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.

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.

A Multi-Scale Analysis for an Evaluation of the Mechanical Properties of Composite Materials

2007 ◽  
Vol 334-335 ◽  
pp. 585-588
Author(s):  
Makoto Imura ◽  
Tetsusei Kurashiki ◽  
Hiroaki Nakai ◽  
Masaru Zako
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Composite Materials ◽  
Material Properties ◽  
Woven Fabric ◽  
Scale Analysis ◽  
Multi Scale ◽  
Woven Fabric Composites ◽  
Fabric Composites ◽  
Multi Scale Analysis

Fiber reinforced composite materials have been applied widely to many structures, because they have some advantages like easy handling, high specific strength, etc. The numerical method like finite element method has been applied to design and to evaluate the material properties and behavior as the development of Computer Aided Engineering. It is very difficult to calculate with accuracy not only in structural scale but also in detail material scale (for example, the order of fiber diameter) by the traditional FEM, becausecompositematerials like woven fabric composites have the geometrical complexityand the large difference between above mentioned scales. The development of multi-scale analysis method is one of the major topics in computational mechanics. Mesh superpositionis one of multi-scale analysis methods and is an effective method to solve the problems which have the large difference between the structure scale and the reinforcement scale. We have expanded the finite element mesh superposition method with 3 scales and have defined as M3 (Macro-Meso-Micro) method. In this paper, we have proposed a new approach method combined with M3 method and homogenized method to obtain the mechanical properties and to simulate the behavior of woven fabric composites. In addition, the elastic-plastic mechanics and the damage mechanics have been introduced into M3 method to investigate the effects of matrix-crack on the structural and material properties. From the numerical results, it is revealed that it is very useful for the evaluation of mechanical properties of composite materials.

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