A continuum-kinematics-inspired peridynamic model of anisotropic continua: Elasticity, damage, and fracture

•A novel linearized elastic anisotropic constitutive model is proposed for continuum-kinematics-inspired peridynamics (CPD).•For the first time, the critical stretch-based failure criteria and critical micropotential energy-based failure criteria are incorporated into CPD.•The numerical convergence of the proposed anisotropic CPD models is studied.•A 2D orthotropic CPD formulation and a 3D transversely isotropic CPD formulations are obtained.•The eight-order double Fourier series is employed to achieve the anisotropy. In this work, linearized elastic isotropic continuum-kinematics-inspired-peridynamics (CPD) is further generalized to study the elastic, damage, and fracture behavior of anisotropic continua, focusing on 3D transversely isotropic and 2D orthotropic body. The anisotropy is generated by changing the material properties, including the micromodulus, critical stretch, and critical micropotential energy of basic finite kinematic elements with their direction in the principal material axes in terms of eight-order double Fourier expansion. It is critically proven that the volumetric micromodulus of finite volume elements in the 3D case is independent of their direction, which is similarly applied to the areal micromodulus in the 2D case. For this reason, the 2D orthotropic CPD formulation characterized by three independent elastic moduli and the 3D transversely isotropic CPD formulation characterized by four independent elastic moduli are distinguished. The accuracy of the computational models applied to elastic analysis is assessed by comparing the predicted displacement fields with the results from finite element analysis. Quantitative simulation of an orthotropic lamina with a central rectangular hole under a tensile load, eccentric three-point bending test for orthotropic lamina, and compact tension test for cortical bone are performed to verify the ability of the proposed model to describe the damage and fracture behavior of anisotropic materials. [Display omitted]