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A physically nonlinear dual mixed finite element formulation. (English) Zbl 0892.73071

Summary: This paper presents the formulation and numerical implementation of a physically nonlinear BDM element for plane stress. The BDM element is based on the dual extended Prange-Hellinger-Reissner functional. We discuss in detail the linearization of the extended functional for solving the nonlinear equations with a Newton procedure. In the case of elasto-plasticity at small strains, the weak form is modified to fulfill the kinematical field equations. The Euler-Lagrange equations satisfied approximately in the discretized form are pointed out. A concept for the storage and update of the internal variables is shown in detail. For two specified model problems, nonlinear elasticity and von Mises plasticity with linear hardening, numerical examples are given.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B10 Linear elasticity with initial stresses
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References:

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