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Adhesives can be made by patterning surfaces with discrete adhesive elements. Nature uses this approach to provide animals with highly adaptive and robust approaches towards gaining an effective grip on surfaces. The mechanism of patterned surface adhesion involve many different attachment principles, adhesive site interactions, and probabilistic effects, the interplay of which is not understood. This limits our ability to design patterned surface adhesives for engineering applications. In this work, we quantify how a mechanically patterned adhesive based on passive mushroom-shaped elements performs. We explore a range of surface design features and model the mechanical adhesion dynamics with an approach based on the fiber bundle model (FBM). We find that the fiber bundle model can be used to rationalize the observations after modifying it to capture the initial non-linear force response of the adhesives. Additionally, we investigate the behavior of the system's elastic energy and damage energy, as it is stretched under strain-controlled conditions. Our experimental data indicates that the elastic energy has a maximum that appears after the macroscopic strength (σc), corresponding to strains where a full rupture of the system can no longer be prevented. Moreover, we observed that below the maximum of the constitutive curve σc, the elastic energy consistently exceeds the damage energy. Finally, we found that the derivative of the elastic energy has a maximum, which always appears before σc. Therefore, the derivative of the elastic energy would serve as a reliable signal of upcoming catastrophic failure in experiments under stress-controlled conditions. [ABSTRACT FROM AUTHOR]

Acrylic is an ideal material for some components in underwater engineerings, such as observation windows and fully-transparent hulls of Human-Occupied Vehicle (HOV). The safety of these acrylic structures is quite essential for the integrity of the underwater facility and the research on the acrylic performance used in the deep sea is not very systematic. To capture the accurate properties of the acrylic used for these structures, several compression experiments are carried out to identify the compressive elasticity of acrylic under different loading rates, including the elastic region, upper yield point and lower yield point. Non-linear performance and rate-dependent characteristics are found in the experiments. Based on the experimental data, polynomial form of hyper-elasticity is well-matched to describe the non-linear stress and strain diagram. Numerical analysis of acrylic specimen and observation window are conducted based on the hyper-elastic model. The results show good consistency between simulations and experiments. The illustrated material model provides a basis for establishing a more accurate design-by-analysis-methodology for acrylic structures used in underwater facilities. [ABSTRACT FROM AUTHOR]

This paper focuses on the simultaneous homogenization and dimension reduction of periodic composite plates within the framework of non-linear elasticity. The composite plate in its reference (undeformed) configuration consists of a periodic perforated plate made of stiff material with holes filled by a soft matrix material. The structure is clamped on a cylindrical part. Two cases of asymptotic analysis are considered: one without pre-strain and the other with matrix pre-strain. In both cases, the total elastic energy is in the von-Kármán (vK) regime ( ε 5 ). A new splitting of the displacements is introduced to analyze the asymptotic behavior. The displacements are decomposed using the Kirchhoff–Love (KL) plate displacement decomposition. The use of a re-scaling unfolding operator allows for deriving the asymptotic behavior of the Green St. Venant's strain tensor in terms of displacements. The limit homogenized energy is shown to be of vK type with linear elastic cell problems, established using the Γ-convergence. Additionally, it is shown that for isotropic homogenized material, our limit vK plate is orthotropic. The derived results have practical applications in the design and analysis of composite structures. [ABSTRACT FROM AUTHOR]

Adhesives can be made by patterning surfaces with discrete adhesive elements. Nature uses this approach to provide animals with highly adaptive and robust approaches towards gaining an effective grip on surfaces. The mechanism of patterned surface adhesion involve many different attachment principles, adhesive site interactions, and probabilistic effects, the interplay of which is not understood. This limits our ability to design patterned surface adhesives for engineering applications. In this work, we quantify how a mechanically patterned adhesive based on passive mushroom-shaped elements performs. We explore a range of surface design features and model the mechanical adhesion dynamics with an approach based on the fiber bundle model (FBM). We find that the fiber bundle model can be used to rationalize the observations after modifying it to capture the initial non-linear force response of the adhesives. Additionally, we investigate the behavior of the system’s elastic energy and damage energy, as it is stretched under strain-controlled conditions. Our experimental data indicates that the elastic energy has a maximum that appears after the macroscopic strength (σc), corresponding to strains where a full rupture of the system can no longer be prevented. Moreover, we observed that below the maximum of the constitutive curve σc, the elastic energy consistently exceeds the damage energy. Finally, we found that the derivative of the elastic energy has a maximum, which always appears before σc. Therefore, the derivative of the elastic energy would serve as a reliable signal of upcoming catastrophic failure in experiments under stress-controlled conditions.

