Search

The aim of this paper is to prove the existence of weak solutions to thermo‐visco‐elastic system of equations. In considered problem, the temperature term is included in the elastic constitutive equations (generalized Hooke's law) as well as in describing the evolution of visco‐elastic strain. The main idea of presented proof is to analyze reformulated model, in which visco‐elastic strain (internal variable) is eliminated. For such system of equations, we propose a two‐level Galerkin approximation, which allows us to show a non‐negativity of temperature during the entire deformation process. In order to characterize the weak limits in the nonlinearities occurring in the system at different levels of approximation, the following tools are used: Truncation methods for heat equation proposed in the paper of D. Blanchard [Nonlinear Analysis, 21(10):725‐743, 1993], modified Boccardo‐Gallouët's approach, and Minty‐Browder trick. [ABSTRACT FROM AUTHOR]

In this paper, we notice a property of the extension operator from the space of tangential traces of H(curl; Ω) in the context of the linear relaxed micromorphic model, a theory that is recently used to describe the behavior of some metamaterials showing unorthodox behaviors with respect to elastic wave propagation. We show that the new property is important for existence results of strong solution for non‐homogeneous boundary condition in both the dynamic and the static case. [ABSTRACT FROM AUTHOR]

We study the existence of solutions arising from the modelling of elastic materials using generalized theories of continua. In view of some evidence from physics of metamaterials, we focus our effort on two recent nonstandard relaxed micromorphic models including novel micro-inertia terms. These novel micro-inertia terms are needed to better capture the band-gap response. The existence proof is based on the Banach fixed-point theorem. [ABSTRACT FROM AUTHOR]

We consider the quasi-static evolution of the thermo-plasticity model in which the evolution equation law for the inelastic strain is given by the Prandtl–Reuss flow rule. The thermal part of the Cauchy stress tensor is not linearized in the neighbourhood of a reference temperature. This nonlinear thermal part is imposed to add a damping term to the balance of the momentum, which can be interpreted as external forces acting on the material. In general, the dissipation term occurring in the heat equation is an integrable function only and the standard methods can not be applied. Combining truncation techniques and Boccardo-Gallouët approach with monotone methods, we prove an existence of renormalized solutions. [ABSTRACT FROM AUTHOR]

We study a thermodynamically consistent model describing phenomena in a visco‐plastic metal subjected to temperature changes. We complete the model with the mixed boundary condition on displacement and stress and Neumann‐type condition for temperature. The main result is an existence of solutions. [ABSTRACT FROM AUTHOR]

We consider the quasi-static evolution of thermo-visco-elastic material. The main goal of this paper is to present how taking into account the additional effects may improve the result of solutions' existence. We added a micropolarity effect to thermo-visco-elastic model regarding Norton-Hoff-type constitutive function. This additional phenomenon improves the regularity of solution. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to prove the existence and uniqueness of solutions to an initialboundary value problem corresponding to the Biot model. The existence theorem is proved by Galerkin method and the passage to the limit in the approximation process is shown in a standard way. Assuming that the given data satisfy some natural regularity requirements a better regularity of solutions is obtained than it could be found in the literature. [ABSTRACT FROM AUTHOR]