A new algorithmic approach treating nonlocal effects at finite rate-independent deformation using the Rousselier damage model

The aim of this contribution is a demonstration of a new iterative approach for the algorithmic treatment of a nonlocal damage formulation in the scope of the finite element method. The damage model of Rousselier is used in a finite strain formulation to represent the material behaviour in the specimens of interest.

The new method uses a set of constitutive equations with a Bažant-type nonlocal regularization. An iterative Newton–Raphson scheme is applied, which requires the determination of the global stiffness and residuum of the system by the assembling of local solutions at every integration point many times during an iteration loop.

The numerical treatment is held in a general form and a three-dimensional example is used to illustrate the performance of this method in comparison with the classical local approach. To effectively represent the shear band localization 20-nodes-brick elements with 2×2×2-integration are used.