Peridynamics for Isotropic Materials

Abstract

The auxiliary parameters, C in Eq. 2.43 and A and B in Eq. 2.48, can be determined by using the relationship between the force density vector and the strain energy density, ${W_{(k) }}$, at material point $k$ given by Eq. 2.49 in the form,

$$ {{\mathbf{t}}_{(k)(j) }}\left( {{{\mathbf{u}}_{(j) }}-{{\mathbf{u}}_{(k) }},{{\mathbf{x}}_{(j) }}-{{\mathbf{x}}_{(k) }},t} \right)=\frac{1}{{{V_{(j) }}}}\frac{{\partial {W_{(k) }}}}{{\partial \left( {\left| {{{\mathbf{y}}_{(j) }}-{{\mathbf{y}}_{(k) }}} \right|} \right)}}\frac{{{{\mathbf{y}}_{(j) }}-{{\mathbf{y}}_{(k) }}}}{{\left| {{{\mathbf{y}}_{(j) }}-{{\mathbf{y}}_{(k) }}} \right|}}, $$