Peridynamic modeling of elastic instability and failure in lattice beam structures

Abstract

A Simo-Reissner peridynamic (PD) beam theory is presented to model elastic instability and subsequent failure in a lattice beam structure. Governing equations of the beam are derived from the three-dimensional PD equations of motion invoking Simo’s displacement approximation. Principle of virtual work is employed to determine the deformation states. The PD force and moment resultants are related to their classical counterparts using constitutive correspondence approach. The solution method employs a geometrically exact rotation update based on exponential map. A new failure criterion is introduced using critical stretch and critical relative rotation. The Newton–Raphson and two variants of arc length method are employed to solve the governing equations under quasi-static loading conditions. Numerical simulations concern the snap-back instability of a right-angle frame and its subsequent failure in the post-buckling stage, finite deformation of an octet lattice cell and instability of a portal frame. These simulations are verified against the finite element predictions to establish the efficacy of the present approach.