Efficient and modular algorithms in modeling finite inelastic deformations: Objective integration, parameter identification and sub-stepping techniques

This paper presents a general algorithmic formulation for constitutive equations describing inelastic material deformation. The algorithmic representation focuses on the generality and modularity which is a key aspect within the development phase of constitutive equations. It is shown explicitly how to solve the incremental constitutive equations by use of objective algorithms and an implicit integration scheme applying numerical as well as analytical derivatives. Although it is shown that using numerical gradients is significantly slower, their application is easier especially in the development phase. It is also demonstrated that having the constitutive equations modeled in the general context introduced, the issue of parameter identification can be tackled by the same implementation using a driver algorithm. Besides parameter identification, the general structure is also applied to two different FE simulations: First, the objectivity of different integration methods will be presented considering a simple shear loading superposed by a rigid rotation using a strain-rate independent material model as example. In the second example it is shown for a strain-rate-dependent material model how the simulation of the wire drawing process can be accelerated crucially by using sub-stepping techniques.