Some equilibrium problems for compressible, anisotropic, laminated nonlinearly elastic bodies
type: Item
instance of: scholarly article
title: Some equilibrium problems for compressible, anisotropic, laminated nonlinearly elastic bodies
zbMATH Open document ID: 0759.73012
DOI: 10.1007/BF00376008
author: S. Singh
published in: Archive for Rational Mechanics and Analysis
publication date: 1993-01-16T00:00:00Z
review text: In this paper, being a generalization of \textit{C.-C. Wang's} work [Arch. Ration. Mech. Anal. 114, No. 3, 195-236 (1991; Zbl 0728.73019)], the authors introduce a class of nonlinearly elastic materials which they call laminated materials (either planar or cylindrical). Such materials consist essentially of sheets of anisotropic materials that are stacked one upon another, and such that each sheet is obtained as the result of a homogeneous deformation that may depend on the transverse variable, from a reference configuration that is the same on each sheet, but may also depend on the transverse variable. The sheets can be planar or cylindrical. The transverse direction can also be prestretched arbitrarily. After discussing the response function of such materials, the initial deformation field and associated metric, they consider laminated configurations similar to the above reference configurations, in which the Cauchy stress tensor depends only on the transverse variable. Four families of semi-inverse deformations that map laminated configurations into laminated configurations are introduced. They depend generally on three functions of the transverse variables in the reference configuration. Equilibrium requires these functions to be solutions of implicit nonlinear ordinary differential equations. After a brief discussion as to whether or not, and how, the constitutive law may be inverted for such deformations, a few examples are further detailed.
reviewed by: Hervé Le Dret
Mathematics Subject Classification ID: 74B20
zbMATH DE Number: 94649
zbMATH Keywords: laminated materials
zbMATH Keywords: sheets of anisotropic materials
zbMATH Keywords: response function
zbMATH Keywords: Cauchy stress tensor
zbMATH Keywords: transverse variable
zbMATH Keywords: semi-inverse deformations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 94649