A gradient-enhanced damage implementation for the simulation of damage in metal forming processes

Richard Ostwald, Institute of Mechanics, TU Dortmund, Dortmund, Germany
Leon Sprave, Institute of Mechanics / TU Dortmund, Dortmund, Germany
Robin Schulte, Institute of Mechanics / TU Dortmund, Dortmund, Germany
Andreas Menzel, Institute of Mechanics / TU Dortmund, Dortmund, Germany

We present a gradient-enhanced damage formulation that allows for the mesh-objective simulation of three-dimensional bodies undergoing regularised damage with consideration of finite strain deformations. The gradient-enhanced damage formulation used in our work was proposed by Waffenschmidt et al. in 2014 and represents a finite strain extension of a concept introduced by Dimitrijevic and Hackl in 2008. The local free energy function associated with the material undergoing regularised damage is extended by two additional additive contributions that enable the regularisation of the damage formulation. In particular, one non-local free energy contribution essentially contains the gradient of the introduced non-local damage field variable, whereas another penalty-type free energy term is introduced in order to couple the locally evolving internal damage variable to the global damage field variable.

The presented implementation solves the evolution of the local damage variable using standard implicit time-integration schemes, whereas the additional balance equation associated with the global damage field variable is solved using the solution capabilities of thermo-mechanically coupled finite element formulations. This is possible since both the steady state heat equation and the damage balance equation are second order partial differential equations of elliptic type and thus can be represented as formally equivalent relations.

The framework allows for the consideration of different local constitutive models, such as, e.g., plasticity formulations, which then can be conveniently coupled with damage evolution and solved in a monolithic manner within existing finite element codes providing interfaces for thermo-mechanically coupled user subroutines. In order to highlight the applicability of the overall framework to the simulation of damage in metal forming processes, we show the solutions of different three-dimensional boundary value problems involving large deformations and advanced element features such as contact in combination with regularised damage.

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