An equivalent damage force approach to modelling of strain softening materials

The work presented in this paper is related to the problem of damage/deformation localisation typical for the finite element analysis of softening materials based on local constitutive models and continuum damage mechanics. This problem is characterised with change of the type of partial differential equations, due to material softening, leading to ill-posed boundary value problem and mesh dependency. In the equivalent damage force (EDF) approach damage effects are represented as a force on the right-hand side of the balance of linear momentum equation [23]. The main advantages of this approach are that the problem remains well posed, i.e. partial differential equations remain unchanged when the material starts softening. Numerical stability is maintained, and mesh dependency significantly reduced. The EDF model implemented in the explicit transient non-linear finite element code DYNA3D [12] is undergoing further validation in modelling several impact experiments presented here. The numerical results have nonlocal character with a finite size damaged zone. The size of the zone is controlled with the damage characteristic length, which is an input parameter independent of the discretisation density. This is work in progress and more comprehensive analysis of the validation cases will be completed in near future.