New models of viscoelastic solids at small and finite deformations are proposed that
describe material failure by enforcing the energy limiter — the average bond energy.
Basically, the bond energy defines the energy that is necessary to separate
two attracting particles. In the case of a solid composed of many particles
there exists a magnitude of the average bond energy that is necessary to
separate particles in a small material volume. The average bond energy can be
calculated if a statistical distribution of the bond density is known for a
particular material. Alternatively, the average bond energy can be determined in
macroscopic experiments if the energy limiter is introduced in a material
constitutive model. Traditional viscoelastic models of materials do not have energy
limiters and, consequently, they allow for unlimited energy accumulation
under the strain increase. The latter is unphysical, of course, because no
material can sustain large enough deformations without failure. The average
bond energy is the energy limiter that controls material softening, which
indicates failure. Thus, by limiting the stored energy we include a description of
material failure in the constitutive model. Viscoelasticity including energy
limiters can be called softening hyperviscoelasticity. We present two softening
hyperviscoelasticity models for small and finite deformations. In all cases the elastic
and viscoelastic responses are described by potentials with limiters, which
control material softening. The models are studied in the case of simple shear
and uniaxial tension. The results of the calculations show that softening
hyperviscoelasticity can be used for analysis of rate-dependent failure of
materials.
