Hyperelasticity with softening for modeling materials failure

Traditional hyperelastic models of materials allow for the unlimited increase of the strain energy under the strain increase. It is clear, however, that no real material can accumulate the energy unlimitedly sustaining large enough strains. In the present work, we introduce a limiter for the strain energy—the critical failure energy, which can be interpreted as a failure constant characterizing the material ‘toughness’. We show that the critical failure energy controls materials softening. The softening can enrich any existing model of the intact material with a failure description. We demonstrate the efficiency of the softening hyperelasticity approach on a variety of analytically tractable boundary value problems with a variety of material models. The proposed softening hyperelasticity approach is a possible alternative to the simplistic pointwise failure criteria of strength of materials on the one hand and the sophisticated approach of damage mechanics involving internal variables on the other hand.