Related papers: Deriving peridynamic influence functions for one-d…
The fracture simulation of random particle reinforced composite structures remains a challenge. Current techniques either assumed a homogeneous model, ignoring the microstructure characteristics of composite structures, or considered a…
Microstructural models of soft tissue deformation are important in applications including artificial tissue design and surgical planning. The basis of these models, and their advantage over their phenomenological counterparts, is that they…
The accurate mathematical modeling of droplet impact dynamics on micro-structured surfaces is fundamental to understanding and predicting complex fluid behaviors relevant to a wide range of engineering and scientific applications. In…
Functionally graded materials (FGMs) are two-phase composites with continuously changing microstructure adapted to performance requirements. Traditionally, the overall behavior of FGMs has been determined using local averaging techniques or…
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely…
Equations for dislocation evolution bridge the gap between dislocation properties and continuum descriptions of plastic behavior of crystalline materials. Computer simulations can help us verify these evolution equations and find their…
Composites are ideally suited to achieve desirable multifunctional effective properties since the best properties of different materials can be judiciously combined with designed microstructures. Here we establish cross-property relations…
Peridynamic (PD) theories have gained widespread diffusion among various research areas, due to the ability of modeling discontinuities formation and evolution in materials. Bond-Based Peridynamics (BB-PD), notwithstanding some modeling…
A state-based peridynamic formulation for linear elastic shells is presented. The emphasis is on introducing, possibly for the first time, a general surface based peridynamic model to represent the deformation characteristics of structures…
Peridynamics provides a versatile tool for fracture modelling in materials where fracture pathways cannot be predicted beforehand, but must be envisaged as an emergent features of the deformation process. One class of materials where this…
We consider a class of nonconvex energy functionals that lies in the framework of the peridynamics model of continuum mechanics. The energy densities are functions of a nonlocal strain that describes deformation based on pairwise…
Inelastic mechanical responses in solids, such as plasticity, damage and crack initiation, are typically modeled in constitutive ways that display microstructural and loading dependence. Nevertheless, {linear} elasticity at infinitesimal…
Nonlocal models, including peridynamics, often use integral operators that embed lengthscales in their definition. However, the integrands in these operators are difficult to define from the data that are typically available for a given…
We wish to understand the macroscopic plastic behaviour of metals by upscaling the micro-mechanics of dislocations. We consider a highly simplified dislocation network, which allows our microscopic model to be a one dimensional particle…
We study the nucleation dynamics of a model solid state transformation and the criterion for microstructure selection using a molecular dynamics (MD) simulation. Our simulations show a range of microstructures depending on the depth of…
A methodology is presented for investigating the dynamics of heterogeneous media using the nonlocal continuum model given by the peridynamic formulation. The approach presented here provides the ability to model the macroscopic dynamics…
Peridynamics (PD) represents a new approach for modelling fracture mechanics, where a continuum domain is modelled through particles connected via physical bonds. This formulation allows us to model crack initiation, propagation, branching…
We establish the a-priori convergence rate for finite element approximations of a class of nonlocal nonlinear fracture models. We consider state based peridynamic models where the force at a material point is due to both the strain between…
Plastic deformation in microscale differs from the macroscopic plasticity in two respects: (i) the flow stress of small samples depends on their size (ii) the scatter of plasticity increases significantly. In this work we focus on the…