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Mathematics and Mechanics of Solids
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Article

A Note on Plane Strain and Plane Stress Problems for a New Class of Elastic Bodies

R. Bustamante1* and K R Rajagopal2

1 Departamento de Ingeniería Mecánica, Universidad de Chile, Santiago, Chile
2 Department of Mechanical Engineering, Texas A&M University, College Station, TX 77845, USA

* To whom correspondence should be addressed.


  Abstract

In this paper we explore the consequences of prescribing constitutive relations for elastic bodies wherein deformations are given as functions of stresses. For this class of constitutive relations in, the particular case of small deformations, we study boundary value problems for plane strain and plane stresses, and we develop a weak formulation that can be considered as the starting point for numerical computations.

Key Words: implicit constitutive relations, Airy stress function, biharmonic equation, weak formulation

First published on March 11, 2009
Mathematics and Mechanics of Solids 2009, doi:10.1177/1081286508098178
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