Related papers: Yet another best approximation isotropic elasticit…
We studied the elastic properties of bone to analyze its mechanical behavior. The basic principles of ultrasonic methods are now well established for varying isotropic media, particularly in the field of biomedical engineering. However,…
Third-order elastic coefficients (TOECs) have been measured experimentally and tabulated with pretty good accuracy since the middle of the previous century. In the classical acoustic measurement method the recalculation of instantaneous…
In this article, we consider the problem of finding the support of an inhomogenous possibly anisotropic inclusion in a background of constant electric conductivity from the electrical impedance tomography data at the boundary of a bounded…
An efficient procedure using a novel semi-analytical forward solver for identifying heterogeneous and anisotropic elastic parameters from only one full-field measurement is proposed and explored. We formulate the inverse problem as an…
We investigate non-linear elastic deformations in the phase field crystal model and derived amplitude equations formulations. Two sources of non-linearity are found, one of them based on geometric non-linearity expressed through a finite…
The hardness of materials plays an important role in material design. There are numerous experimental methods to measure the hardness of materials, but theoretical prediction of hardness is challenging. By investigating the correlation…
This work puts forth a new optimal design formulation for planar elastic membranes. The goal is to minimize the membrane's compliance through choosing the material distribution described by a positive Radon measure. The deformation of the…
In this paper, a two-scale approach for elastic shape optimization of fine-scale structures in additive manufacturing is investigated. To this end, a free material optimization is performed on the macro-scale using elasticity tensors in a…
An asymptotic analysis is performed for thin anisotropic elastic plate clamped along its lateral side and also supported at a small area $\theta_{h}$ of one base with diameter of the same order as the plate thickness $h\ll1.$ A…
We derive closed-form solutions for reverberant elastography in anisotropic elastic media by adapting the framework used in electromagnetic theory to treat transverse isotropic materials. Different sample-setup geometries are analyzed,…
We consider 3D free-boundary compressible elastodynamic system under the Rayleigh-Taylor sign condition. It describes the motion of an isentropic inviscid elastic medium with moving boundary. The deformation tensor satisfies the neo-Hookean…
The deformation problem for a transversely isotropic elastic layer bonded to a rigid substrate and coated with a very thin elastic layer made of another transversely isotropic material is considered. The leading-order asymptotic models (for…
We present the first calculations of the pressure tensor profile in the vicinity of the planar interface between isotropic liquid and nematic liquid crystal, using Onsager's density functional theory and computer simulation. When the liquid…
This paper extends our earlier work [arXiv:2309.13595] on the $L^p$ approximation of the shape tensor by Laurain and Sturm. In particular, it is shown that the weighted $L^p$ distance to an affine space of admissible symmetric shape tensors…
In this paper, we study new exact solutions of Einstein's field equations with the motivation of the relativistic elasticity theory. We construct the static conformal elastic solution by applying conformal transformations to the…
In this article, we derive a mathematical model for a shell (i.e. a thin elastic body) bonded to an elastic foundation by modifying Koiter's linear shell equations. We prove the existence and the uniqueness of solutions, and we explicitly…
This work is devoted to establishing a regularity result for the stress tensor in quasi-static planar isotropic linearly elastic - perfectly plastic materials obeying a Drucker-Prager or Mohr-Coulomb yield criterion. Under suitable…
In this paper we present a new general framework for anisotropic elastoplasticity at large strains. The new framework presents the following characteristics: (1) It is valid for non-moderate large strains, (2) it is valid for both elastic…
Finite plasticity theories are still a subject of controversy and lively discussions. Among the approaches to finite elastoplasticity two became especially popular. The first, implemented in the commercial finite element codes, is based on…
Incompressible nonlinearly hyperelastic materials are rarely simulated in Finite Element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying this constraint. Most…