Anisotropic peridynamics for homogenized microstructured materials

An anisotropic continuum-molecular model based on pair potentials for describing the linear static and dynamic behavior of periodic heterogeneous Cauchy materials is derived in the framework of peridynamic theory. Non-central pairwise actions are assumed as work-conjugates to specific pairwise deformation variables. A pairwise constitutive law, depending trigonometrically on the material fiber direction and preserving the elastic symmetries of the material, is properly defined. Based on this theoretical ground, a bond-based type continuum model with oriented material points, governed by six independent material micro-moduli, is obtained. Considering microstructured materials featuring periodic rigid massive blocks connected by soft elastic interfaces, the elastic potential functions of the continuum-molecular model are consistently identified in terms of geometrical and constitutive parameters of the microstructure. The identification is based on the formal analogy with the overall constitutive tensors of a homogeneous continuum obtained through continualization schemes and equivalent to the microstructured material. Consequently, the macroscopic elastic properties of the continuum-molecular model are described in terms of pairwise material properties, but its micro-moduli are also explicitly related to the specific properties of the linear elastic interfaces of the microstructured material. The accuracy of the proposed model in the static and dynamic response is successfully verified by comparison with high-fidelity finite element models of an auxetic tetrachiral block lattice considering different periodic cell orientations and elastic interface properties, as well as by comparison with analytical solutions for fully anisotropic elasticity.