A full orthotropic bond-based peridynamic formulation for linearly elastic solids

An original full orthotropic model for in-plane linear elasticity is proposed in the micropolar peridynamic analysis framework. The analytical formulation is derived from the definition of a specific microe-lastic energy function for micropolar nonlocal lattices which allows to obtain, for the first time, an orthotropic bond-based model characterized by four independent elastic moduli. An important feature of the model is that the bond properties, i.e. the elastic constants, are continuous functions of the bond orientation in the principal material axes. The introduction of the bond shear stiffness and the definition of a bond shear deformation measure which accounts for particle’s rotation, on one hand eliminates the restriction of two independent constants that affects other bond-based orthotropic peridynamic formulations, and on the other makes the model suitable in predicting the mechanical behavior of a wide variety of Cauchy orthotropic materials undergoing homogeneous and non-homogeneous deformations. The accuracy of the proposed model in linear elasticity has been verified through simulating uniaxial extension test of a composite lamina with a central circular hole and natural frequency analyses considering different orientations of the principal material reference system.