Multi-Scale Analysis for Visco-Elastic Characteristics of Filled Rubber with Molecular Dynamics and Finite Element Method

Numerical simulation of the behavior of materials can be used as a versatile, efficient and low cost tool for developing an understanding of material behavior [. The numerical simulation methods include quantum mechanics, molecular dynamics, Voronoi cell finite element method and finite element method et al. These methods themselves are not sufficient for many fundamental problems in computational mechanics, and the deficiencies lead to the thrust of multiple-scale methods. The multi-scale method to model micro-scale systems by coupled continuum mechanics and molecular dynamics was introduced. This paper describes the basic methods of multi-scale and general simulation process of molecular dynamics was reviewed.

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A posteriori error estimates for a multi-scale finite-element method

Computational and Applied Mathematics ◽

10.1007/s40314-021-01426-5 ◽

2021 ◽

Vol 40 (4) ◽

Author(s):

Khallih Ahmed Blal ◽

Brahim Allam ◽

Zoubida Mghazli

Keyword(s):

Finite Element Method ◽

Finite Element ◽

A Posteriori Error Estimates ◽

Numerical Test ◽

Posteriori Error ◽

Diffusion Problem ◽

A Posteriori ◽

Essential Information ◽

Multi Scale ◽

Element Method

AbstractWe are interested in the discretization of a diffusion problem with highly oscillating coefficient, by a multi-scale finite-element method (MsFEM). The objective of this method is to capture the multi-scale structure of the solution via local basis functions which contain the essential information on small scales. In this paper, we perform an a posteriori analysis of this discretization. The main result consists of building error indicators with respect to both small and large meshes used in this method. We present a numerical test in which the experiments are in good coherency with the results of analysis.

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THE ATOMIC FINITE ELEMENT METHOD AS A BRIDGE BETWEEN MOLECULAR DYNAMICS AND CONTINUUM MECHANICS

Journal of Multiscale Modelling ◽

10.1142/s1756973711000339 ◽

2011 ◽

Vol 03 (01n02) ◽

pp. 39-47 ◽

Cited By ~ 6

Author(s):

R. NEUGEBAUER ◽

R. WERTHEIM ◽

U. SEMMLER

Keyword(s):

Finite Element Method ◽

Molecular Dynamics ◽

Finite Element ◽

High Performance ◽

Cutting Tools ◽

Deposition Process ◽

Dislocation Behavior ◽

Crystal Plasticity Fem ◽

The Continuum ◽

Element Method

On cutting tools for high performance cutting (HPC) processes or for hard-to-cut materials, there is an increased importance in so-called superlattice coatings with hundreds of layers each of which is only a few nanometers in thickness. Homogeneity or average material properties based on the properties of single layers are not valid in these dimensions any more. Consequently, continuum mechanical material models cannot be used for modeling the behavior of nanolayers. Therefore, the interaction potentials between the single atoms should be considered. A new, so-called atomic finite element method (AFEM) is presented. In the AFEM the interatomic bonds are modeled as nonlinear spring elements. The AFEM is the connection between the molecular dynamics (MD) method and the crystal plasticity FEM (CPFEM). The MD simulates the atomic deposition process. The CPFEM considers the behavior of anisotropic crystals using the continuum mechanical FEM. On one side, the atomic structure data simulated by MD defines the interface to AFEM. On the other side, the boundary conditions (displacements and tractions) of the AFEM model are interpolated from the CPFEM simulations. In AFEM, the lattice deformation, the crack and dislocation behavior can be simulated and calculated at the nanometer scale.

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