A database of non-linear elastic parameters in axial tension and compression is provided for continuous carbon fibre polymer composites and carbon fibres of different stiffnesses. Composite laminates manufactured by conventional or automated processes are tested in bending, and parameters are extracted for strains of less than 0.5%. While fibre composites with fibres of standard and intermediate moduli exhibit a stiffening of ∼15 GPa/% (of strain) and a softening of ∼20 GPa/%, those with high-modulus carbon fibres exhibit much higher values of ∼50 GPa/% for both. This database is useful for designing composite structures in a stiffness-based design and for correlating the processing of carbon fibres with their nanostructure and induced properties. The latter is discussed in terms of reorientation of crystallites of graphene sheets vis-à-vis the carbon fibre axis during loading. [ABSTRACT FROM AUTHOR]

A comparative analysis is performed on the effects of heterogeneity in both linear and non-linear material characteristics of half-space on the propagation of bright and dark solitary Love waves in a non-linear layered half-space. The layer is assumed to be homogeneous, non-linear and elastic, while the half-space is vertically heterogeneous. The problem is formulated for two types of elastic materials, incompressible and generalized neo-Hookean materials, and the differences caused by the two materials in the formulation are revealed. For the media composed of generalized neo-Hookean materials, a non-linear Schrödinger equation describing the self interaction of Love waves is obtained using multiple scales method. The differences in the effects of linear and non-linear material properties of the half-space on both the existence and non-linear evolution of bright and dark solitary Love waves are compared graphically. [ABSTRACT FROM AUTHOR]

The FE2$$ {}^2 $$ computational homogenization method is a predictive multi‐scale method without the need for constitutive assumptions and/or potential function postulates at the macro engineering scale. Instead, the effective micro‐structural responses are extracted directly from a representative volume element (RVE) underlying each macro point. However, the FE2$$ {}^2 $$ method is still computationally too expensive for most practical uses, since the micro‐macro FE coupling is done at each loading step/iteration for the entire domain. To this end, the machine learning method has been utilized in the literature for the offline training of a surrogate model to predict the RVE homogenized response for general loading conditions. In this contribution, the neural network (NN) is incorporated into the macro finite element framework in a non‐intrusive manner. This is termed as the FE‐NN framework, in analogy to the FE2$$ {}^2 $$ method. In general, online simulations in the FE‐NN method is very efficient, with predictions matching closely to those obtained from reference direct numerical simulations (DNS). A bottleneck with the FE‐NN framework, however, is the high computational cost associated with the data generation for offline NN model setup. In this paper, focusing on the FE‐NN multi‐scale framework for non‐linear elastic deformation of heterogeneous materials, a sequential training strategy with knowledge transfer is proposed, to enable an efficient offline microscopic NN model setup. For a given target RVE, we first consider a simplified source RVE, where data can be generated rapidly, for the NN pre‐training of surrogate model. The pre‐trained network parameters are next downloaded to initialize the target NN surrogate model, followed by a fine‐tuning training process, using only a small dataset generated by the computationally expensive high‐fidelity RVE. The efficiency of the proposed sequential learning method over the conventional NN training, as well as, its excellent predictive capability for multi‐scale analyses, are demonstrated for a multi‐phase composite material. The proposed FE‐NN‐KT approach can be implemented easily without complicated pre‐processing procedures, since the data generation only involves the standard extraction of effective responses from RVEs, together with a standard NN architecture. [ABSTRACT FROM AUTHOR]

Following the experimental lead, we construct a general mathematical model which, depending on whether the uniaxial scalar order parameter is constant or not, can predict either the classical shear striping instability or the molecular auxetic response and mechanical Fréedericksz transition observed in different liquid crystal elastomers. Our theoretical model can shed some light on the role of nematic order in these stretch-induced mechanical instabilities not observed in conventional rubber-like solids. [ABSTRACT FROM AUTHOR]

Summary: In this contribution we introduce a novel space‐time formulation for non‐linear elasticity, able to calculate large deformations and displacements with high efficiency using structured and unstructured meshes in the space‐time cylinder without changing the required regularity and thus, enabling the use of Lagrangian shape functions including tetrahedron and hypertetrahedron or tesseract elements. The common and indiscriminate treatment of spatial and temporal directions allows us to remove one of the major bottlenecks in parallel computations: The design of time‐stepping schemes, which can neither been parallelized efficiently in time nor allow for local refinements as no information transfer backwards in time is possible. Moreover, stability of time‐stepping schemes depend on the accumulation of local approximation errors in each time‐step, in contrast to space‐time formulation, characterized by enhanced stability and robustness. Eventually, we will demonstrate superiority in the convergence against classical time‐stepping schemes using various examples including highly sensitive systems in the context of non‐linear elasticity. [ABSTRACT FROM AUTHOR]

