Journal of Elasticity最新文献

We describe via semigroup techniques the space decaying solutions to the system modeling an isotropic and homogeneous elastostatic semi-infinite band, both in the isothermal case and when thermal effects are present. The semigroup approach allows us to transfer some properties that typically occur in evolution problems to our model, such as analyticity and exponential decay at infinity. These results are closely related to the Saint-Venant principle. We conclude the article by recalling some consequences of the analyticity of the semigroup. The resulting properties are rather innovative compared to the usual results in the literature concerning the spatial decay of solutions.

By revisiting a model proposed in Zurlo and Truskinovsky (Mech. Res. Commun. 93:174–179, 2018), we address the accretive growth of a viscoelastic solid at large strains. The accreted material is assumed to accumulate at the boundary of the body in an unstressed state. The growth process is driven by the deformation state of the solid. The progressive build-up of incompatible strains in the material is modeled by considering an additional backstrain. The model is regularized by postulating the presence of a fictitious compliant material surrounding the accreting body. We show the existence of solutions to the coupled accretion and viscoelastic equilibrium problem.

In this work, we consider two dynamic systems arising in micropolar viscoelasticity. In this sense, the material structure is assumed to have macroscopic and microscopic levels. First, an existence and uniqueness result is proved by using the theory of linear semigroups and, secondly, the decay of the solutions to the equilibrium state is shown. Then, the polynomial energy decay is obtained applying a characterization of the system operator. In a second part, we consider the numerical approximation of a variational version of the above problem. This is done by using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A discrete stability property is proved and an a priori error analysis is provided. The linear convergence of the approximations is deduced under some additional regularity conditions on the continuous solution. Finally, some numerical simulations are shown to demonstrate numerical convergence and the behavior of the discrete energy.

This paper is concerned with a linear theory of porous thermoelastic materials in which the second temperature gradient is included in the classical set of independent constitutive variables. The paper is based on the theory of microstretch thermoelastic solids, as well as on Green-Naghdi thermomechanics. We use thermal displacement and an entropy production inequality. The introduction of the entropy flux tensor allows the constitutive equations to depend on the second gradient of temperature. We first present the basic equations of the theory as well as the boundary conditions for this class of non-simple materials. We then study the case of isotropic and homogeneous materials and present a general solution of the field equations similar to that obtained by Mindlin in strain gradient elasticity. In the context of anisotropic solids we discuss the uniqueness question appropriate to the fundamental initial-boundary-value problems. The continuous dependence of solutions on initial data and body loads is established. The Mindlin-type solution is used to study the deformation produced by a concentrated heat source in a body occupying an unbounded region.

In isotropic and incompressible elastodynamics, Carroll’s solutions for plane, circularly polarized shear waves represent an important class of controllable, non-universal solutions. It has already been shown that these solutions can be obtained in a compact way by rewriting the equations governing transverse waves as a single complex differential wave equation. In this work, we show that a complex wave equation formally identical to Carroll’s one can be used to construct new classes of solutions, still in the isotropic and incompressible setting, but in a more general case involving plane wave superimposed to homogeneous deformations. We analyze these new solutions and observe that they also exist in an interesting asymptotic regime frequently encountered in non-linear acoustics. Moreover, we demonstrate that these solutions are closely linked to symmetry properties of the complex wave equation and satisfy a nonlinear universal relation—a noteworthy and rare result.

We investigate universal deformations in compressible isotropic Cauchy elastic solids with residual stress, without assuming any specific source for the residual stress. We show that universal deformations must be homogeneous, and the associated residual stresses must also be homogeneous. Since a non-trivial residual stress cannot be homogeneous, it follows that residual stress must vanish. Thus, a compressible Cauchy elastic solid with a non-trivial distribution of residual stress cannot admit universal deformations. These findings are consistent with the results of Yavari and Goriely (Proc. R. Soc. A 472(2196):20160690, 2016), who showed that in the presence of eigenstrains, universal deformations are covariantly homogeneous and in the case of simply-connected bodies the universal eigenstrains are zero-stress (impotent).

A new proof is presented for the plane version of Ericksen’s theorem.

This work proposes a cono-spherical indentation method for characterizing the parameters of Mooney-Rivlin and Arruda-Boyce constitutive models in rubber-like hyperelastic materials. The cono-spherical indentation model (CSIM) is formulated based on the principle of equivalent energy to establish a relationship between load-depth responses and constitutive model parameters. This model enables the efficient, in-situ and non-destructive properties characterization of hyperelastic materials during service conditions. Validation of CSIM is performed through extensive finite element simulations covering a broad spectrum of hyperelastic constitutive parameters, encompassing the Mooney-Rivlin and Arruda-Boyce models. The constitutive model parameters for four rubber-like materials are inversely identified from load-depth curves obtained through cono-spherical indentation using CSIM, and stress-stretch curves are derived from the inversely identified parameters. The accuracy of the reverse-predicted results is confirmed by comparing them with results from uniaxial tensile tests conducted over a wide range of deformations. These results highlight the efficacy of CSIM, utilizing the Mooney-Rivlin and Arruda-Boyce constitutive models, as a precise and dependable approach for predicting constitutive parameters of rubber-like materials.

Steady shock wave shapes are studied in a size-dependent Cosserat continuum. The Cosserat continuum enriches a standard continuum by introducing a deformable triad of linearly independent director vectors that are determined by additional balances of director momentum, which introduce size-dependence. Limiting attention to purely mechanical nonlinear elastic response, it is shown that steady shock waves in uniaxial strain admit non-trivial trailing wave shapes after the jump at the shock front. The dependence of the wave shapes on the Cosserat material parameters are investigated for weak and strong shocks.