FFT based approaches in micromechanics: fundamentals, methods and applications

2021 ◽  
Author(s):  
Sergio Lucarini ◽  
Manas Vijay Upadhyay ◽  
Javier Segurado
Keyword(s):  
Dislocation Dynamics ◽  
Homogenization Problem ◽  
Multi Scale ◽  
Discrete Dislocation Dynamics ◽  
Scale Modeling ◽  
Damage And Fracture ◽  
Discrete Dislocation ◽  
Displacement Based ◽  
Selection Of ◽  
Computational Micromechanics

Abstract FFT methods have become a fundamental tool in computational micromechanics since they were first proposed in 1994 by H. Moulinec and P. Suquet for the homogenization of composites. From that moment on many dierent approaches have been proposed for a more accurate and efficient resolution of the non- linear homogenization problem. Furthermore, the method has been pushed beyond its original purpose and has been adapted to many other problems including continuum and discrete dislocation dynamics, multi-scale modeling or homogenization of coupled problems as fracture or multiphysical problems. In this paper, a comprehensive review of FFT approaches for micromechanical simulations will be made, covering the basic mathematical aspects and a complete description of a selection of approaches which includes the original basic scheme, polarization based methods, Krylov approaches, Fourier-Galerkin and displacement-based methods. The paper will present then the most relevant applications of the method in homogenization of composites, polycrystals or porous materials including the simulation of damage and fracture. It will also include an insight into synergies with experiments or its extension towards dislocation dynamics, multi-physics and multi-scale problems. Finally, the paper will analyze the current limitations of the method and try to analyze the future of the application of FFT approaches in micromechanics.

Stress Patterns of Deformation Induced Planar Dislocation Boundaries

2001 ◽  
Vol 683 ◽  
Author(s):  
Shafique M. A. Khan ◽  
Hussein M. Zbib ◽  
Darcy A. Hughes
Keyword(s):  
Boundary Conditions ◽  
Dislocation Dynamics ◽  
Scale Model ◽  
Element Analysis ◽  
Multi Scale ◽  
Discrete Dislocation Dynamics ◽  
Discrete Dislocation ◽  
Planar Dislocation ◽  
The Right ◽  
Stress Patterns

ABSTRACTA Multi-scale model coupling discrete dislocation dynamics with continuum plasticity and finite element analysis is used to study the self-stress field of geometrically necessary (dislocation) boundaries (GNBs). The results for a single GNB are presented here. The internal structure of the GNB is obtained from the Frank's formula using experimentally measured misorientation angle/axis pair as the input. Several different types of model boundary conditions (using FEA) are analyzed together with the effect of different parameters like the domain length and mesh sensitivity. It is shown that choosing the right boundary conditions for the FEA strongly affects the predicted internal stress fields of these dislocation boundaries, particularly the long-range effect.

Modelling of Irradiated Materials

2006 ◽  
Author(s):  
B. K. Dutta ◽  
P. V. Durgaprasad ◽  
A. K. Pawar ◽  
H. S. Kushwaha ◽  
S. Banerjee
Keyword(s):  
Radiation Damage ◽  
Energetic Particles ◽  
Dislocation Dynamics ◽  
Length Scale ◽  
Multi Scale ◽  
Discrete Dislocation Dynamics ◽  
Discrete Dislocation ◽  
Stacking Fault Tetrahedra ◽  
Wide Range ◽  
Materials Used

Irradiation of materials by energetic particles causes significant degradation of the mechanical properties, most notably an increased yield stress and decrease ductility, thus limiting lifetime of materials used in nuclear reactors. The microstructure of irradiated materials evolves over a wide range of length and time scales, making radiation damage and inherently multi-scale phenomenon. At atomic length scale, the principal sources of radiation damage are the primary knock-on atoms that recoil under collision from energetic particles such as neutrons or ions. These knock-on atoms in turn produce vacancies and self-interstitial atoms, and stacking fault tetrahedra. At higher length scale, these defect clusters form loops around existing dislocations, leading to their decoration and immobilization, which ultimately leads to radiation hardening in most of the materials. All these defects finally effect the macroscopic mechanical and other properties. An attempt is made to understand these phenomena using molecular dynamics studies and discrete dislocation dynamics modelling.

The Effect of Multipoles on the Elasto-Plastic Properties of a Crystal: Theory and 3D Dislocation Dynamics Modeling

2021 ◽  
pp. 1-22
Author(s):  
Abu Bakar Siddique ◽  
Hojun Lim ◽  
Tariq Khraishi
Keyword(s):  
Plastic Deformation ◽  
Dislocation Dynamics ◽  
Dynamics Modeling ◽  
Proportional Limit ◽  
Softening Effect ◽  
Plastic Properties ◽  
Discrete Dislocation Dynamics ◽  
Scale Modeling ◽  
Discrete Dislocation ◽  
Elastoplastic Properties

Abstract Plastic deformation in metals is dominated by the interactions among dislocations and other defects inside the crystal. A large number of dislocation multipoles (dipoles, tripoles, quadrupoles, etc.) can form during plastic deformation. Depending on the relative position and the orientation of the dislocations, interactions in and between multipoles can change the elastoplastic properties of a material. The authors of this article investigate the effect of dislocation multipoles on the elastoplastic properties of a material. This is performed under different multipole configurations (i.e. the distance between active glide planes and the signs of the dislocations) using a 3D Discrete Dislocation Dynamics (DDD) code. The simulations show that multipoles exhibit a hardening/softening effect when the sign of the dislocations involved is the same, and a hardening effect only when the dislocations are of opposite sign to nearby ones. The distance between the two neighboring dislocations was also affecting the proportional limit for the material. Such hardening or flow stress results, as in this study, can be incorporated into larger-scale modeling work.

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