Existence and smoothness for a class of d-dimensional models in elasticity theory of small deformations

被引：2

作者：

Bulicek, Miroslav ^{[1
]}

Burczak, Jan ^{[2
]}

机构：

[1] Charles Univ Prague, Math Inst, Sokolovska 83, Prague 18675 8, Czech Republic

[2] Polish Acad Sci, Inst Math, Sniadeckich 8, PL-00656 Warsaw, Poland

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2018年 / 69卷 / 01期

关键词：

Nonlinear small strain elasticity; Regularity; Fully nonlinear bulk modulus; REGULARITY; SYSTEMS;

D O I：

10.1007/s00033-018-0917-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a model for deformations of a homogeneous isotropic body, whose shear modulus remains constant, but its bulk modulus can be a highly nonlinear function. We show that for a general class of such models, in an arbitrary space dimension, the respective PDE problem has a unique solution. Moreover, this solution enjoys interior smoothness. This is the first full regularity result for elasticity problems that covers the most natural space dimension 3 and that captures the behaviour of real-life elastic materials (considered in small deformations), primarily certain beta-phase titanium alloys.

引用

页数：11