Semi-implicit finite strain constitutive integration and mixed strain/stress control based on intermediate configurations

摘要

A new semi-implicit stress integration algorithm for finite strain plasticity (compatible with hyperelas-ticity) is introduced. Its most distinctive feature is the use of different parameterizations of equilibriumand reference configurations. Rotation terms (nonlinear trigonometric functions) are integrated explicitlyand correspond to a change in the reference configuration. In contrast, relative Green–Lagrange strains(which are quadratic in terms of displacements) represent the equilibrium configuration implicitly. Inaddition, the adequacy of several objective stress rates in the semi-implicit context is studied. We para-metrize both reference and equilibrium configurations, in contrast with the so-called objective stressintegration algorithms which use coinciding configurations. A single constitutive framework providesquantities needed by common discretization schemes. This is computationally convenient and robust,as all elements only need to provide pre-established quantities irrespectively of the constitutive model.In this work, mixed strain/stress control is used, as well as our smoothing algorithm for the complemen-tarity condition. Exceptional time-step robustness is achieved in elasto-plastic problems: often fewerthan one-tenth of the typical number of time increments can be used with a quantifiable effect inaccuracy. The proposed algorithm is general: all hyperelastic models and all classical elasto-plasticmodels can be employed. Plane-stress, Shell and 3D examples are used to illustrate the new algorithm.Both isotropic and anisotropic behavior is presented in elasto-plastic and hyperelastic examples.