Geometrically non‐linear enhanced strain mixed methods and the method of incompatible modes

International Journal for Numerical Methods in Engineering - Tập 33 Số 7 - Trang 1413-1449 - 1992
J. C. Simo1,2, F. Armero2,3
1Associate Professor of Applied Mechanics.
2Division of Applied Mechanics, Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-4040, U.S.A.
3Graduate Research Assistant,

Tóm tắt

AbstractA class of ‘assumed strain’ mixed finite element methods for fully non‐linear problems in solid mechanics is presented which, when restricted to geometrically linear problems, encompasses the classical method of incompatible modes as a particular case. The method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part, formulated in the context of a three‐field variational formulation. The resulting class of mixed methods provides a possible extension to the non‐linear regime of well‐known incompatible mode formulations. In addition, this class of methods includes non‐linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements. The good performance of the proposed methodology is illustrated in a number of simulations including 2‐D, 3‐D and axisymmetric finite deformation problems in elasticity and elastoplasticity. Remarkably, these methods appear to be specially well suited for problems involving localization of the deformation, as illustrated in several numerical examples.

Từ khóa


Tài liệu tham khảo

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Thông tin
Thông tin xuất bản

International Journal for Numerical Methods in Engineering

Tập 33 Số 7

1413-1449

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