Peridynamics is a non-local continuum mechanics that replaces the differential operator embodied by the stress term divS in Cauchy’s equation of motion by a non-local force functional L to take into account long-range forces. The resulting equation of motion reads

u··=Lu+b(u=displacement,b=body force,=density).

If the characteristic length of the interparticle interaction approaches 0, the operator L admits an expansion in that, for a linear isotropic material, reads

Lu=(+μ)divu+μu+22·4u+43·6u+...,

where and μ are the Lamé moduli of the classical elasticity, and the remaining higher-order corrections contain products of the type Tsu:= s·2su of even-order gradients 2su (i.e., the collections of all partial derivatives of u of order 2s) and constant coefficients s collectively forming a tensor of order 2s. Symmetry arguments show that the terms Tsu have the form

2s–2(s+μs)s–1divu+2s–2μssu,

where s and μs are scalar constants. This article explicitly determines s and μs in terms of the properties of the material (i.e., of the operator L) in all dimensions n (typically, n=1,2 or 3).