The connection between macroscopic deformation and microscopic chain stretch is a key element in constitutive models for rubber-like materials that are based on the statistical mechanics of polymer chains. A new micro-macro chain stretch relation is proposed, using the Irving–Kirkwood–Noll procedure to construct a Cauchy stress tensor from forces along polymer chains. This construction assumes that the deformed polymer network remains approximately isotropic for low to moderate macroscopic stretches, a starting point recently adopted in the literature to propose a non-affine micro-macro chain stretch relation (Amores et al., 2021). Requiring the constructed Cauchy stress to be consistent with the stress tensor derived from the strain energy density results in a new chain stretch relation involving the exponential function. A hybrid chain stretch relation combining the new chain stretch with the well-known affine relation is then proposed to account for the whole range of stretches in experimental datasets. Comparison of the model predictions to experimental data in the literature shows that the two new micro-macro chain stretch relations in this work result in two-parameter constitutive models that outperform those based on existing chain stretches with no increase in the number of fitting parameters used. • New chain stretch relations are proposed for modelling rubber-like materials. • The Irving–Kirkwood–Noll procedure gives these relations a physical basis. • Full-network models using these relations capture experimental data accurately. • Improvements in accuracy are achieved when using only two model parameters. • The model parameters have molecular interpretations. [ABSTRACT FROM AUTHOR]

The classical reduced model for film/substrate bilayers is the one in which the film is governed by the Euler–Bernoulli beam equation, and the substrate is replaced by an array of springs (the so-called Winkler foundation assumption). We derive a refined model in which the normal and shear tractions at the bottom of the film are expressed in terms of the corresponding horizontal and vertical displacements, and the response of the half-space is described by the exact theory. The self-consistency of the refined model is confirmed by showing that it yields a four-term (in the incompressible case) or six-term (in the compressible case) expansion for the critical strain that agrees with the expansion given by the exact theory. [ABSTRACT FROM AUTHOR]

A well known result from the non-linear theory of elasticity applied to spherical shells is that the classical Mooney-Rivlin constitutive law may give either a monotonic or a non-monotonic pressure-inflation response for finite deformation. Specifically, this is determined by two factors: the relative shell thickness, and the relative I 1 to I 2 contribution in the M-R constitutive law. Here we consider how a residual stress field may affect this behavior. Using a constitutive framework for hyperelastic materials with residual stress that has been especially applied to tubes, this paper focuses on finite thickness spherical shells while using a similar prototypical energy response. In this context we examine different residual stress states, and show how certain of these lead to more workable analytical results than others. All of them enable Taylor and asymptotic expansions in the small and large inflation limit. On this basis it is shown how particular residual stress fields can cause a monotonic inflation graph to become non-monotonic, and vice versa. [ABSTRACT FROM AUTHOR]

Ultrasound elastography performed under small strain conditions has been intensively studied. However, small deformations may be not sufficiently large to differentiate some abnormal tissues. By combining quasi-static and shear wave elastography, we developed a non-invasive method to estimate the localized stress- strain curve of materials. This method exerts progressive multistep uniaxial compression on the materials, and shear wave measurements were performed at every compression step. This method estimates the 2-D displacements between steps via a 2-D region growing motion tracking method and accumulates these displacements to obtain the large material displacements with respect to the initial configuration. At each step, the shear modulus and stress were calculated according to linear elastic theory. The proposed method was tested on custom-made tissue-mimicking phantoms. Mechanical compression testing was conducted on the samples made of the same material as the phantoms and taken as the reference. The stress-strain curves for the same material from the proposed method and from mechanical testing are in good agreement. The root mean square error (RMSE) and area percentage error (APE) of the stress-strain curve between ultrasound measurement and mechanical testing for soft materials ranged from 0.18 to 0.26 kPa and from 5.6% to 7.8%, respectively. The RMSE and APE for stiff materials ranged from 0.56 to 1.17 kPa and 8.0% to 17.9%. Therefore, our method was able to provide good estimates of the stress-strain curve for tissue-mimicking materials. [ABSTRACT FROM AUTHOR]

Let Ω ⊆ ℝ2 be a domain, let X be a rearrangement invariant space and let f ∈ W1X (Ω, ℝ2) be a homeomorphism between Ω and f(Ω). Then there exists a sequence of diffeomorphisms fk converging to f in the space W1X (Ω, ℝ2). [ABSTRACT FROM AUTHOR]

Classical analytical solutions of linear elasticity are used as auxiliary solutions to solve non‐linear, and elastically heterogeneous problems on fluid‐saturated media. The 2D Kelvin's solution for a homogeneous space is considered here for simplicity sake. The material non‐linearity could be due to irreversible deformations or non‐linear elasticity response typical of 4D analysis as it is done here. The general procedure relies on a discrete collocation method and a fixed point iterative approach to construct the displacement field. The method is validated by comparing the numerical results with the analytical solution for a layered cylinder embedded in an infinite space. The h‐convergence is checked numerically illustrating the strong influence of the number of facets used to discretize the boundaries. The convergence of the iterative process based on the displacement norm is of a quasi‐quadratic rate for near homogeneous materials and declines to sub‐linear rates as the contrast in elasticity modulus exceeds 15% of the values considered for the Green's function. The method is then applied to a 2D tilted block region where the depleting reservoir has elasticity parameters function of the volumetric strain, to shed some light on the 4D effects. It is shown that the velocity changes are sensitive to the volumetric strain as well as to the strain in the wave propagating direction. Differences, including the anisotropy due to the structural response at the field scale, between the predictions based on this non‐linear isotropic elasticity and the classical R‐factor approach are finally discussed. [ABSTRACT FROM AUTHOR]

