Atomistic-to-continuum coupling

Atomistic-to-continuum (a/c) coupling methods are a class of computational multiscale schemes that combine the accuracy of atomistic models with the efficiency of continuum elasticity. They are increasingly being utilized in materials science to study the fundamental mechanisms of material failure such as crack propagation and plasticity, which are governed by the interaction between crystal defects and long-range elastic fields. In the construction of a/c coupling methods, various approximation errors are committed. A rigorous numerical analysis approach that classifies and quantifies these errors can give confidence in the simulation results, as well as enable optimization of the numerical methods for accuracy and computational cost. In this article, we present such a numerical analysis framework, which is inspired by recent research activity

Investigation of the effect of shape of inclusions on homogenized properties by using peridynamics

Fiber-reinforced composite materials are widely used in many different industries due to their superior properties with respect to traditional metals including their light weight, corrosion resistance, high strength, impact resistance, etc. Fiber-reinforced composite materials are composed of a strong fiber material, which mainly carries the applied load, and soft matrix material, which transfers the load to the fiber material and keep the fibers together. Macroscopic analysis of fiber-reinforced composite materials is done by utilising the homogenised material properties which mainly depends on individual material properties of fiber and matrix. In this study, in addition to the effect of individual material properties of constituents, the effect of the shape of fibers (inclusions) on homogenised properties is investigated by using a new methodology called peridynamics

Bond-based peridynamics: A tale of two Poisson's ratios

This paper explores the restrictions imposed by bond-based peridynamics, particularly with respect to plane strain and plane stress models. We begin with a review of the derivations in [2] wherein for isotropic materials a Poisson's ratio restriction of 1/4 for plane strain and 1/3 for plane stress is deduced. Next, we show Cauchy's relations are an intrinsic limitation of bond-based peridynamics and specialize this result to plane strain and plane stress models, generalizing the results of [2] and demonstrating the Poisson's ratio restrictions in [2] are simply a consequence of Cauchy's relations. We conclude with a discussion of the validity of peridynamic plane strain and plane stress models formulated from two-dimensional bond-based peridynamic models.</p