and mechanical characteristics, size and weight parameters of seeds and crushed mass allowed to substantiate the main kinematic and design parameters of the screw press. The principle of operation of an energy-efficient screw oil press is described. The design of the press is improved by a steam sprayer installed in the receiving hopper under the threaded rollers, which is equipped with a steam generator, which makes it possible to carry out moisture-thermal treatment with steam within one device. The proposed constructive solution includes: determination of the coefficient of friction of seeds on an inclined plane, study of the components of the crushed mass obtained with the help of an energy-efficient oil press, and theoretical aspects of oilseed pressing. A study of the design and operating parameters of the screw press has been carried out, namely: determination of the screw press productivity, use of an energy-efficient press for oil separation makes it possible to improve the quality of the technological process, determination of the press power consumption and its efficiency. It has been concluded that the improved design solution of the press meets the modern requirements for oil production machines. The use of the proposed constructive solution will reduce oil losses during pressing, which will significantly increase the efficiency of the process, reduce operating costs and promote the development of oil production in small and medium-sized oilseed enterprises. [ABSTRACT FROM AUTHOR]

We develop a theory of existence of minimizers of energy functionals in vectorial problems based on a nonlocal gradient under Dirichlet boundary conditions. The model shares many features with the peridynamics model and is also applicable to nonlocal solid mechanics, especially nonlinear elasticity. This nonlocal gradient was introduced in an earlier work, inspired by Riesz' fractional gradient, but suitable for bounded domains. The main assumption on the integrand of the energy is polyconvexity. Thus, we adapt the corresponding results of the classical case to this nonlocal context, notably, Piola's identity, the integration by parts of the determinant and the weak continuity of the determinant. The proof exploits the fact that every nonlocal gradient is a classical gradient. [ABSTRACT FROM AUTHOR]

The results of 3D modeling of the distribution and accumulation of dislocations and low-angle boundaries in the volume of a layered metal-intermetallic composite under uniaxial compression are obtained. The calculations are performed using a synthesis model of dislocation kinetics and mechanics of a deformable solid. The model is preliminarily tested on a single-phase intermetallic compound and pure metal, which shows a good agreement between the calculated values and the earlier obtained experimental results. The patterns of stress distribution, plastic deformation intensity, dislocation density, and low-angle boundaries density in the plane of the central longitudinal section of a deformed rectangular sample of a layered metal-intermetallic composite are presented. The inhomogeneities of internal stresses and strength properties of the selected-configuration layered metal-intermetallic composite under compression are evaluated. [ABSTRACT FROM AUTHOR]

This article presents an experimental investigation on the fatigue and fracture properties of R350HT rail steel. The study aims to improve the strength, toughness, and wear resistance of railway steels. Various tests were conducted to quantify the fracture mechanics properties of the steel, including tensile tests, fatigue crack growth rate tests, and plane strain fracture toughness tests. The results provide valuable information for assessing the damage tolerance of railway rails and further developing rail steels. The findings suggest that R350HT steel has similar properties to other pearlitic rail steels but may have lower damage tolerance. [Extracted from the article]

This document is a compilation of research articles that discuss various methods for measuring and analyzing stress intensity factors (SIF) in fracture mechanics. The articles cover topics such as digital image correlation, finite element processing, and the effects of material properties on fracture behavior. They provide valuable insights and findings for researchers and engineers studying fracture mechanics and its applications. [Extracted from the article]

In solid mechanics, Maxwell stresses are known to be induced if a body is exposed to magnetic and, in the case of dielectrics, electric fields. Acting as tractions at outer or inner surfaces as well as volume forces, they are superimposed with tractions and stresses due to mechanical loads and provide a more or less significant contribution, depending on loading, material properties and geometric aspects. The Maxwell stress tensor, constituting the physical and mathematical basis, however, is controversially discussed to date. Several formulations are known, most of them having been suggested more than 100 years ago. Being equivalent in vacuum, they differ qualitatively just as quantitatively in solid or fluidic matter. In particular, the dissimilar effect of body forces, emanating from a choice of established Maxwell stress tensor approaches, on crack tip loading in dielectric solids is investigated theoretically in this paper. Due to the singularity of fields involved, their impact is basically non-negligible compared to external mechanical loading. The findings obtained indicate that fracture mechanics could be the basis of an experimental validation of Maxwell stress tensors. [ABSTRACT FROM AUTHOR]

