Finite deformation micropolar peridynamic theory: Variational consistency of wryness measure

Abstract

This paper concerns developments in both classical and peridynamic (PD) finite deformation micropolar elasticity theory. The first part presents an alternative proof of a theorem that demonstrates variational consistency of the wryness measure in classical finite deformation micropolar elasticity which is one of the novel contributions of this work. The linearized version of the proposed wryness measure is compared with the wryness measure of small deformation micropolar elasticity. In the second part of this work, a finite deformation micropolar PD theory is presented. After proposing an additional integro-differential equation along with the standard PD equation of motion, the global balance of angular momentum is proved to be satisfied. The balance of virtual work is derived for the micropolar PD theory. Next, constitutive correspondence approach is used to relate PD force and moment states with their classical counterparts. The nonlocal versions of the strain and the proposed wryness measure are used in the constitutive correspondence. The constitutive equations of the classical micropolar theory are presented and how they can be incorporated in PD framework is discussed. We introduce a new bond breaking criterion for PD micropolar materials based on critical stretch and critical relative rotation. Quasi-static numerical simulations on deformations of plate with a hole and fracture of a double notched sheet are presented. Dynamic simulations concern wave propagation through a solid specimen and plate with a hole. Validation of the simulation results with the finite element solutions, boundary element solutions, and experimental observations demonstrate the potential of our approach.