Numerically efficient and robust interior-point algorithm for finite strain rate-independent crystal plasticity

Abstract

The challenges of classic rate-independent crystal plasticity models regarding the determination of active slip systems and computation of solutions due to linear dependent slip systems are still a field of active research. In that regard, interior-point methods are promising approaches because a logarithmic barrier term naturally avoids the combinatorial active set search, and these methods are applicable even when the gradient of inequality constraints is linearly dependent. In this paper, a new interior-point algorithm suitable for rate-independent crystal plasticity at finite strains is developed. For that purpose, the postulate of maximum dissipation is recast as a constrained optimization problem whose optimality conditions are derived by utilizing interior-point approaches. This optimization problem is discretized in time by means of an exponential time integration of the flow rule, and the time-discrete equations are solved by a Newton scheme. The focus of this paper is the efficiency and robustness of the implementation of this approach. In particular, the effect of different line search procedures, favorable residual forms, preconditioning methods, barrier parameter updates and the consistent algorithmic tangent modulus are discussed and further elaborated. In addition, aspects regarding uniqueness and well-posedness of the algorithm are analyzed in a geometrically linearized setting. Efficiency and robustness of the developed algorithm are shown by numerical examples of an FCC crystal including finite element simulations without stabilizing hardening or rate-dependent effects. Furthermore, the results are compared to the well-established augmented Lagrangian formulation.