The deformation theory of plasticity of anisotropic media
type: Item
instance of: scholarly article
title: The deformation theory of plasticity of anisotropic media
zbMATH Open document ID: 0566.73034
DOI: 10.1016/0021-8928(84)90100-X
author: B. Pobedria
published in: Journal of Applied Mathematics and Mechanics
publication date: 1985-01-01T00:00:00Z
review text: Mutually inverse defining equations of the deformation theory of plasticity of media with arbitrary anisotropy are written assuming the relations between the stresses and deformations to be quasilinear. The conditions of plasticity and unloading are considered. Theorems are proved on the existence and uniqueness of solutions of the quasistatic problem of the deformation theory of plasticity and of simple loading. The method of successive approximations for solving the problem is considered, and its convergence is proved. Various means of simplifying the theory are considered. Theorems of minimum Lagrangian and the maximum of the Castiglianian are proved.
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74D99
Mathematics Subject Classification ID: 74G30
Mathematics Subject Classification ID: 74H25
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74E10
zbMATH DE Number: 3904072
zbMATH Keywords: transversely isotropic
zbMATH Keywords: generalized solution
zbMATH Keywords: isotropic
zbMATH Keywords: incompressible
zbMATH Keywords: Mutually inverse defining equations
zbMATH Keywords: arbitrary anisotropy
zbMATH Keywords: relations between the stresses and deformations
zbMATH Keywords: quasilinear
zbMATH Keywords: conditions of plasticity
zbMATH Keywords: unloading
zbMATH Keywords: existence
zbMATH Keywords: quasistatic problem
zbMATH Keywords: simple loading
zbMATH Keywords: convergence
zbMATH Keywords: minimum Lagrangian
zbMATH Keywords: maximum of the Castiglianian
MaRDI profile type: Publication
cites work: Q5736758
cites work: On the postulate of plasticity
cites work: Q3282437
cites work: Adequacy of a nonlinear theory of viscoelasticity
cites work: Q4725258
cites work: Q5586501
cites work: Q3940944
cites work: Q3698430
cites work: Q5511735
cites work: Some general theorems of the mechanics of a deformable solid
cites work: Q5843829
description: scientific article; zbMATH DE number 3904072