A return mapping algorithm for plane stress elastoplasticity

International Journal for Numerical Methods in Engineering - Tập 22 Số 3 - Trang 649-670 - 1986
J.C. Simo1, Robert L. Taylor2
1Applied Mechanics Division, Stanford University, Stanford, California, U.S.A.
2Structural Engineering and Structural Mechanics Division, University of California, Berkeley, California, U.S.A.

Tóm tắt

Abstract

An unconditionally stable algorithm for plane stress elastoplasticity is developed, based upon the notion of elastic predictor‐return mapping (plastic corrector). Enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation. Consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm. Use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of Newton methods. The accuracy of the algorithm is assessed by means of iso‐error maps. The excellent performance of the algorithm for large time steps is illustrated in numerical experiments.

Từ khóa


Tài liệu tham khảo

Wilkins M. L., 1964, Methods of Computational Physics 3

Krieg R. D., 1976, Constitutive Equations in Viscoplasticity: Computational and Engineering Aspects, 125

10.1115/1.3454568

10.1115/1.3454627

P. J.YoderandR. L.Whirley ‘OTHERCIT’ preprint (1983).

Sandler I. S., 1979, An algorithm and a modular subroutine for the cap mode, J. Geotech. Eng. Div., 3, 173

M.Ortiz ‘Topics in constitutive theory for inelastic solids’ Ph.D. dissert. Dept. of Civil Engineering Univ. of California Berkeley (1981).

10.1002/nme.1620200913

Simo J. C., A unified approach to finite deformation elastoplasticity based on the use of hyperelastic constitutive equations, Comp. Meth. Appl. Mech. Eng., 49, 221, 10.1016/0045-7825(85)90061-1

10.1016/0167-6636(85)90039-0

10.1016/0045-7825(79)90025-2

10.1002/nme.1620210902

J. O.Hallquist ‘NIKE2D: a vectorized implicit finite deformation finite element code for analyzing the static and dynamic response of 2‐D solids’ Rep. UCID‐19677 Univ. of California Lawrence Livermore National Laboratory (1984).

10.1108/eb023559

Zienkiewicz O. C., 1977, The Finite Element Method

J. C.Nagtegaal Private communication(1985).

Hallquist J. O., 1985, Implemention of a modified Hughes–Liu shell into a fully vectorized explicit finite element code

Rice, 1973, Proc. Symp. Numer. Comp. Meths. Struct. Mech

10.1016/0045-7949(78)90019-6

10.1016/0045-7825(85)90070-2

Hinton E., 1980, Finite Elements in Plasticity: Theory and Practice

Hughes T. J. R., 1983, Computational Methods for Transient Analysis

10.1002/cpa.3160310205

10.1061/(ASCE)0733-9399(1983)109:1(231)

Ortiz M., 1986, An analysis of a new class of algorithms for elastoplastic constitutive relations, Int. j. numer. methods eng., 23, 353, 10.1002/nme.1620230303

Dennis J. E., 1983, Numerical Methods for Unconstrained Optimization

Luenberger D. G., 1984, Linear and Nonlinear Programming

10.1002/nme.1620141104

Hughes T. J. R., 1983, Workshop on Theoretical Foundations for Large Scale Computations of Nonlinear Material Behaviour

10.1016/0045-7825(82)90120-7

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Thông tin xuất bản

International Journal for Numerical Methods in Engineering

Tập 22 Số 3

649-670

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