• Beading of soft tubes under surface tension is studied as a localization problem. • Bifurcation conditions are presented for a general strain-energy function. • Further insight into the post-bifurcation behaviour is provided. • Theoretical predictions are verified by numerical simulations. We investigate localised bulging or necking in an incompressible, hyperelastic cylindrical tube under axial stretching and surface tension. Three cases are considered in which the tube is subjected to different constraints. In case 1 the inner and outer surfaces are traction-free and under surface tension, whilst in cases 2 and 3 the inner and outer surfaces (respectively) are fixed to prevent radial displacement and surface tension. However, each free surface in these latter two cases is still under surface tension. We first state the analytical bifurcation conditions for localisation and then validate them numerically whilst determining whether localisation is preferred over bifurcation into periodic modes. It is shown that bifurcation into a localised solution is unattainable in case 1 but possible and favourable in cases 2 and 3. In contrast, in case 1 any bifurcation must necessarily take the form of a periodic mode with a non-zero wave number. Our results are validated using Finite Element Method (FEM) simulations. [ABSTRACT FROM AUTHOR]

An implicit constitutive relation is proposed to study transversely isotropic bodies. The relation is obtained assuming the existence of a Gibbs potential that depends on the second Piola–Kirchhoff stress tensor, from which the Green Saint-Venant strain tensor is obtained as the derivative with respect to the stress. The responses of unconstrained as well as inextensible bodies are studied, and some boundary value problems are analysed. An inextensible body, where the constraint of inextensibility appears only in tension is also considered. [ABSTRACT FROM AUTHOR]

Materials with a stochastic fiber network as the main structural constituent are broadly encountered in engineering and in biology. These materials are characterized by multiscale heterogeneity and hence their properties evaluated numerically or experimentally are generally dependent on the size of the sample considered. In this work we evaluate the size effect on the linear and non-linear mechanical response of three-dimensional stochastic fiber networks and determine its dependence on material parameters and on the degree of affinity of network deformation. The size effect is more pronounced in non-affine networks than in affine networks and decreases slowly when the model size increases. In order to eliminate this effect, models lager than can be effectively solved with current computers have to be considered. To address this issue, we propose a method that allows using relatively small models, while accurately predicting the small and large strain behaviors of the network. The method is based on the generalized boundary conditions introduced in (Glüge 2013, Computational Materials Science 79, 408–416), which are being adapted here to the requirements imposed by fibrous materials. [ABSTRACT FROM AUTHOR]

• We propose two particular fiber arrangements with the intention of realizing ultra-stiff and ultra-soft composites. • In particular, we also consider the case of curved fibers. • We introduce a model for these lattice plates that is able to describe the behavior of an in-plane orthotropic lamina within the framework of the strain-gradient elasticity theory. • Numerical simulations have been performed using the finite element method to investigate the mechanical behavior of the considered textures. Fiber-reinforced composites are materials that display a great potentiality in many applications for their multifaceted features. The employment of curved fibers contributes to enhancing this already wide range of possibilities further. In this paper, we propose two particular fiber arrangements with the intention of realizing ultra-stiff and ultra-soft composites. For this purpose, we explore the texture based on isostatic lines, which is bio-inspired to obtain a high strength composite and the pantographic pattern, which enables considerable displacement with very low resistance. To model these particular lattice plates, we consider an in-plane orthotropic lamina within the framework of the strain-gradient elasticity theory. Numerical simulations have been performed using the finite element method to investigate the mechanical behavior of the considered textures. A regular straight texture with fibers parallel to the edges of a rectangular sample has been taken into account as reference texture for comparison. Through some tests, we show that for the considered textures, namely the isostatic and the pantographic ones, the displacement force graphs differ by several orders of magnitude, justifying the characterization of their behavior. [ABSTRACT FROM AUTHOR]

