A continuum-molecular model for anisotropic electrically conductive materials. (1st December 2021) - Diana, Vito; Carvelli, Valter
Abstract: An anisotropic model for two-dimensional electrical conduction, elasticity and fracture is proposed in the peridynamic theoretical framework. Material points interact through elastic non-central pair potentials and inelastic pair potential functions of pairwise elastic and inelastic deformation measure, allowing to obtain a bond-based type model for conductive Cauchy orthotropic media without restrictions in the number of independent material constants. The elasticity of pair interactions can be described mechanistically by equivalent normal and shear springs, whose stiffness varies continuously with the spatial orientation of the ligament and, preserving the elastic symmetries of the material, depends on four material parameters defining in-plane orthotropic classical elasticity. The macroscopic anisotropic conductivity is described instead by continuous functions of the micro-conductive properties of the interparticles interactions. Moreover, non-uniform material toughness is modeled adopting an anisotropic energetic failure criterion related to direction-dependent fracture energy functionals. The accuracy of the proposed model has been assessed by several problems including the anisotropic electrical conduction in multi-phases laminae with a central hole and evolving cracks, and the fracture and damage sensing in cortical bone considering different orientation of the material reference system. Graphical abstract: Highlights: A peridynamic model with pair potentials for anisotropic conductive materials is proposed. The model is not affected by restrictions in the number of independent material constants. A purely pairwise description of deformation, strength and constitutive properties is used. Model constitutive micro-parameters are derived using a generalized approach based on energetic equivalence. The model has been validated by several examples including crack propagation and damage sensing in cortical bone.