Within the context of the consistent tangent update, this paper outlines a stress update algorithm for combined creep and plasticity. The algorithm is implicit, providing unconditional stability, and utilizes local Newton iteration to solve SCALAR forms of the coupled constitutive equations for the creep and plastic strain increments. The tangent for the local iteration is obtained accurately providing quadratic convergence at the Gauss point level. Quadratic convergence of the global iteration procedure is also maintained using an explicitly derived consistent tangent for combined plasticity and creep. Further, combination with an automatic time-stepping scheme provides an efficient, stable, accurate and robust computational algorithm.The algorithm has been implemented in the general purpose FE package LUSAS.'
This paper presents a framework to describe a mixed element method in the context of pressure-dependent elastoplasticity at moderate ÿnite strain. A mixed strain element with one-point quadrature and hourglass control at moderate ÿnite strain is developed on the basis of the Hu-Washizu principle and the co-rotational formulation. The element is formulated with reference to the so-called natural co-ordinate system, 1 which allows to derive the consistent tangent modulus matrix and the single step backward Euler integration scheme at the element quadrature point for pressure-dependent elastoplasticity in an elegant and numerically e cient form.In addition, with the introduction of the natural co-ordinate system, a new deÿnition of internal state variable for the pressure-dependent elasto-plasticity is proposed to allow for the simultaneous description of the two strain hardening=softening paths in tension and compression. Numerical examples are given to demonstrate the performance of the mixed element method presented in this paper. ?
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