In nature, limbless locomotion is adopted by a wide range of organisms at various length scales. Interestingly, undulatory, crawling and inching/looping gait constitutes a fundamental class of limbless locomotion and is often observed in many species such as caterpillars, earthworms, leeches, larvae, and C. elegans. In this work, we developed a computationally efficient 3D Finite Element (FE) unified framework for the locomotion of limbless organisms on frictional substrates. Muscle activity is simulated with a multiplicative decomposition of the deformation gradient, which allows mimicking a broad range of locomotion patterns in 3D contractile elastic solids. We propose a two-field FE formulation based on positions and velocities. Governing partial differential equations are transformed into equivalent time-continuous differential–algebraic equations (DAEs). Next, the optimal locomotion strategies are studied in the framework of optimal control theory. We resort to adjoint-based methods and deduce the first-order optimality conditions, that yield a system of DAEs with two-point end conditions. Hidden symplectic structure is discussed, and Symplectic Euler time integration of optimality conditions are employed. The resulting discrete first-order optimality conditions form a non-linear programming problem that is solved efficiently with the Forward Backward Sweep Method. Finally, some numerical examples are provided to demonstrate the comprehensiveness of the proposed computational framework and investigate the energy-efficient optimal strategy out of distinct locomotion patterns adopted by limbless organisms. [Display omitted] • A deformation gradient decomposition is proposed for modelling 3D contractile bodies. • Optimal body locomotion on frictional substrates are deduced and discretised with FE. • Optimality equations are numerically solved with Forward Backward Sweep Method. • Different gait strategies found in Nature are compared and its efficiency discussed. [ABSTRACT FROM AUTHOR]

We study instability of a Newtonian Couette flow past a gel-like film in the limit of vanishing Reynolds number. Three models are explored including one hyperelastic (neo-Hookean) solid, and two viscoelastic (Kelvin–Voigt and Zener) solids. Instead of using the conventional Lagrangian description in the solid phase for solving the displacement field, we construct equivalent “differential” models in an Eulerian reference frame, and solve for the velocity, pressure, and stress in both fluid and solid phases simultaneously. We find the interfacial instability is driven by the first-normal stress difference in the base-state solution in both hyperelastic and viscoelastic models. For the neo-Hookean solid, when subjected to a shear flow, the interface exhibits a short-wave (finite-wavelength) instability when the film is thin (thick). In the Kelvin–Voigt and Zener solids where viscous effects are incorporated, instability growth is enhanced at small wavenumber but suppressed at large wavenumber, leading to a dominant finite-wavelength instability. In addition, adding surface tension effectively stabilizes the interface to sustain fluid shear.

Abstract Deriving the amplitude equation for a buckling mode is an important issue in non-linear elasticity. Focusing on pattern formations in growing tubular tissues, many existing literature often adopted the numerical methods. In this paper, we propose a semi-analytical approach for the bilayer tubular structures under growth to derive the amplitude equation of a single wrinkling mode, from which a transition between supercritical and subcritical bifurcations can be determined. In the framework of finite elasticity, a weakly non-linear analysis is carried out and the amplitude equation is deduced by the virtual work method. A semi-analytical solution is obtained, with an analytical expression whose exact coefficients are determined numerically. Then a parametric study is carried out by use of the semi-analytical solution. When the total growth factor is prescribed, the critical mode number governs the amplitude, and a lower mode corresponds to a higher amplitude. When the incremental growth factor after bifurcation is fixed, it turns out that the dependence of the amplitude on the modulus ratio is non-monotonic if the thicknesses of the two layers are specified. For a given geometry, when the modulus ratio ξ>5, the wrinkled amplitude is mainly dominated by the critical mode number, and a smaller critical mode number deepens the wrinkle. However, the amplitude is a decreasing function of ξ when ξ < 5. The obtained analytical solutions are also validated by the corresponding numerical solutions based on the finite element method. The proposed semi-analytical approach is applicable for most variable coefficient problems arising from cylindrical and spherical structures. [ABSTRACT FROM AUTHOR]

• Fracture toughness and non-linear elastic properties evaluated in a single test. • Three-dimensional displacement fields obtained by digital volume correlation of in situ laboratory X-ray computed tomographs. • Tensile softening obtained by inverse finite element analysis of the strain field. • Strain energy release rate obtained by contour integral method in a finite element model. • The model uses the derived non-linear properties and measured displacement field. • The fracture toughness was constant with crack length. Effective small specimen tests are needed to obtain fracture toughness and elastic properties as the limited availability of irradiated graphite restricts the quantity and dimensions of test specimens. Both properties have evaluated simultaneously in a crack propagation test with the double cleavage drilled compression (DCDC) specimen geometry of a fine-grained graphite (SNG742) that has non-linear elastic properties in the unirradiated condition. Three-dimensional displacement fields were obtained by digital volume correlation of in situ laboratory X-ray computed tomographs, and the 3D crack geometry (crack tip position, crack opening displacements and angle) was determined objectively by a wavelet variance method. The tensile softening of the Young modulus was determined by inverse analysis of the strain field using the finite element model updating (FEMU) method. The strain energy release rate of the quasi-static propagating crack was calculated using the contour integral method in a finite element model with the derived non-linear elastic properties and the measured displacements as boundary conditions. The critical strain energy release rate was constant with crack length (118 ± 14 J m−2) and equivalent to a fracture toughness of 1.13 ± 0.07 MPa m1/2. [ABSTRACT FROM AUTHOR]

