scholarly journals A Coupled VEM-BEM Approach for Computational Homogenization of Heterogeneous Materials

2021 ◽  
Author(s):  
M. Lo Cascio ◽  
A. Milazzo ◽  
I. Benedetti
Keyword(s):  
Heterogeneous Materials ◽  
Computational Homogenization

Computational Homogenization of Heterogeneous Materials by a Novel Hybrid Numerical Scheme

2020 ◽  
Vol 11 (04) ◽  
pp. 2050008
Author(s):  
Marco Lo Cascio ◽  
Marco Grifò ◽  
Alberto Milazzo ◽  
Ivano Benedetti
Keyword(s):  
Numerical Technique ◽  
Matrix Material ◽  
Heterogeneous Materials ◽  
Computational Effort ◽  
Computational Homogenization ◽  
Surrounding Matrix ◽  
Unit Cells ◽  
Virtual Element ◽  
Solution Accuracy ◽  
Element Method

The Virtual Element Method (VEM) is a recent numerical technique capable of dealing with very general polygonal and polyhedral mesh elements, including irregular or non-convex ones. Because of this feature, the VEM ensures noticeable simplification in the data preparation stage of the analysis, especially for problems whose analysis domain features complex geometries, as in the case of computational micro-mechanics problems. The Boundary Element Method (BEM) is a well known, extensively used and effective numerical technique for the solution of several classes of problems in science and engineering. Due to its underlying formulation, the BEM allows reducing the dimensionality of the problem, resulting in substantial simplification of the pre-processing stage and in the reduction of the computational effort, without jeopardizing the solution accuracy. In this contribution, we explore the possibility of a coupling VEM and BEM for computational homogenization of heterogeneous materials with complex microstructures. The test morphologies consist of unit cells with irregularly shaped inclusions, representative e.g., of a fiber-reinforced polymer composite. The BEM is used to model the inclusions, while the VEM is used to model the surrounding matrix material. Benchmark finite element solutions are used to validate the analysis results.

MULTISCALE CONTINUOUS AND DISCONTINUOUS MODELING OF HETEROGENEOUS MATERIALS: A REVIEW ON RECENT DEVELOPMENTS

2011 ◽  
Vol 03 (04) ◽  
pp. 229-270 ◽  
Author(s):  
VINH PHU NGUYEN ◽  
MARTIJN STROEVEN ◽  
LAMBERTUS JOHANNES SLUYS
Keyword(s):  
Strain Localization ◽  
Computational Cost ◽  
Heterogeneous Materials ◽  
Computational Homogenization ◽  
Cohesive Crack ◽  
Multiscale Simulations ◽  
Numerical Homogenization ◽  
Recent Developments ◽  
Computational Aspects ◽  
Homogenization Methods

This paper reviews the recent developments in the field of multiscale modelling of heterogeneous materials with emphasis on homogenization methods and strain localization problems. Among other topics, the following are discussed (i) numerical homogenization or unit cell methods, (ii) continuous computational homogenization for bulk modelling, (iii) discontinuous computational homogenization for adhesive/cohesive crack modelling and (iv) continuous-discontinuous computational homogenization for cohesive failures. Different boundary conditions imposed on representative volume elements are described. Computational aspects concerning robustness and computational cost of multiscale simulations are presented.

scholarly journals Parametric FEM for computational homogenization of heterogeneous materials with random voids

PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Dmytro Pivovarov ◽  
Julia Mergheim ◽  
Kai Willner ◽  
Paul Steinmann
Keyword(s):  
Heterogeneous Materials ◽  
Computational Homogenization
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