相关论文: Multiple Independent Cavitation in 2D NeoHookean M…

Two mathematical models are developed within the theoretical framework of large strain elasticity for the determination of upper and lower bounds on the total strain energy of a finitely deformed hyperelastic body in unilateral contact with…

In this paper we consider and generalize a model, recently proposed and analytically investigated in its quasi-stationary approximation by the authors, for visco-elasticity with large deformations and conditional compatibility, where the…

This note collects some results on the behaviour of screw dislocation in an elastic medium. By using a semi-discrete model, we are able to investigate two specific aspects of the dynamics, namely (i) the interaction with free boundaries and…

The linear stability with variable coefficients of the vortex sheets for the two-dimensional compressible elastic flows is studied. As in our earlier work on the linear stability with constant coefficients, the problem has a free boundary…

It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the…

We consider vectorial variational problems in nonlinear elasticity of the form $I[u]=\int W(Du)dx$, where $W$ is continuous on matrices with positive determinant and diverges to infinity long sequences of matrices whose determinant is…

In this paper, we prove the local well-posedness of the free boundary problem in incompressible elastodynamics under a natural stability condition, which ensures that the evolution equation describing the free boundary is strictly…

This paper establishes finite-time splash singularity formation for 3D viscous incompressible neo-Hookean elastodynamics with free boundaries. The system features mixed stress-kinematic conditions where viscous-elastic stresses balance…

The development of a nonlinear structural theory (model) for isotropic linear-elastic finite continua is the main objective of the study. To derive the theory, we used Taylor's multivariable expansion and Bubnov-Galerkin's weak formulation.…

Treatises on vibrations devote large space to study the dynamical behavior of an elastic system subject to known external tractions. In fact, usually a "system" is not an isolated body but it is part of a chain of mechanisms which disturb…

This paper concerns with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization. We establish uniform optimal regularity estimates for solutions of Neumann…

Two classes of non-linear elastic materials are derived via two-dimensional homogenization. These materials are equivalent to a periodic grid of axially-deformable and axially-preloaded structural elements, subject to incremental…

We exploit a two-dimensional model [7], [6] and [1] describing the elastic behavior of the wall of a flexible blood vessel which takes interaction with surrounding muscle tissue and the 3D fluid flow into account. We study time periodic…

In \cite{Lei}, the author derived an exact rotation-strain model in two dimensions for the motion of incompressible viscoelastic materials via the polar decomposition of the deformation tensor. Based on the rotation-strain model, the author…

We study the second order elliptic equations of non-divergence form in a planar domain with complicated geometry. In this case the domain winds around a fixed circle infinitely many times and converges to it when the rotating angle goes to…

This paper deals with regularity theory for two-phase free boundary variational problems ruled by degenerate elliptic operators.

Contact problems with Coulomb friction in linear elasticity are notoriously difficult and their mathematical analysis is still largely incomplete. In this paper, a model problem with heterogeneous friction coefficient is considered in…

In this work, a higher-order irrotational strain gradient plasticity theory is studied in the small strain regime. A detailed numerical study is based on the problem of simple shear of a non-homogeneous block comprising an elastic-plastic…

The paper studies the initial boundary value problem related to the dynamic evolution of an elastic beam interacting with a substrate through an elastic-breakable forcing term. This discontinuous interaction is aimed to model the phenomenon…

We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at a high temporal frequency, we use limit theorems for multipower variations and…