The effect of long-range forces on the dynamics of a bar

Crack nucleation in a peridynamic solid

“…A result closely related to (18) was also obtained in Weckner and Abeyaratne (2005) in a more restrictive setting. In this reference, it was shown that in a homogeneous, bond-based, linear microelastic bar, jumps in an initial displacement field grow exponentially over time if…”

“…To see this, consider the form of (19) for a one-dimensional homogeneous bar: On the other hand, the tangent modulus (Weckner and Abeyaratne 2005) is given by…”

The peridynamic model in non‐local elasticity theory

“…If the stiffness distribution is of convolution type, one may solve the initial-value problem for the peridynamic equation of motion exactly by means of Fourier transforms (see [1,7]). It then can be shown that different stiffness distributions correlate with different nonlinear dispersion relations.…”

“…The interaction is often restricted to the peridynamic horizon B δ (x) := {x ∈ V : x − x < δ} for prescribed δ > 0, where · denotes the Euclidean norm, such that f = 0 if x / ∈ B δ (x). For the study of the dynamics of an infinite bar in [1,6,7,8], however, no horizon is assumed and the interaction takes place between all material particles but decreases with increasing distance. Note that the peridynamic model implies a Poisson ratio ν = 1/4.…”

Impact Mechanics and High-Energy Absorbing Materials: Review

“…An in-depth study of the effect of van der Waals forces on the failure of nanofibers networks is presented in Bobaru (2007). Other numerical and computational aspects of peridynamics are given in Weckner and Abeyaratne (2005) and Weckner and Emmrich (2005). Adaptive refinement strategies helpful in large-scale simulations of impact and damage in composites are currently being developed (Bobaru et al 2008).…”