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The variational formulation and solution of problems of finite‐strain elastoplasticity based on the use of a dissipation function
Author(s) -
Eve R. A.,
Reddy B. D.
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620371004
Subject(s) - discretization , finite element method , mathematics , dissipation , boundary value problem , function (biology) , rotational symmetry , constraint (computer aided design) , mathematical optimization , mathematical analysis , geometry , structural engineering , physics , engineering , evolutionary biology , biology , thermodynamics
The solution of initial‐boundary value problems involving finite elastoplastic deformations is discussed. The formulation considered differs from conventional formulations in that the evolution law is expressed in terms of the dissipation function. A generalized midpoint rule is used to obtain an incremental problem, a variational form of which is derived. The finite element method is used for spatial discretization, and an algorithm to solve the resulting discrete problem is developed. This algorithm has the predictor–corrector structure common to most solution procedures for problems in plasticity. Methods for imposing the plastic incompressibility constraint are investigated. Solutions to two axisymmetric examples obtained using the proposed algorithm are presented and compared with those obtained by other authors.