A Variational Asymptotic Model for Predicting Initial Yielding Surface and Elastoplastic Behavior of Metal Matrix Composite Materials

2007 ◽  
Author(s):  
Tian Tang ◽  
Wenbin Yu
Keyword(s):  
Metal Matrix ◽  
Energy Functional ◽  
Unit Cell ◽  
Asymptotic Model ◽  
Matrix Composites ◽  
The Finite Element Method ◽  
Elastoplastic Behavior ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method ◽  
Variational Statement

The focus of this paper is to develop a micromechanics model based on the variational asymptotic method for unit cell homogenization (VAMUCH) for predicting of the initial yielding surface, overall instantaneous moduli, and elastoplastic behavior of metal matrix composites. Considering the size of the microstructure as a small parameter, we can formulate a variational statement of the unit cell through an asymptotic expansion of the energy functional. To handle realistic microstructures, we implement this new model using the finite element method. For model validation, we used a few examples to demonstrate the application and accuracy of this theory and the companion code.

Micromechanics Modeling of the Nonlinear Behavior of Electrostrictive Multiphase Composites

2008 ◽  
Author(s):  
Tian Tang ◽  
Wenbin Yu
Keyword(s):  
Nonlinear Behavior ◽  
Present Theory ◽  
Unit Cell ◽  
Numerical Examples ◽  
Multiphase Composites ◽  
Variational Asymptotic ◽  
Incremental Formulation ◽  
Variational Asymptotic Method ◽  
Micromechanics Modeling ◽  
Variational Statement

The micromechanics modeling of the nonlinear behavior of the electrostrictive multiphase composites is developed using an incremental formulation based on the variational asymptotic method for unit cell homogenization (VAMUCH), a recently developed micromechanics modeling scheme. The microstructure of composites is assumed to be periodic. Taking advantage of the small size of the microstructure, we formulate a variational statement of energy change of the unit cell through an asymptotic analysis of the functional by invoking only two essential assumptions within the concept of micromechanics. Finally, the expression of the effective instantaneous tangential electromechanical matrix of the composites are established. Several numerical examples will be used to demonstrate the capability of the present theory.

Finite Element Modeling for Prediction of Residual Stresses in Fiber Reinforced Metal Matrix Composites

1993 ◽  
Author(s):  
Partha Rangaswamy ◽  
N. Jayaraman
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Residual Stresses ◽  
Metal Matrix Composites ◽  
Metal Matrix ◽  
Matrix Material ◽  
Unit Cell ◽  
Experimental Results ◽  
Matrix Composites ◽  
Layer Removal

Abstract In metal matrix composites residual stresses developing during the cool-down process after consolidation due to mismatch in thermal expansion coefficients between the ceramic fibers and metal matrix have been predicted using finite element analysis. Conventionally, unit cell models consisting of a quarter fiber surrounded by the matrix material have been developed for analyzing this problem. Such models have successfully predicted the stresses at the fiber-matrix interface. However, experimental work to measure residual stresses have always been on surfaces far away from the interface region. In this paper, models based on the conventional unit cell (one quarter fiber), one fiber, two fibers have been analyzed. In addition, using the element birth/death options available in the FEM code, the surface layer removal process that is conventionally used in the residual stress measuring technique has been simulated in the model. Such layer removal technique allows us to determine the average surface residual stress after each layer is removed and a direct comparison with experimental results are therefore possible. The predictions are compared with experimental results of an eight-ply unidirectional composite with Ti-24Al-11 Nb as matrix material reinforced with SCS-6 fibers.

