A cohesive finite element for quasi-continua

Abstract

In this paper, a cohesive finite element method (FEM) is proposed for a quasi-continuum (QC), i.e. a contin- uum model that utilizes the information of underlying atomis- tic microstructures. Most cohesive laws used in conventional cohesive FEMs are based on either empirical or idealized constitutive models that do not accurately reflect the actual lattice structures. The cohesive quasi-continuum finite element method, or cohesive QC-FEM in short, is a step forward in the sense that: (1) the cohesive relation between interface traction and displacement opening is now obtained based on atomistic potentials along the interface, rather than empirical assumptions; (2) it allows the local QC method to simulate certain inhomogeneous deformation patterns. To this end, we introduce an interface or discontinuous Cauchy- Born rule so the interfacial cohesive laws are consistent with the surface separation kinematics as well as the atomistically enriched hyperelasticity of the solid. Therefore, one can sim- ulate inhomogeneous or discontinuous displacement fields by using a simple local QC model. A numerical example of a screw dislocation propagation has been carried out to dem- onstrate the validity, efficiency, and versatility of the method.