Coupling Peridynamic Continuum Mechanics with an Analytical Solution

an extended continuum mechanics formulation enhanced by direct coupling with molecular dynamics

based on the notion of micro-structure in linear elasticity presented by mindlin, a newextended continuum mechanics (ecm) formulation is derived which can be utilized to model thematerial behavior at atomic scale. an attempt has been made to present a formulation capable ofproducing the molecular dynamics (md) simulation results with less computational effort. to thisend, some new kinematical v...

Peridynamic Theory of Solid Mechanics

Mathematical Analysis for the Peridynamic Nonlocal Continuum

We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The co...

Kinetics of phase transformations in the peridynamic formulation of continuum mechanics

We study the kinetics of phase transformations in solids using the peridynamic formulation of continuum mechanics. The peridynamic theory is a nonlocal formulation that does not involve spatial derivatives, and is a powerful tool to study defects such as cracks and interfaces. We apply the peridynamic formulation to the motion of phase boundaries in one dimension. We show that unlike the classi...

Wear modelling: analytical, computational and mapping: a continuum mechanics approach

As a result of its widespread and pervasive economic consequences wear, the almost inevitable companion of friction, has been the subject of much scientific and empirical investigation; the literature is rich with ‘wear equations’ so that, on occasion, the practitioner can seem to have too much information rather than too little. Some guidance and reconciliation between analytical and computati...