Figure 5

Generation of fractures and cracks with linear and nonlinear peridynamics kernels. In red, a typical linear peridynamics kernel \(c(\boldsymbol{\xi },\delta ) \frac{|\boldsymbol{\xi }+\boldsymbol{\eta }|-|\boldsymbol{\xi }|}{|\boldsymbol{\xi }|}\mu (s)\boldsymbol{n} \) is represented. After a bond is broken, the pairwise force remains indefinitely equal to the zero function. In black, a nonlinear peridynamics kernel \(\kappa p \frac{|\boldsymbol{\eta}+\boldsymbol{\xi }|^{p-2} }{|\boldsymbol{\xi}|^{N+\alpha p}}( \boldsymbol{\eta +\xi})\) is represented. Nonlinearity allows the formation of abrupt force and so potential energy peaks such that there is the occurrence of singularity in the displacement function