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.

Recent developments in dislocation pattern dynamics: Current opinions and perspectives

2018 ◽  
Vol 03 (03n04) ◽  
pp. 1840002 ◽  
Author(s):  
Dandan Lyu ◽  
Shaofan Li
Keyword(s):  
Crystal Plasticity ◽  
Materials Science ◽  
Pattern Dynamics ◽  
Future Challenges ◽  
Recent Developments ◽  
Computational Aspects ◽  
Stochastic Events ◽  
The Individual ◽  
Micro Structures ◽  
Dislocation Patterns

The development of crystal plasticity theory based on dislocation patterns dynamics has been an outstanding problem in materials science and condensed matter of physics. Dislocation is the origin of crystal plasticity, and it is both the individual dislocation behavior as well as the aggregated dislocations behaviors that govern the plastic flow. The interactions among dislocations are complex statistical and stochastic events, in which the spontaneous emergence of organized dislocation patterns formations is the most critical and intriguing events. Dislocation patterns consist of quasi-periodic dislocation-rich and dislocation poor regions, e.g. cells, veins, labyrinths, ladders structures, etc. during cyclic loadings. Dislocation patterns have prominent and decisive effects on work hardening and plastic strain localization, and thus these dislocation micro-structures are responsible to material properties at macroscale. This paper reviews the recent developments of experimental observation, physical modeling, and computer modeling on dislocation microstructure. In particular, we focus on examining the mechanism towards plastic deformation. The progress and limitations of different experiments and modeling approaches are discussed and compared. Finally, we share our perspectives on current issues and future challenges in both experimental, analytical modeling, and computational aspects of dislocation pattern dynamics.

Migration with reduced artifacts from internal multiple reflections

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. A25-A29
Author(s):  
Lele Zhang
Keyword(s):  
Seismic Reflection ◽  
Computational Cost ◽  
Data Sets ◽  
Square Root ◽  
Multiple Reflections ◽  
Data Set ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Recent Developments ◽  
Multiple Elimination

Migration of seismic reflection data leads to artifacts due to the presence of internal multiple reflections. Recent developments have shown that these artifacts can be avoided using Marchenko redatuming or Marchenko multiple elimination. These are powerful concepts, but their implementation comes at a considerable computational cost. We have derived a scheme to image the subsurface of the medium with significantly reduced computational cost and artifacts. This scheme is based on the projected Marchenko equations. The measured reflection response is required as input, and a data set with primary reflections and nonphysical primary reflections is created. Original and retrieved data sets are migrated, and the migration images are multiplied with each other, after which the square root is taken to give the artifact-reduced image. We showed the underlying theory and introduced the effectiveness of this scheme with a 2D numerical example.

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.

Molecular Dynamics and Multiscale Simulations of Nanoindentation and Nanoscratch

2010 ◽  
Author(s):  
Peng-zhe Zhu ◽  
Hui Wang ◽  
Yuan-zhong Hu
Keyword(s):  
Molecular Dynamics ◽  
Computational Cost ◽  
Three Dimensional ◽  
Multiscale Model ◽  
Md Simulations ◽  
System Size ◽  
Multiscale Simulations ◽  
First Case ◽  
Chip Volume ◽  
Indenter Shape

Three-dimensional molecular dynamics (MD) simulations have been performed to investigate behaviors of nanoindentation and nano-scratch. The first case concerns the effects of material defect on the nanoindentation of nickel thin film. The defect is modeled by a spherical void embedded in the substrate and located under the surface of indentation. The simulation results reveal that compared to the case without defect, the presence of the void softens the material and allows for larger indentation depth at a given load. MD simulations are then performed for nano-scratch of single crystal copper, with emphasis on the effect of indenter shape (sharp and blunt) on the substrate deformation. The results show that the blunt indenter causes larger deformation region and much more dislocations at both the indentation and scratch stages. It is also found that during the scratching stage the blunt indenter results in larger chip volume in front of the indenter and gives rise to more friction than the sharp indenter. The scope of the simulations has been extended by introducing a multiscale model which couples MD simulations with Finite Element Method (FEM), and multiscale simulations are performed for two-dimensional nanoindentation of copper. The model has been validated by well-consistent load-depth curves obtained from both multiscale and full MD simulations, and by good continuity of deformation observed in the handshake region. The simulations also reveal that indenter radius and indentation velocity significantly affect the nanoindentation behavior. By use of multiscale method, the system size to be explored can be greatly expanded without increasing much computational cost.

scholarly journals REDUCTION OF THE RESONANCE ERROR — PART 1: APPROXIMATION OF HOMOGENIZED COEFFICIENTS

2011 ◽  
Vol 21 (08) ◽  
pp. 1601-1630 ◽  
Author(s):  
ANTOINE GLORIA
Keyword(s):  
Elliptic Equations ◽  
Length Scale ◽  
Numerical Homogenization ◽  
Cell Problem ◽  
Typical Size ◽  
Effective Coefficients ◽  
Homogenization Methods

This paper is concerned with the approximation of effective coefficients in homogenization of linear elliptic equations. One common drawback among numerical homogenization methods is the presence of the so-called resonance error, which roughly speaking is a function of the ratio ε/η, where η is a typical macroscopic length scale and ε is the typical size of the heterogeneities. In the present work, we propose an alternative for the computation of homogenized coefficients (or more generally a modified cell-problem), which is a first brick in the design of effective numerical homogenization methods. We show that this approach drastically reduces the resonance error in some standard cases.

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