On micro-to-macro transitions for multi-scale analysis of non-linear heterogeneous materials: unified variational basis and finite element implementation

2010 ◽  
Vol 87 (1-5) ◽  
pp. 149-170 ◽  
Author(s):  
D. Perić ◽  
E. A. de Souza Neto ◽  
R. A. Feijóo ◽  
M. Partovi ◽  
A. J. Carneiro Molina
Keyword(s):  
Finite Element ◽  
Heterogeneous Materials ◽  
Scale Analysis ◽  
Multi Scale ◽  
Finite Element Implementation ◽  
Non Linear ◽  
Multi Scale Analysis

scholarly journals Homogenization of trabecular structures

2020 ◽  
Vol 310 ◽  
pp. 00041
Author(s):  
Tomáš Krejčí ◽  
Aleš Jíra ◽  
Luboš Řehounek ◽  
Michal Šejnoha ◽  
Jaroslav Kruis ◽  
...  
Keyword(s):  
Finite Element ◽  
Effective Properties ◽  
Macro Level ◽  
Truss Structures ◽  
Scale Analysis ◽  
Scale Problem ◽  
Meso Level ◽  
Multi Scale ◽  
Macro Scale ◽  
Multi Scale Analysis

Numerical modeling of implants and specimens made from trabecular structures can be difficult and time-consuming. Trabecular structures are characterized as spatial truss structures composed of beams. A detailed discretization using the finite element method usually leads to a large number of degrees of freedom. It is attributed to the effort of creating a very fine mesh to capture the geometry of beams of the structure as accurately as possible. This contribution presents a numerical homogenization as one of the possible methods of trabecular structures modeling. The proposed approach is based on a multi-scale analysis, where the whole specimen is assumed to be homogeneous at a macro-level with assigned effective properties derived from an independent homogenization problem at a meso-level. Therein, the trabecular structure is seen as a porous or two-component medium with the metal structure and voids filled with the air or bone tissue at the meso-level. This corresponds to a two-level finite element homogenization scheme. The specimen is discretized by a reasonable coarse mesh at the macro-level, called the macro-scale problem, while the actual microstructure represented by a periodic unit cell is discretized with sufficient accuracy, called the meso-scale problem. Such a procedure was already applied to modeling of composite materials or masonry structures. The application of this multi-scale analysis is illustrated by a numerical simulation of laboratory compression tests of trabecular specimens.

scholarly journals NUMERICAL PLATE TESTING FOR NON-LINEAR MULTI-SCALE ANALYSIS OF PLATE-SHAPED DEVICE

2017 ◽  
Vol 73 (2) ◽  
pp. I_283-I_294 ◽  
Author(s):  
Masami SATO ◽  
Mayu MURAMATSU ◽  
Seishiro MATSUBARA ◽  
Shinnosuke NISHI ◽  
Kenjiro TERADA ◽  
...  
Keyword(s):  
Scale Analysis ◽  
Multi Scale ◽  
Non Linear ◽  
Multi Scale Analysis

Multi-scale analysis of optic chiasmal compression by finite element modelling

2014 ◽  
Vol 47 (10) ◽  
pp. 2292-2299 ◽  
Author(s):  
Xiaofei Wang ◽  
Andrew J. Neely ◽  
Gawn G. McIlwaine ◽  
Christian J. Lueck
Keyword(s):  
Finite Element ◽  
Finite Element Modelling ◽  
Scale Analysis ◽  
Element Modelling ◽  
Chiasmal Compression ◽  
Multi Scale ◽  
Multi Scale Analysis

Multi-scale analysis for helically wound structures with one-dimensional periodicity

2019 ◽  
Vol 36 (8) ◽  
pp. 2911-2928
Author(s):  
Jun Yan ◽  
Haitao Hu ◽  
Zhixun Yang ◽  
Rui Wan ◽  
Yang Li
Keyword(s):  
Finite Element ◽  
Axial Length ◽  
Homogenization Theory ◽  
Scale Analysis ◽  
Asymptotic Homogenization ◽  
Content Type ◽  
One Dimensional ◽  
Multi Scale ◽  
The One ◽  
Multi Scale Analysis

Purpose The purpose of this study is to present a multi-scale analysis methodology for calculating the effective stiffnesses and the micro stresses of helically wound structures efficiently and accurately. The helically wound structure is widely applied in ocean and civil engineering as load-bearing structures with high flexibility, such as wire ropes, umbilical cables and flexible risers. Their structures are usually composed of a number of twisted subcomponents with relatively large slender ratio and have the one-dimensional periodic characteristic in the axial direction. As the huge difference between the axial length and the cross-section size of this type of structures, the finite element modeling and theoretical analysis based on some assumption are usually unavailable leading to the reduction of computability; even the optimization design becomes infeasible. Design/methodology/approach Based on the asymptotic homogenization theory, the one-dimensional periodic helically wound structure is equivalent to the one-dimensional homogeneous beam. A novel implementation of the homogenization is derived for the analysis of the effective mechanical properties of the helically wound structure, and the tensile, bending, torsional and coupling stiffness properties of the effective beam model are obtained. On this basis, a downscaling analysis formation for the micro-component stress in the one-dimensional periodic wound structure is constructed. The stress of micro-components in the specified geometry position of the helically wound structure is obtained basing on the asymptotic homogenization theory simultaneously. Findings By comparing with the result from finite element established accurately, the established multi-scale calculation method of the one-dimensional periodic helically wound structure is verified. The influence of size effects on the macro effective performance and the micro-component stress is discussed. Originality/value This paper will provide the theoretical basis for the efficient elastoplastic analysis of the helically wound structure, even the fatigue analysis. In addition, it is necessary to point out that the axial length of the helically wound structure in the general engineering problems that such as deep-sea risers and submarine cables.

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