On the consistency between nearest-neighbor peridynamic discretizations and discretized classical elasticity models
31
Citation
54
Reference
10
Related Paper
Citation Trend
Keywords:
Peridynamics
Quadrature (astronomy)
Elasticity
Peridynamics
Continuum hypothesis
Displacement field
Field theory (psychology)
Cite
Citations (0)
Abstract Continuum mechanics is widely used to analyse the response of materials and structures to external loading conditions. Without paying attention to atomistic details, continuum mechanics can provide us very accurate predictions as long as continuum approximation is valid. There are various continuum mechanics formulations available in the literature. The most common formulation was proposed by Cauchy 200 years ago and the equation of motion for a material point is described by using partial differential equations. Although these equations have been successfully utilised for the analysis of many different challenging problems of solid mechanics, they encounter difficulties when dealing with problems including discontinuities such as cracks. In such cases, a new continuum mechanics formulation, peridynamics, can be more suitable since the equations of motion in peridynamics are in integro-differential equation form and do not contain any spatial derivatives. In nano-materials, material properties close to the surfaces can be different than bulk properties. This variation causes surface stresses. In this study, modified core–shell model is utilised to define the variation of material properties in the surface region by considering surface effects. Moreover, directional effective material properties are obtained by utilising analytical and peridynamic solutions.
Peridynamics
Classification of discontinuities
Elasticity
Cite
Citations (2)
Abstract Peridynamics is a nonlocal theory of continuum mechanics expressing the dynamic equilibrium of forces by using integro‐differential equations instead of partial differential equations. Thus, the equilibrium equations are still valid in case of discontinous displacement fields. In this study, we investigate the coupling between a harmonically excited peridynamic rod with a rod based on classical continuum mechanics by using the Arlequin‐method. The peridynamic region is solved by finite elements whereas for the classical region an analytical solution can be used.
Peridynamics
Continuum hypothesis
Cite
Citations (0)
The traditional multiscale approach couples two models operating at different scales. An alternative modelling strategy, called peridynamics originally developed by [1], is to continualize the molecular dynamic models, thus replacing inhomogeneities present on smaller length scales by an enhanced continuum description on larger length scales resulting in a nonlocal reformulation of continuum mechanics. Peridynamics is a single multiscale model valid over wide range of length scales and can be considered as an upscaling of molecular dynamics. Therefore peridynamics models should recover the same dynamics and preserve all characteristic properties of molecular dynamics, which are lost by classical continuum mechanics models. The advantage of the peridynamic models is that they can be solved more cheaply than the corresponding molecular dynamic models. Peridynamics is a generalized continuum theory employing a nonlocal model of force interaction. Each material point interacts with its neighborhood within a sphere, called the horizon that serves as an internal length scale in the model. The interaction between the material points is described by a bond force which is not an electrostatic force but can be related to the strain energy of classical continuum mechanics. The objective of this study is to investigate whether the horizon in peridynamics can model the size dependence of the Young’s modulus at the nanoscale, shown experimentally and with molecular dynamic simulation in many previous works. Peridynamic simulations of copper beams with different sizes under traction have been performed employing the molecular dynamics code LAMMPS, see [2]. The force-displacement curves have been compared directly to molecular dynamics simulation and an appropriate value for the horizon has been chosen. The results showed that the Young’s modulus changes with the size and seems to tend to a limit which is the macroscopic value of the Young’s modulus for copper. (Less)
Peridynamics
Continuum hypothesis
Length scale
Cite
Citations (1)
Peridynamics
Body force
Computational mechanics
Cite
Citations (41)
Peridynamics
Morphing
Linearization
Cite
Citations (141)
A Hybrid Local/Nonlocal Continuum Mechanics Modeling and Simulation of Fracture in Brittle Materials
Classical continuum mechanics which leads to a local continuum model, encounters challenges when the discontinuity appears, while peridynamics that falls into the category of nonlocal continuum mechanics suffers from a high computational cost. A hybrid model coupling classical continuum mechanics with peridynamics can avoid both disadvantages. This paper describes the hybrid model and its adaptive coupling approach which dynamically updates the coupling domains according to crack propagations for brittle materials. Then this hybrid local/nonlocal continuum model is applied to fracture simulation. Some numerical examples like a plate with a hole, Brazilian disk, notched plate and beam, are performed for verification and validation. In addition, a peridynamic software is introduced, which was recently developed for the simulation of the hybrid local/nonlocal continuum model.
Peridynamics
Brittleness
Discontinuity (linguistics)
Cite
Citations (28)
This paper describes an elegant statistical coarse-graining of molecular dynamics at finite temperature into peridynamics, a continuum theory. Peridynamics is an efficient alternative to molecular dynamics enabling dynamics at larger length and time scales. In direct analogy with molecular dynamics, peridynamics uses a nonlocal model of force and does not employ stress/strain relationships germane to classical continuum mechanics. In contrast with classical continuum mechanics, the peridynamic representation of a system of linear springs and masses is shown to have the same dispersion relation as the original spring-mass system.
Peridynamics
Continuum hypothesis
Statistical Mechanics
Granularity
Dynamics
Representation
Cite
Citations (16)
Peridynamics
Continuum hypothesis
Cite
Citations (4)