Journal of Elasticity最新文献

It is shown that some of the assumptions and further restrictions imposed in Reference (Muki and Sternberg in Z. Angew. Math. Phys. 16:611–648, 1965) in relation to development of the plane strain version of the conventional couple-stress theory are invalid. This finding comes a result a new development presented in the first part of this study (Soldatos in J. Elast. 153:185–206, 2023), according to which a refined couple-stress theory of isotropic linear elasticity enables determination of the trace of the couple-stress tensor and, henceforth, of the antisymmetric part of the stress and, thus, the total stress tensors. The present communication reconsiders those assumptions and restrictions (Muki and Sternberg in Z. Angew. Math. Phys. 16:611–648, 1965), separates the ones that are still valid from their invalid counterpart, and, to the extent that this is possible and acceptable, rebuilds the foundation that the plane strain concept can be based upon in polar isotropic linear elasticity. It is accordingly found, and also demonstrated with a couple of relevant boundary value problem applications, that, while the assumption of plane strain naturally guarantees that displacements and strains depend only on in-plane co-ordinates parameters, the couple-stress and the stress tensors generally depend on the out-of-plane co-ordinate parameter as well.

A general semi-analytical solution is developed for the time-dependent, axisymmetric problem of elastoplastic stress concentration around expanding cavities in the presence of heat conduction. The formulation is based on the incremental theory of plasticity within a Lagrangian framework of thermo-elastoplastic constitutive relations, while incorporating the von Mises yield criterion, strain hardening, and the associated flow rule. The transient heat conduction problem is treated through application of the Laplace integral transform. It is shown that the problem constitutive equations reduce to a system of three nonlinear ordinary differential equations describing the path-dependent evolution of the elastoplastic stress components with time. The long-time asymptotic solution provides the distribution of residual stresses. The proposed general solution for the thermal cavity expansion problem offers a rigorous benchmark for verification of relevant numerical solvers. The application of the proposed solution to the stress analysis of shrink-fit assemblies is demonstrated by examining the mechanical interaction between a solid shaft and a hollow hub, wherein the hub undergoes elastoplastic deformation due to the thermal expansion of the inner shaft. The results show that the strain-hardening parameter plays a critical role in controlling the extent of plastic deformation in the hub. Furthermore, a case study highlights the influence of constitutive behavior and stress-path dependency on the development of residual stresses in shrink-fit assemblies.

In this paper the nonlinear elasticity theory of volumetric growth based on residual stress that was introduced in previous contribution (Huang et al. in J. Elast. 145:223–241, 2021) is developed further, and is then focused on an applications of the theory with computational examples. The main idea here is to use residual stress in an intact unloaded configuration, or the deformation from a fixed and intact reference configuration (which may itself be residually stressed), as a means to assess the growth in a soft solid, the developing unloaded configuration and the accompanying developing residual stress. The general theory is presented in terms of the free energy per unit mass and the associated energy functions relative to the reference configuration and the unloaded configuration. Growth of a thick-walled spherical shell is examined in order to illustrate the theory using simple prototype energy functions. A general programme for obtaining the developing deformed configuration is outlined and several possible growth laws are discussed for the growth of a spherical shell under internal pressure. This study shows that growth modelling based on the unloaded configurations may provide insights into the development of residual stress and morphology, both of which are, in principle, accessible to experimental observation. For several possible growth laws detailed numerical results are provided to illustrate the evolution of growth and the associated residual stress.

The representation theory of tensor functions is essential to constitutive modeling of materials including both mechanical and physical behaviors. Generally, material symmetry is incorporated in the tensor functions through a structural or anisotropic tensor that characterizes the corresponding point group. The general mathematical framework was well-established in the 1990s. Nevertheless, the traditional theory suffers from a grand challenge that many point groups involve fourth or sixth order structural tensors that hinder its practical applications in engineering. Recently, researchers have reformulated the representation theory and opened up opportunities to model anisotropic materials using lower-order (i.e., 2nd- order and lower) structural tensors only, although the theory was not fully established. This work aims to fully establish the reformulated representation theory of tensor functions for all two-dimensional point groups. It was found that each point group needs a structural tensor set to characterize the symmetry. For each two-dimensional point group, the structural tensor set is proposed and the general tensor functions are derived. Only lower-order structural tensors are introduced so researchers can readily apply these tensor functions for their modeling applications. The theory presented here is useful for constitutive modeling of materials in general, especially for composites, nanomaterials, soft tissues, etc.