Food digestion is important for human health. Advances have been made using in vitro models to study food digestion, but there is considerable potential for numerical approaches in stomach modeling, as they can provide a comprehensive understanding of the complex flow and chemistry in the stomach. The focus of this study is to provide a concise review of the developed numerical stomach models over the past two decades. The gastric physiological parameters that are required for a computational model to represent the human gastric digestion process are discussed, including the stomach geometry, gastric motility, gastric emptying, and gastric secretions. Computational methods used to model gastric digestion are introduced and compared, including different computational fluid dynamics as well as solid mechanics methods. The challenges and limitations of current studies are discussed, as well as the areas for future research that need to be addressed. There has been progress in simulating gastric fluid flow with stomach wall motion, but much work remains to be done. The complex food breakdown mechanisms and a comprehensive chemical digestion process have not been implemented in any developed models. Numerical method that was once computationally expensive will be revolutionized as computing power continues to improve. Ultimately, the advancement of modeling of gastric food digestion will allow for additional hypothesis testing to streamline the development of food products that are beneficial to human health. [ABSTRACT FROM AUTHOR]

The coalbed methane (CBM) productivity is directly determined by the fracture permeability during hydraulic fracturing, which is regulated by the distribution of proppants. The proppant may be unevenly distributed in the fracture because of variables like the architecture of the fracture and the characteristics of the sand‐carrying fluid. This study used two types of random functions to produce different ununiform distributions of proppant clusters in large‐scale fractures, with the aim of investigating the effect of these distributions on the overall permeability of the fracture. A model of fluid‐structure coupling is proposed. The closure of large‐scale fractures under in‐situ stress is analyzed using solid mechanics and the penalty function; the CBM flowing in proppant clusters and the high‐speed channel between them is simulated using Darcy's law and the Navier–Stokes equation, respectively; and the overall permeability of fractures is computed using the fluid pressure drop throughout the fracture and the fluid flowing velocity in the fracture's outlet. Since most CBM flows along high‐speed channels between the proppant clusters, the simulated findings show that the overall permeability of fractures with an uneven distribution of proppant clusters is significantly higher than that of the proppant cluster itself. As CBM becomes more discretely distributed, the proportion of CBM flowing within the proppant cluster continuously drops. As the permeability of the proppant cluster increases, the volume ratio of proppant clusters decreases, and the distribution of proppant clusters becomes more discrete, the overall permeability of the fracture continuously increases. [ABSTRACT FROM AUTHOR]

Tiltmeters have the potential to resolve ground deformation due to changes in hydraulic head induced by conduit pressurization. Conduit pressure variations cause groundwater to be stored or released from storage within the surrounding rock matrix. We modeled this process and infer whether the resulting deformation is measurable with tiltmeters and what behavior to expect by fully coupling porous media flow and solid mechanics in a poroelastic, 2D finite element model. Parameter sets globally representative of Paleozoic, Mesozoic, and Cenozoic confined and unconfined aquifers are considered. Our analysis focuses on the impact of the parameterization on pore pressure, vertical displacement, and tilt. We find that the spatial distribution of the poroelastic signal depends on the hydraulic diffusivity, and its magnitude depends on the mechanical and coupling parameters. Additional analysis of the impacts of conduit radius and depth suggests that tilt polarity could be an indicator of conduit location and relative conduit size. We calibrated the model to data observations acquired at the Santa Fe River Sink‐Rise system in north‐central Florida, US. We find that an overlying clay‐rich layer may act to partially confine the aquifer. Although the observed tilt signal is present in radial and transverse components and polarity reversals occur, we were able to recover the magnitude and general trend of the tilt response. Plain Language Summary: Our study focused on understanding how changes in ground deformation can be caused by groundwater flow induced by a pressurized karst conduit. We modeled this process in different types of aquifers to determine if the deformation can be measured using tiltmeters, instruments that measure changes in the angle of the ground. We also explored the effect of conduit size and depth. Our findings show that the distribution and magnitude of the ground response depend on the physical parameters of the aquifer. Additionally, we find that tilt data can provide information about conduit location, size, and depth. We tested the model using data from the Santa Fe River Sink‐Rise system in Florida. We find this system may behave as a partially confined aquifer due to the presence of clay in the overlying unit. From the use of our simplified numerical formulation, we were able to recover the magnitude and overall trend of the observed tilt data. Key Points: Poroelastic response is governed by an interconnection between aquifer hydraulic diffusivity, Biot‐Willis coefficient, and elastic moduliSmall tilt arrays can potentially provide information on relative conduit location and sizeHeterogeneity, complex geometry, and non‐uniqueness present challenges in progressing from synthetic simulations to real‐world predictions [ABSTRACT FROM AUTHOR]