A database of non-linear elastic parameters in axial tension and compression is provided for continuous carbon fibre polymer composites and carbon fibres of different stiffnesses. Composite laminates manufactured by conventional or automated processes are tested in bending, and parameters are extracted for strains of less than 0.5%. While fibre composites with fibres of standard and intermediate moduli exhibit a stiffening of ∼15 GPa/% (of strain) and a softening of ∼20 GPa/%, those with high-modulus carbon fibres exhibit much higher values of ∼50 GPa/% for both. This database is useful for designing composite structures in a stiffness-based design and for correlating the processing of carbon fibres with their nanostructure and induced properties. The latter is discussed in terms of reorientation of crystallites of graphene sheets vis-à-vis the carbon fibre axis during loading.

Light-weight origami-inspired mechanisms can provide advantages in deployable space systems and other applications. However, a significant challenge in their design is ensuring that they are sufficiently stiff. Compliant, deployable stiffeners utilizing a profile that approximates the Euler Spiral are proposed as one possible solution. It is shown that a structure with this specific profile, called a lenticular stiffener, permits stiffeners to be flattened using a force applied at their edge. Formulas for calculating the increase in stiffness are developed. Relations needed to design the deployment behavior of the stiffeners are also derived. Finally, advantages of different configurations of stiffeners are evaluated. These results are verified through simulation and experiments. [ABSTRACT FROM AUTHOR]

Highlights • Local stability analysis for incompressible elastic solids under dead-load surface tractions. • Explicit necessary and sufficient algebraic local stability conditions are found. • The special case of a Gent-Thomas incompressible, isotropic elastic parallelepiped is considered. • The response of the parallelepiped as the material parameters vary is described. Abstract We study the equilibrium and the local stability for an incompressible elastic solid under arbitrary dead-load surface tractions on the boundary. We particularize the analysis to homogeneous deformations of a homogeneous, isotropic parallelepiped, finding necessary and sufficient algebraic local stability conditions consistent with the further requirement of the zero moment condition. We specialize the study for a uniform distribution of dead-load surface tractions s > 0 on two pairs of faces and –s on the remaining two faces, and we find that two classes of equilibrium solutions may occur: symmetric and asymmetric solutions, respectively. For the symmetric solutions we also determine local stability inequalities. For the special case of a Gent-Thomas material we show that both equilibrium symmetric and asymmetric solutions may occur if the material parameters satisfy certain inequalities. Then, we completely describe the response of the parallelepiped in a loading process starting from the unloaded state for five ranges of the values of the material parameters. In particular, for one of these ranges we show that symmetric solutions are the unique locally stable homogenous equilibrium deformations until a critical value s cr of the load; at s cr , symmetric solutions lose their uniqueness, and a bifurcation into asymmetric solutions may occur. [ABSTRACT FROM AUTHOR]

This paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. For the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed by using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. A well posed topology optimization problem is formulated by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed. [ABSTRACT FROM AUTHOR]

Nowadays, strain and displacement can be measured using techniques such as electronic speckle pattern interferometry and digital image correlation. However, usually, only some part of the domain of interest is accessible for measurement devices. In order to assess also inaccessible areas of the structure, a fundamental task for structural health monitoring is the inference of full-field displacements from sparse measurements. Another important task is the inference of mechanical stress from displacement or strain data. In computational mechanics, the link between such data and stress is established via constitutive models. A well-established approach for inferring full displacement and stress fields from possibly sparse data is to calibrate the parameter of a given constitutive model using a Bayesian update. After calibration, a (stochastic) forward simulation is conducted with the identified model parameters to resolve physical fields in regions that were not accessible to the measurement device. A shortcoming of model calibration is that the model is deemed to best represent reality, which is only sometimes the case, especially in the context of the aging of structures and materials. While this issue is often addressed with repeated model calibration, a different approach is followed in the recently proposed statistical Finite Element Method (statFEM). Instead of using Bayes' theorem to update model parameters, the displacement is chosen as the stochastic prior and updated to fit the measurement data more closely. For this purpose, the statFEM framework introduces a so-called model-reality mismatch, parametrized by only three hyperparameters. This makes the inference of full-field data computationally efficient in an online stage: If the stochastic prior can be computed offline, solving the underlying partial differential equation (PDE) online is unnecessary. Compared to solving a PDE, identifying only three hyperparameters and conditioning the state on the sensor data requires much fewer computational resources. Computational efficiency is an essential requirement for online applications. It is noted that conditioning a model-based prior field on sensor data represents a variant of physics-based regression. This paper presents two contributions to the existing statFEM approach: First, we use a non-intrusive polynomial chaos method to compute the prior, enabling the use of complex mechanical models in deterministic formulations. Second, we examine the influence of prior material models (linear elastic and St.Venant Kirchhoff material with uncertain Young's modulus) on the updated solution. We present statFEM results for 1D and 2D examples, while an extension to 3D is straightforward. [ABSTRACT FROM AUTHOR]