We analyze shear stress distributions in an arterial wall and torques with torsion around the vessel axis depending on the axial stretch ratio. A Riemannian stress-free configuration of artery is adopted to analyze stress distributions. It is determined from experimentally investigated deformations of arterial ring radially cut and axial strip sectioned. The stress-free configuration is considered as a Riemannian manifold that is not Euclidean. A strain energy function is adopted to analyze stresses. Torque is linearly related to torsion of vessel axis under a physiological condition. The shear component of deformation gradient almost linearly increases from the inner surface of vessel to the outer surface with discontinuity at the boundary between media and adventitia. The shear stress also increases from the inner surface to the outer surface. The shear stress is greatly larger in the adventitia than in the media-intima.

We present a variational characterization of mechanical equilibrium in the planar strain regime for systems with incompatible kinematics. For non-simply connected domains, we show that the equilibrium problem for a non-liftable strain-stress pair can be reformulated as a well-posed minimization problem for the Airy potential of the system. We characterize kinematic incompatibilities on internal boundaries as rotational or translational mismatches, in agreement with Volterra’s modeling of disclinations and dislocations. Finally, we establish that the minimization problem for the Airy potential can be reduced to a finite-dimensional optimization involving cell formulas.

Liquid crystalline networks (LCNs) are stimuli-responsive materials formed from polymeric chains cross-linked with rod-like mesogenic segments, which, in the nematic phase, align along a non-polar director. A key characteristic of these nematic systems is the existence of singularities in the director field, known as topological defects or disclinations, and classified by their topological charge. In this study, we address the open question of modeling theoretically the coupling between mesogens disclination and polymeric network by providing a mathematical framework describing the out-of-plane shape changes of initially flat LCN sheets containing a central topological defect. Adopting a variational approach, we define an energy associated with the deformations consisting of two contributions: an elastic energy term accounting for spatial director variations, and a strain-energy function describing the elastic response of the polymer network. The interplay between nematic elasticity, which seeks to minimize distortions in the director field, variations in the degree of order, with the consequent tendency of monomers in the polymer chains to distribute anisotropically in response to an external stimulus, and mechanical stiffness, which resists deformation, determines the resulting morphology. We analyze the transition to instability of the ground-state flat configuration and characterize the corresponding buckling modes.

This work reveals the geometric interpretability of hyperelastic constitutive models fitted to mechanics data of biological tissue, addressing the long-overlooked prediction reliability issue arising from dual constraints of model limitations (structural complexity and physical idealization) and data challenges (finiteness and uncertainty). We evaluate three representative models—the eight-chain model, the Ogden model, and the neural network-derived gray matter model—under Bayesian model calibration, which naturally extends from the inherent uncertainties in biological tissue mechanical response data. By combining diverse mechanics datasets and priors with varying levels of informativeness, we analyze how data and prior constraints influence sloppiness. Posterior samples of model parameters are used to derive the sensitivity matrix of the cost function, uncovering the local geometric features of the cost landscape. Our results demonstrate the pervasive sloppiness in multi-parameter hyperelastic constitutive models, which can only be mitigated by high-quality data and informative priors. Beyond defining robust sloppiness metrics, this work provides actionable insights, such as guiding model selection and offering geometric constraints in machine learning-based automated model discovery.

This paper introduces a novel approach for constructing, at the same scale, a continuum model equivalent to a given nanoscale discrete system, effectively capturing scale effects. Starting from a general formulation of (m)-particle interaction potentials for discrete particle systems, we propose the use of the Euler–Maclaurin (E–M) summation formula to construct the equivalent continuum model at the same scale. The proposed theory is developed for arbitrary 3D domains. The resulting novel continuum model captures scale effects in both statics and dynamics through additional edge, surface, and volume integrals, which are analytically obtained and driven by the nanostructure. For an arbitrary domain, the proposed approach provides a pathway for its integration into a computational framework. Since nanoscale and microscale systems are inevitably affected by uncertainties, the geometric and constitutive parameters must be modeled as random fields and their identification of must be conducted within a statistical framework. Consequently, we present a discussion on this identification in a probabilistic framework.

Eringen’s original linear theory of nonlocal elasticity involves integral operators. We apply it to the problem of waves in an elastic half-space, hoping to find a generalization of Rayleigh waves. We solve the governing equations exactly and show that such a generalization does not exist.