A micropolar peridynamic theory in linear elasticity

On conservation integrals in micropolar elasticity

Two conservation laws of nonlinear micropolar elasticity (Jk = 0 and Lk = 0) are derived within the framework of Noether’s theorem on invariant variational principles, thereby extending the earlier authors’ results from the couple stress elasticity. Two non-conserved M -type integrals of linear micropolar elasticity are then derived and their values discussed. The comparison with related work i...

Analysis of the volume-constrained peridynamic Navier equation of linear elasticity

Well-posedness results for the state-based peridynamic nonlocal continuum model of solid mechanics are established with the help of a nonlocal vector calculus. The peridynamic strain energy density for an elastic constitutively linear anisotropic heterogenous solid is expressed in terms of the field operators of that calculus, after which a variational principle for the equilibrium state is def...

The Cauchy Relations in Linear Elasticity Theory

c = c = c . (2) 1 We use the notation of Schouten [9]. Symmetrization over two indices is denoted by parentheses, A(ij) := (Aij + Aji)/2!, antisymmetrization by brackets, B[ij] := (Bij − Bji)/2!. The analogous is valid for more indices, as, e.g., in (13): c i[jk]l = (c − c)/2!. If one or more indices are exempt from (anti)symmetrization, they are enclosed by vertical bars, as, e.g., in (12), c ...

Linearized Theory of Peridynamic States

A state-based peridynamic material model describes internal forces acting on a point in terms of the collective deformation of all the material within a neighborhood of the point. In this paper, the response of a state-based peridynamic material is investigated for a small deformation superposed on a large deformation. The appropriate notion of a small deformation restricts the relative displac...

Peridynamic Theory of Solid Mechanics