The inverse-deformation approach to fracture

We propose a one-dimensional, nonconvex elastic constitutive model with higher gradients that can predict spontaneous fracture at critical load via bifurcation analysis. It overcomes the problem of discontinuous deformations without additional field variables, such as damage or phase-field and priori specified surface energy. Our main tool is inverse deformation, which be extended to piecewise smooth mapping even when original deformation has discontinuities describing cracks opening. exploit this inverse-deformation formulation finite elasticity due Shield Carlson, including in The amenable rigorous global analysis presence unilateral constraint. Fracture under hard loading occurs on bifurcating solution branch applied stretch level, sudden drop zero stress. Fractured solutions are found have sharply defined energy arising from gradient effects.