A Variational Asymptotic Method for Unit Cell Homogenization of Elasto-Viscoplastic Heterogeneous Materials

2013 ◽  
Author(s):  
Liang Zhang ◽  
Wenbin Yu
Keyword(s):  
Asymptotic Method ◽  
Heterogeneous Materials ◽  
Unit Cell ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method

A Variational Asymptotic Method for Unit Cell Homogenization of Elastoplastic Heterogeneous Materials

2012 ◽  
Author(s):  
Liang Zhang ◽  
Wenbin Yu
Keyword(s):  
Asymptotic Method ◽  
Effective Properties ◽  
Kinematic Hardening ◽  
Plastic Anisotropy ◽  
Heterogeneous Materials ◽  
Unit Cell ◽  
Elastoplastic Material ◽  
Stress Strain ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method

The variational asymptotic method for unit cell homogenization (VAMUCH) is a unified micromechanical numerical method that is able to predict the effective properties of heterogeneous materials and to recover the microscopic stress/strain field. The objective of this paper is to incorporate elastoplastic material behaviors into the VAMUCH to predict the nonlinear macroscopic/microscopic response of elastoplastic heterogeneous materials. The constituents are assumed to exhibit various behaviors including elastic/plastic anisotropy, isotropic/kinematic hardening, and plastic non-normality. The constitutive relations for the constituents are derived and implemented into the theory of VAMUCH. This theory is implemented using the finite element method, and an engineering code, VAMUCH, is developed for the micromechanical analysiso of unit cells. The applicability, power, and accuracy of the theory and code of VAMUCH are validated using several examples including predicting the initial and subsequent yield surfaces, stress-strain curves, and stress-strain hysteresis loops of fiber reinforced composites. The VAMUCH code is also ready to be implemented into many more sophisticated user-defined material models.

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.

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.

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