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Constitutive Equations, Stability and Bifurcation of Elastoplastic Structures
Author(s) -
Germain P.
Publication year - 1987
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19870670101
Subject(s) - bifurcation , simple (philosophy) , constitutive equation , stability (learning theory) , brittleness , mathematics , matrix (chemical analysis) , mathematical analysis , materials science , structural engineering , computer science , physics , finite element method , nonlinear system , engineering , composite material , quantum mechanics , machine learning , philosophy , epistemology
This review paper gives a uniform presentation of some recent results on the. stability of elastic plastic structures. It starts by recalling a general method to write constitutive equations in finite deformations with the introduction of an internat variable– generally a matrix – which describes the modification of material properties. First, this formulation is shown to be quite convenient to study cracks and their evolution under a varying load for brittle or ductile materials. Then, a quite general method for the treatment of the stability and bifurcations of equilibrium of an elastic plastic structure is presented and applied to some simple examples. The results already published in the literature are recovered.