Elasticity with energy limiters for modeling dynamic failure propagation

Abstract

Separation of two particles is characterized by a magnitude of the bond energy, which limits the accumulated energy of the particle interaction. In the case of a solid composed of many particles a magnitude of the average bond energy – the failure energy – exists, which limits the energy that can be accumulated in an infinitesimal material volume under strain. The energy limiter controls material softening, which indicates failure. Thus, by limiting the stored energy density it is possible to include a description of material failure in the constitutive model. When the failure energy, i.e. the energy limiter, is introduced in the constitutive model it can be calibrated in macroscopic experiments. Traditional elasticity models do not have energy limiters and they allow for the unlimited energy accumulation under the strain increase, which is physically meaningless because no material can sustain large enough strains without failure. We use elasticity with energy limiters for modeling dynamic failure propagation in brittle solids. Two models of isotropic Hookean solids with energy limiters are introduced and examined in simulations of the penetration of a projectile into a brittle plate in the present work. The first model uses the energy limiter with the overall energy term while the second model has separate energy limiters for the volumetric and deviatoric components. The results of the penetration simulation obtained by using both models are similar qualitatively. It is remarkable that the penetration depth is mesh-independent for fine meshes even without the special regularization procedures. This is the first work where the methods of elasticity with energy limiters are used in dynamic analysis of brittle failure.