Journal of Elasticity最新文献

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.

This work deals with the well-posedness and asymptotic behavior of a Shear beam model subject to internal dissipation of the fractional derivative-type. The energy functional is presented, and the dissipative property of the system is stablished. We use the semigroup theory in order to deal with the well-posedness and we prove the strong stability of the (C_{0})-semigroup using the Arendt-Batty and Lyubich-Vũ’s general criterion and also we prove the polynomial stability result applying Borichev and Tomilov’s theorem.

We address a nonlinear boundary homogenization problem associated to the deformations of a block of an elastic material with small reaction regions periodically distributed along a plane. We assume a nonlinear Winkler-Robin law which implies that a strong reaction takes place in these reaction regions. Outside, on the plane, the surface is traction-free while the rest of the surface is clamped to an absolutely rigid profile. When dealing with critical sizes of the reaction regions, we show that, asymptotically, they behave as stuck regions, the homogenized boundary condition being a linear one with a new reaction term which contains a capacity matrix depending on the macroscopic variable. This matrix is defined through the solution of a parametric family of microscopic problems, the macroscopic variable being its parameter. Among others, to show the convergence of the solutions, we develop techniques that extend those both for nonlinear scalar problems and linear vector problems in the literature. We also address the extreme cases.

We study large deformations of hyperelastic membranes using a purely two-dimensional formulation derived from basic balance principles within a modern geometric setting, ensuring a framework that is independent of an underlying three-dimensional formulation. To assess the predictive capabilities of membrane theory, we compare numerical solutions to experimental data from axisymmetric deformations of a silicone rubber film. Five hyperelastic models—Neo-Hookean, Mooney-Rivlin, Gent, Yeoh, and Ogden—are evaluated by fitting their material parameters to our experimental data using TensorFlow. Our results provide a systematic comparison of these models based on their accuracy in capturing observed deformations, establishing a framework for integrating theory, experiment, and data-based parameter identification.

This article derives homogenized bending shell theories starting from three-dimensional nonlinear elasticity. The original three-dimensional model contains three small parameters: the two homogenization scales (varepsilon ) and (varepsilon ^{2}) of the material properties and the thickness (h) of the shell. We obtain different limiting behaviors depending on the limit of various ratios of these three parameters.