Large strain elastic-plastic theory and nonlinear finite element analysis based on metric transformation tensors |
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Authors: | M Brünig |
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Affiliation: | Lehrstuhl für Baumechanik – Statik, Universit?t Dortmund, D-44221 Dortmund, Germany, DE
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Abstract: | The present paper is concerned with an efficient framework for a nonlinear finite element procedure for the rate-independent
finite strain analysis of solids undergoing large elastic-plastic deformations. The formulation relies on the introduction
of a mixed-variant metric transformation tensor which will be multiplicatively decomposed into a plastic and an elastic part.
This leads to the definition of an appropriate logarithmic strain measure whose rate is shown to be additively decomposed
into elastic and plastic strain rate tensors. The mixed-variant logarithmic elastic strain tensor provides a basis for the
definition of a local isotropic hyperelastic stress response in the elastic-plastic solid. Additionally, the plastic material
behavior is assumed to be governed by a generalized J
2 yield criterion and rate-independent isochoric plastic strain rates are computed using an associated flow rule. On the numerical
side, the computation of the logarithmic strain tensors is based on 1st and higher order Padé approximations. Estimates of
the stress and strain histories are obtained via a highly stable and accurate explicit scalar integration procedure which
employs a plastic predictor followed by an elastic corrector step. The development of a consistent elastic-plastic tangent
operator as well as its implementation into a nonlinear finite element program will also be discussed. Finally, the numerical
solution of finite strain elastic-plastic problems is presented to demonstrate the efficiency of the algorithm.
Received: 17 May 1998 |
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