Micromechanical Analysis and Multi-Scale Modeling Using the Voronoi Cell Finite Element Method

2011 ◽  
Author(s):  
Somnath Ghosh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Voronoi Cell ◽  
Micromechanical Analysis ◽  
Multi Scale ◽  
Scale Modeling ◽  
Multi Scale Modeling ◽  
Element Method

Research Advances on Multi-Scale Modeling of Properties of Cement-Based Materials

2012 ◽  
Vol 195-196 ◽  
pp. 291-296
Author(s):  
Hai Tao Zhao ◽  
Dong Hui Huang ◽  
Pan Xiu Wang ◽  
Qiao Li ◽  
Qing Ning
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Simulation Model ◽  
Multi Scale ◽  
Scale Modeling ◽  
Cement Based Materials ◽  
Multi Scale Modeling ◽  
And Performance ◽  
Modeling Of Properties

Cement-based material is a complex multi-scale material which is difficult to comprehend. With the simulation model, the methods and examples of multi-scale modeling of structure and performance of cement-based materials are presented based on coupled cementitious composites and structural mechanics. This paper discuss on the properties of cement-based materials as shrinkage, elasticity, durability which are carried out by numerical methods such as Finite Element Method (FEM) and eXtended FEM(XFEM).

Molecular Dynamics Approach and its Application in the Analysis of Multi-Scale

2013 ◽  
Vol 444-445 ◽  
pp. 1364-1369
Author(s):  
Wen Hai Gai ◽  
R. Guo ◽  
Jun Guo
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Molecular Dynamics ◽  
Finite Element ◽  
Low Cost ◽  
Multiple Scale ◽  
Voronoi Cell ◽  
Material Behavior ◽  
Multi Scale ◽  
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.

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

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.

Fracture simulations using edge-based smoothed finite element method for isotropic damage model via Delaunay/Voronoi dual tessellations

2021 ◽  
pp. 105678952110405
Author(s):  
Young Kwang Hwang ◽  
Suyeong Jin ◽  
Jung-Wuk Hong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Voronoi Tessellation ◽  
Damage Model ◽  
Time Integration ◽  
Voronoi Cell ◽  
Smoothed Finite Element Method ◽  
Isotropic Damage ◽  
Edge Based ◽  
Element Method

In this study, an effective numerical framework for fracture simulations is proposed using the edge-based smoothed finite element method (ES-FEM) and isotropic damage model. The duality between the Delaunay triangulation and Voronoi tessellation is utilized for the mesh construction and the compatible use of the finite element solution with the Voronoi-cell lattice geometry. The mesh irregularity is introduced to avoid calculating the biased crack path by adding random variation in the nodal coordinates, and the ES-FEM elements are defined along the Delaunay edges. With the Voronoi tessellation, each nodal mass is calculated and the fractured surfaces are visualized along the Voronoi edges. The rotational degrees of freedom are implemented for each node by introducing the elemental formulation of the Voronoi-cell lattice model, and the accurate visualizations of the rotational motions in the Voronoi diagram are achieved. An isotropic damage model is newly incorporated into the ES-FEM formulation, and the equivalent elemental length is introduced with an additional geometric factor to simulate the consistent softening behaviors with reducing the mesh sensitivity. The full matrix form of the smoothed strain-displacement matrix is constructed for optimal use in the element-wise computations during explicit time integration, and parallel computing is implemented for the enhancement of the computational efficiency. The simulated results are compared with the theoretical solutions or experimental results, which demonstrates the effectiveness of the proposed methodology in the simulations of the quasi-brittle fractures.

MOLECULAR ELEMENT METHOD (MEM) FOR MULTI-SCALE MODELING AND SIMULATIONS OF NANO/MICRO-SYSTEMS

2005 ◽  
Vol 29 (3) ◽  
pp. 403-421
Author(s):  
Kamran Behdinan ◽  
Yigui Xu ◽  
Zouheir Fawaz
Keyword(s):  
Molecular Dynamics ◽  
Classical Method ◽  
Computational Time ◽  
Physical Parameters ◽  
Modeling And Simulations ◽  
Multi Scale ◽  
Scale Modeling ◽  
Multi Scale Modeling ◽  
Micro Systems ◽  
Element Method

A new technique called Molecular Element Method is proposed for multi-scale modeling and simulations of nano/micro-systems. In this technique, the system is divided into molecular elements whose properties are represented by sets of equivalent physical parameters obtained from atomic information. The discrete system is solved based on continuum mechanics theories. The resultant element information from system solving is then used as an external constraint for the elements, to investigate the atomic information within, using molecular dynamics calculations. Both system properties and atomic information at local zones can be obtained accurately and efficiently in this way, A crystal of Cu having 285,883 atoms with a through the thickness hole inside is investigated using this technique. Tension stresses of the crystal and the slip of atoms around the hole’s edge are revealed corresponding to five strain loads. Compared with the results obtained from the classical molecular dynamics method, the maximum stress error is 2.7%, while the computational time is only 7.2-11.8% of that taken by the classical method.

Sign in / Sign up

Export Citation Format

Share Document