Presents a robust and unconditionally stable return‐mapping algorithm based on the discrete counterpart of the principle of maximum plastic dissipation. Develops the explicit expression for the consistent elasto‐plastic tangent modulus. All expressions are derived via tensor formulation showing the advantage over the classical matrix notation. The integration algorithm is implemented in the formulation of the four‐node isoparametric assumed‐strain finite‐rotation shell element employing the Mindlin‐Reissner‐type shell model. By applying the layered model, plastic zones can be displayed through the shell thickness. Material non‐linearity described by the von Mises yield criterion and isotropic hardening is combined with a geometrically non‐linear response assuming finite rotations. Numerical examples illustrate the efficiency of the present formulation in conjunction with the standard Newton iteration approach, in which no line search procedures are required. Demonstrates the excellent performance of the algorithm for large time respective load steps.
Engineering Computations – Emerald Publishing
Published: Feb 1, 1997
Keywords: Consistent tangent modulus; Finite element analysis; Elasto‐plastic behaviour; Integration algorithm; Shell structures; Tangent matrices
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