Distal and non-symmetrical crack nucleation in delamination of plates via dimensionally-reduced peridynamics

R Cavuoto, A Cutolo, K Dayal, L Deseri *, M Fraldi*, Journal of the Mechanics and Physics of Solids 172 (2023) 105189 https://doi.org/10.1016/j.jmps.2022.105189

Abstract

Exploiting the framework of peridynamics, a dimensionally-reduced formulation for plates is developed that allows for the through-thickness nucleation and growth of fracture surfaces,

enabling the treatment of delamination in a lower-dimensional model. Delamination fracture nucleation and propagation are treated by choosing the kinematics to be composed of an

absolutely continuous part and a zone where jumps in the displacements are allowed. This assumption allows the explicit derivation of the dimensionally-reduced elastic energy, which

shows a hierarchy of terms characterizing the stored energy in the plane element. An interpretation of the various terms of the reduced energy is shown by means of the simplest

paradigm of bond-based peridynamics. A striking feature of the reduced energy is that, despite the small-displacement assumption, there is a coupling between the membrane and bending

terms. Semi-analytical solutions for simplified settings are obtained through a minimization procedure, and a range of nonstandard behaviors such as distal crack nucleation and curved

crack path are captured by the model. Finally, the convergence of the proposed peridynamic reduced model to a local elastic theory for vanishing nonlocal lengthscale is determined, giving

a local cohesive model for fracture.