Crack nucleation in a peridynamic solid

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Peridynamic model for dynamic fracture in unidirectional fiber-reinforced composites (2012, background): “[25]) a material instability condition, that corresponds to the ability of a discontinuous perturbation in the deformation to grow in amplitude over time, only involves the incremental material properties at each point.”
An extended constitutive correspondence formulation of peridynamics based on nonlinear bond-strain measures (2014, background): “A key feature of peridynamics is the ability to naturally describe discontinuities such as cracks [2, 3, 4, 5, 6, 7] and phase transition boundaries [8] within a single continuum framework.”
Linearized Theory of Peridynamic States (2010, background): “The linearized equations also permit softening materials to be studied, including the associated material stability issues [ 2 ].”
Peridynamic Theory of Solid Mechanics (2010, background): “For example, it is demonstrated in [69] that peridynamics reveals a condition for a particular type of material instability, interpreted as the nucleation of a crack, that is not necessarily well described by mathematical conditions such as loss of ellipticity in the classical theory.”