This paper presents a mechanical system with a similar configuration to a human musculo-skeletal system for use in anthropomorphic robots or as artificial limbs for disabled persons. First, a mechanical module called ANLES (Actuator with Non-Linear Elasticity System) is introduced. There are two types of ANLES: the linear-type ANLES and rotary-type ANLES. They can be used as a voluntary muscle in a wide-range of musculo-skeletal structures in which at least double actuators work in an antagonistic setup via some elastic elements. Next, an application of the two types of ANLES to a two-degree-of-freedom (DOF) manipulator that has a similar configuration to the human elbow joint is shown. The experimental results of the joint stiffness and joint angle control elucidate that the developed mechanism effectively regulates joint stiffness in the same way as a musculo-skeletal system.

Application of seismic interferometry in buildings gained interest in the recent years for structural health monitoring. It allows us to derive the shear wave velocity for an equivalent homogeneous medium representing the structure. Previous authors suggested using a shear beam model to compute the fundamental frequency of the structure out of this velocity. This model is however not adapted to a large part of existing buildings having different behaviors. In this paper, we propose a correction factor from shear beam and based on the Timoshenko beam to link the fundamental frequencies with the observed pulse velocity and the relative effects of shear and bending. This factor provides corrections up to 60% in frequency with respect to the shear beam model. The proposed correction factor shows that the higher velocities observed in the literature for shear wall buildings compared to frame buildings is compensated by their bending flexibility, resulting in resonance frequencies scaling similarly with building height. This model is applied to an 18-story reinforced concrete shear wall building (Ophite tower). The observed pulse velocity obtained by seismic interferometry in this building was about 500 m/s correlated to the resonance frequency by the correction factor. We show that variations of velocity in this structure and the well-studied Factor building (California), related to non-linear behavior at low-strains (down to 10 −5 ), can be retrieved with seismic interferometry, demonstrating that this method is sensitive enough for structural health monitoring. [ABSTRACT FROM AUTHOR]

Within the framework of nonlinear elasticity we analyze instability of a uniformly compressed circular two-layered plate with an initially compressed or stretched layer. For a constitutive relation of the material we use the incompressible neo-Hookean model. We assume that the lower layer is subjected to radial tension or compression. As a result in this layer there are initial strains and stresses. The two-layered plate is subjected to a uniform lateral compression. We study the stability of the plate with the use of the static Euler method. Within the method we determine loading parameters for which the linearized boundary-value problem has non-trivial solutions. We derive the three-dimensional linearized equilibrium equations for each layer. The solutions of the latter equations are obtained with the help of the Fourier method. The equation for critical strains is derived. We present an analysis of dependence of critical stress resultants on the initial strains and stiffness parameters. [ABSTRACT FROM AUTHOR]

Shales serve essential functions as seals for conventional hydrocarbon reservoirs, waste storage repositories and unconventional plays. Exploration and evaluation of shales rely on the characterization of their multiscale elastic properties. However, there are limited studies on the geologic controls of elastic stress sensitivity in organic shales. This study investigated dry Lokpanta, Bakken, and Niobrara shales of different thermal maturity stages. First, we used a pulse-transmission ultrasonic setup to conduct multidirectional (0o, 45o and 90o) hydrostatic-stress sensitivity (0–27.58 MPa) tests to measure elastic waves and derive other elastic properties. Furthermore, we inverted microscopic parameters from the elastic measurements based on effective medium theories such as damage parameters (α ij and β ijkl), crack density (ρ), normal to tangential microcrack compliance (B), specific tangential crack compliance (s n B T) and microcracks orientation anisotropy (η). Finally, we studied the effects of organic matter maturity and clay diagenesis on the multi-scaled elastic stress sensitivity. Under applied hydrostatic stress, the non-linear elastic response in the shales is consistent with the closure of aligned microcracks. Microcrack closure decreased the elastic anisotropy at lower stress (<10 MPa), while aligned clays and organic matter control the stress-insensitive anisotropy at higher stress. As organic matter matures and smectite transforms to illite, orthogonal velocity stress sensitivity increases and extrinsic contribution to elastic anisotropy increases. There is also a corresponding increase in orthogonal damage second-rank tensor (α 33) and a decrease in orthogonal damage fourth-rank tensor (β 3333) with organic matter-clay thermal maturity. These relationships are due to the thermally-induced development of new and/or extensional roughly-textured microcracks parallel to the laminated microfabric, which is of higher compliance in the shear than compression. Microcrack closure also decreases ρ under applied pressure. Most of the samples had B < 0.5, suggesting the presence of non-idealized roughly textured microcracks. Generally, s n B T broadly decreases and η increases with clay diagenesis and organic matter maturity also because of the generation and/or enhancement of aligned microcracks resulting in higher tangential stiffness. • Aligned microcracks closure govern the non-linear elasticity in the organic shales. • Microcracks formation is due to organic matter and clay diagenesis. • Roughly-textured microcracks caused a non-linear decrease in crack density. • Organic matter and clay diagenesis affect microscopic-micromechanical properties. [ABSTRACT FROM AUTHOR]