A New Micromechanics Model for Predicting Thermal Properties of Heterogeneous Materials

2006 ◽  
Author(s):  
Wenbin Yu ◽  
Tian Tang
Keyword(s):  
Thermal Properties ◽  
Heterogeneous Materials ◽  
Present Theory ◽  
Unit Cell ◽  
Micromechanics Model ◽  
Micromechanics Models ◽  
Unit Cells ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method ◽  
Complete Set

A new micromechanics model, namely, the variational asymptotic method for unit cell homogenization (VAMUCH), is extended to predict thermal properties of heterogeneous anisotropic materials. In comparison to existing micromechanics models, VAMUCH is unique in the following three aspects: (1) it invokes only essential assumptions within the concept of micromechanics and achieves the same accuracy as mathematical homogenization theories; (2) it calculates the complete set of properties simultaneously without applying any loads; and (3) the dimensionality of the problem is determined by the dimension of the unit cell and the complete set of material properties can be obtained for one-dimensional unit cells. The present theory is implemented in the computer program VAMUCH, a recently developed, versatile engineering code for homogenization of heterogeneous materials. Several examples will be used to demonstrate the application and accuracy of the theory and the code of VAMUCH.

Simulation of Solidification for Metal Matrix Composites

2011 ◽  
Vol 261-263 ◽  
pp. 613-617
Author(s):  
Fu Sheng Hao ◽  
Shi Wu Gao ◽  
Ke Liang Ren
Keyword(s):  
Composite Materials ◽  
Metal Matrix ◽  
Solidification Process ◽  
Metal Composite ◽  
Matrix Composites ◽  
The Finite Element Method ◽  
The Matrix ◽  
Nonlinear Temperature ◽  
Metal Composite Materials ◽  
The Difference

The paper use the finite element method, simulating the solidification process of metal matrix composite. Obtain the changing of temperature field about the solidification process and some temperature curve for special nodes. The results show that, due to the difference of heat transfer coefficient about the matrix and the metal the solidification process for composite materials showed the irregular temperature cloud, namely nonlinear temperature distribution. The simulation actually provides some guidance for synthesis of metal composite materials.

Prediction of Mechanical Properties of Microcellular Plastics Using the Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH) Method

2013 ◽  
Author(s):  
Emily Yu ◽  
Lih-Sheng Turng
Keyword(s):  
Mechanical Properties ◽  
Asymptotic Method ◽  
Thermoplastic Polyurethane ◽  
Three Dimensional ◽  
Unit Cell ◽  
Element Analysis ◽  
Microcellular Plastics ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method ◽  
Injection Molded

This work presents the application of the micromechanical variational asymptotic method for unit cell homogenization (VAMUCH) with a three-dimensional unit cell (UC) structure and a coupled, macroscale finite element analysis for analyzing and predicting the effective elastic properties of microcellular injection molded plastics. A series of injection molded plastic samples — which included polylactic acid (PLA), polypropylene (PP), polystyrene (PS), and thermoplastic polyurethane (TPU) — with microcellular foamed structures were produced and their mechanical properties were compared with predicted values. The results showed that for most material samples, the numerical prediction was in fairly good agreement with experimental results, which demonstrates the applicability and reliability of VAMUCH in analyzing the mechanical properties of porous materials. The study also found that material characteristics such as brittleness or ductility could influence the predicted results and that the VAMUCH prediction could be improved when the UC structure was more representative of the real composition.

A Computational Approach for the Constitutive Modeling of Elastoplastic Behavior of Metal Matrix Composites

2016 ◽  
Vol 14 (05) ◽  
pp. 1750058 ◽  
Author(s):  
M. U. Siddiqui ◽  
Abul Fazal M. Arif
Keyword(s):  
Composite Materials ◽  
Metal Matrix Composites ◽  
Metal Matrix ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Computational Approach ◽  
Matrix Composites ◽  
Elastoplastic Behavior ◽  
Alumina Composite

Computational homogenization provides an excellent tool for the design of composite materials. In the current work, a computational approach is presented that is capable of estimating the elastic and rate-independent plastic constitutive behavior of metal matrix composites using finite element models of representative volume elements (RVEs) of the composite material. For this purpose, methodologies for the generation of three-dimensional computational microstructures, size determination of RVEs and the homogenization techniques are presented. Validation of the approach is carried out using aluminum–alumina composite samples prepared using sintering technique. Using the homogenized material response, effective constitutive models of the composite materials have been determined.

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