Strain energy density failure criterion

The initiation of macroscopic material failure is associated with the collective disruption of atomic bonds, which is driven by the potential energy stored in the atomic bonds. This potential energy, which is represented by specified elastic strain energy density in a mechanical system, is releasable. Thus, a universal macroscopic material failure criterion in a mechanical system can be defined by a specified elastic strain energy density together with its critical value that is determined by preceding irreversible deformation process and current environmental state. A dissipative function based on continuum mechanics and irreversible thermodynamics is proposed to represent the irreversible deformation process. The increase of this dissipative function due to material inelastic deformation, damage and other possible intrinsic dissipative mechanisms in a mechanical system leads to the reduction of material strength. When the material failure is dominated by the dissipation, a dissipative energy density failure criterion can be defined by using the dissipative function. On the other hand when the intrinsic dissipation is negligible during the deformation process before failure, the specified elastic strain energy density and its critical value, which is determined by the initial material bond strength, can be used to define material brittle failure. It also shows the possibility to set up a relationship between fracture mechanics and failure criterion. The proposed method to represent failure criteria is based on continuum mechanics and irreversible thermodynamics and retrieves previously successful failure criteria.