Five types of polyacrylonitrile, PAN, based carbon fibres, differing in modulus, breaking strain and in crystallite orientation, have been studied. Non-Hookean behaviour was investigated by computing the tangent tensile and compression moduli as a function of strain, from the axial stress–strain response obtained in standard tensile, compression, as well as in modified flexural tests of unidirectional carbon/ epoxy composites. The dependences of the tensile modulus on tensile strain of the carbon fibres were extracted from data obtained in single-filament tensile tests. Analytical expressions for the tensile modulus–tensile strain and compression modulus–compression strain dependences in the performed test were deduced. The structural characterization of the carbon fibres was performed by X-ray diffraction on bundle of parallel fibres. The interlayer spacing d002 and the apparent lateral dimension of the crystallites Lc were deduced by processing the 002 diffraction profiles. The established modulus–strain dependences were correlated with the fibre characteristics (breaking strain and mean modulus values), as well as with the characteristic of the 002 diffraction profile and the d002 and Lc values.

Five types of polyacrylonitrile, PAN, based carbon fibres, differing in modulus, breaking strain and in crystallite orientation, have been studied. Non-Hookean behavior was investigated by computing the tangent tensile and compression moduli as a function of strain, from the axial stress-strain response obtained in standard tensile, compression, as well as in modified flexural tests of unidirectional carbon/ epoxy composites. The dependences of the tensile modulus on tensile strain of the carbon fibres were extracted from data obtained in single-filament tensile tests. Analytical expressions for the tensile modulus-tensile strain and compression modulus-compression strain dependences in the performed test were deduced. The structural characterization of the carbon fibres was performed by X-ray diffraction on bundle of parallel fibres. The interlayer spacing d 002 and the apparent lateral dimension of the crystallites L c were deduced by processing the 002 diffraction profiles. The established modulus-strain dependences were correlated with the fibre characteristics (breaking strain and mean modulus values), as well as with the characteristic of the 002 difraction profile and the d 002 and L c values.

Starting from constrained three-dimensional Cosserat elasticity and in a total Lagrangian framework, we derive and discuss a hierarchy of static non-linear micropolar shell models in which the thickness can stretch, and the independence of the micro-rotation on the macro-rotation is not limited to the drilling degree of freedom as in the classical six-parameter theory. If the thickness stretch is considered, unconstrained quaternions allow a singularity-free, non redundant and rational parametrization of the strain measures. Emphasis is placed in the discussion of the differences between curvatures, wryness and director deformation strains. [ABSTRACT FROM AUTHOR]

A sequence of polynomial expressions have been shown to describe the strained surface energy of low-index hexagonal and square transition metal surfaces. Distinguishable functions describe the hexagonal FCC (1 1 1) and HCP (0 0 0 1) surfaces, but a single function describes the FCC (1 0 0) and BCC (1 0 0) surfaces. A far weaker dependence exists between the strained surface energy and the electronic state of the surface, and the competition between geometric and electronic states across is discussed. [ABSTRACT FROM AUTHOR]

We study buckling patterns in pantographic sheets, regarded as two-dimensional continua consisting of lattices of continuously distributed fibers. The fibers are modeled as beams endowed with elastic resistance to stretching, shearing, bending and twist. Included in the theory is a non-standard elasticity due to geodesic bending of the fibers relative to the lattice surface. [ABSTRACT FROM AUTHOR]

We study the equilibrium homogeneous deformations of a homogeneous parallelepiped made of an arbitrary incompressible, isotropic elastic material and subject to a distribution of dead-load surface tractions corresponding to an equibiaxial tensile stress state accompanied by an orthogonal uniaxial compression of the same amount. We show that only two classes of homogeneous equilibrium solutions are possible, namely symmetric deformations, characterized by two equal principal stretches, and asymmetric deformations, with all different principal stretches. Following the classical energy-stability criterion, we then find necessary and sufficient conditions for both symmetric and asymmetric equilibrium deformations to be weak relative minimizers of the total potential energy. Finally, we analyze the mechanical response of a parallelepiped made of an incompressible Mooney–Rivlin material in a monotonic dead loading process starting from the unloaded state. As a major result, we model the actual occurrence of a bifurcation from a primary branch of locally stable symmetric deformations to a secondary, post-critical branch of locally stable asymmetric solutions. [ABSTRACT FROM AUTHOR]