Bond-Based Peridynamics with Stretch and Rotation Kinematics for Modeling Composite Laminates

Abstract

This study presents the bond-based (BB) peridynamics (PD) with stretch and rotation kinematics for modeling the linear elastic deformation of a composite laminate. The laminate experiences only in-plane and transverse shear deformations and disregards the transverse normal deformation. The PD equilibrium equation for a laminate is derived under the assumption of small deformation and is solved by employing implicit techniques. The in-plane PD forces are expressed by considering the PD bond interactions among the points. The forces arising from the interaction of adjacent layers are expressed by considering a pointwise approach that utilizes PD differential operator (PDDO) in conjunction with the shear-lag theory. The micro-moduli associated with stretch and rotation are directly related to the constitutive relations between stress and strain components in continuum mechanics. It is restricted to only one constraint on the material constants leading to a fixed value of in-plane shear modulus. The capability of this approach is demonstrated by considering progressive failure in a quasi-isotropic laminate with a pre-existing crack. It employs critical stretch, the critical skew (relative rotation) angle and critical delamination angle in the bond breakage criteria.