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.

在近场动力学理论框架中提出了二维导电、弹性和断裂的各向异性模型。材料点通过成对弹性和非弹性变形测量的弹性非中心对势和非弹性对势函数相互作用，允许获得基于键的导电柯西正交各向异性介质模型，而不受独立材料常数数量的限制。对相互作用的弹性可以通过等效的法向和剪切弹簧机械地描述，其刚度随韧带的空间方向连续变化，并且保持材料的弹性对称性，取决于定义平面内正交各向异性经典弹性的四个材料参数。宏观各向异性电导率由粒子间相互作用的微导电特性的连续函数来描述。此外，采用与方向相关的断裂能量函数相关的各向异性能量失效准则对非均匀材料韧性进行建模。所提出模型的准确性已通过几个问题进行评估，包括具有中心孔和不断发展的裂缝的多相薄层中的各向异性导电，以及考虑材料参考系统不同方向的皮质骨中的断裂和损伤传感。采用与方向相关的断裂能量函数相关的各向异性能量失效准则对非均匀材料韧性进行建模。所提出模型的准确性已通过几个问题进行评估，包括具有中心孔和不断发展的裂缝的多相薄层中的各向异性导电，以及考虑材料参考系统不同方向的皮质骨中的断裂和损伤传感。采用与方向相关的断裂能量函数相关的各向异性能量失效准则对非均匀材料韧性进行建模。所提出模型的准确性已通过几个问题进行评估，包括具有中心孔和不断发展的裂缝的多相薄层中的各向异性导电，以及考虑材料参考系统不同方向的皮质骨中的断裂和损伤传感。