Multiscale modeling of material failure: From atomic bonds to elasticity with energy limiters

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 comprising many particles, there exist a magnitude of the average bond energy, the failure energy, which limits the energy that can be accumulated in an infinitesimal material volume under strain. The energy limiter controls material softening; the softening indicates failure. Thus, by limiting the stored energy density, we include a description of material failure in the constitutive model. When the failure energy, that is, the energy limiter, is introduced in the constitutive model, it can be calibrated in macroscopic experiments. Traditional material models do not have energy limiters, and they allow for unlimited energy accumulation under the strain increase, which is unphysical because no material can sustain large enough strains without failure. We review the applications of the new approach based on the use of the energy limiters to failure of soft biological tissues and fracture of brittle materials. In addition, we consider new developments concerning the rate-dependent failure in solids and the drop of viscosity in fluids.