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

On the role of the influence function in the peridynamic theory

The influence function in the peridynamic theory is used to weight the contribution of all the bonds participating in the computation of volume-dependent properties. In this work, we use influence functions to establish relationships between bond-based and state-based peridynamic models. We also demonstrate how influence functions can be used to modulate nonlocal effects within a peridynamic model independently of the peridynamic horizon. We numerically explore the effects of influence functions by studying wave propagation in simple one-dimensional models and brittle fracture in three-dimensional models. Key Words: Peridynamics, influence function, nonlocal