scholarly journals Nonuniform transformation field analysis of elastic–viscoplastic composites

2009 ◽  
Vol 69 (1) ◽  
pp. 22-27 ◽  
Author(s):  
S. Roussette ◽  
J.C. Michel ◽  
P. Suquet
Keyword(s):  
Field Analysis ◽  
Transformation Field Analysis

Implementation of the transformation field analysis for inelastic composite materials

1994 ◽  
Vol 14 (3) ◽  
pp. 201-228 ◽  
Author(s):  
G. J. Dvorak ◽  
A. M. Wafa ◽  
Y. A. Bahei-El-Din
Keyword(s):  
Composite Materials ◽  
Field Analysis ◽  
Transformation Field Analysis

A Multiscale Model of Composite Failure Under Impact

2006 ◽  
Author(s):  
Caglar Oskay ◽  
Jacob Fish
Keyword(s):  
Mesoscale Model ◽  
Computational Cost ◽  
Expansion Method ◽  
Multiple Scale ◽  
Multiscale Model ◽  
Field Analysis ◽  
Computationally Efficient ◽  
Composite Failure ◽  
Homogenization Approach ◽  
Transformation Field Analysis

We present a new computationally efficient mesoscale model aimed at predicting the dominant characteristics of failure at the microstructural level. This method combines the multiple scale asymptotic expansion method with the generalized transformation field analysis (GTFA) to reduce the computational cost of the direct homogenization approach. A computational validation methodology was devised for the validation of the proposed mesoscale model against experimental data. The proposed validation methodology permits incorporation of various types of experiments to the validation process by employing an experiment simulator repository.

ASME 1992 Nadai Lecture—Micromechanics of Inelastic Composite Materials: Theory and Experiment

1993 ◽  
Vol 115 (4) ◽  
pp. 327-338 ◽  
Author(s):  
George J. Dvorak
Keyword(s):  
Composite Materials ◽  
General Procedure ◽  
Local Fields ◽  
Field Analysis ◽  
Plastic Strains ◽  
Inelastic Behavior ◽  
Aluminum Composite ◽  
Plastic Strain Increment ◽  
Multiphase Materials ◽  
Transformation Field Analysis

Some recent theoretical and experimental results on modeling of the inelastic behavior of composite materials are reviewed. The transformation field analysis method (G. J. Dvorak, Proc. R. Soc. London, Series A437, 1992, pp. 311–327) is a general procedure for evaluation of local fields and overall response in representative volumes of multiphase materials subjected to external thermomechanical loads and transformations in the phases. Applications are presented for systems with elastic-plastic and viscoelastic constituents. The Kroner-Budiansky-Wu and the Hill self-consistent models are corrected to conform with the generalized Levin formula. Recent experimental measurements of yield surfaces and plastic strains on thin-walled boron-aluminum composite tubes are interpreted with several micromechanical models. The comparisons show that unit cell models can provide reasonably accurate predictions of the observed plastic strains, while models relying on normality of the plastic strain increment vector to a single overall yield surface may not capture the essential features of the inelastic deformation process.

scholarly journals Effective potentials in nonlinear polycrystals and quadrature formulae

2017 ◽  
Vol 473 (2204) ◽  
pp. 20170213 ◽  
Author(s):  
Jean-Claude Michel ◽  
Pierre Suquet
Keyword(s):  
Order Approximation ◽  
High Stress ◽  
Stress Triaxiality ◽  
Local Fields ◽  
Field Analysis ◽  
Effective Potentials ◽  
Quadrature Formulae ◽  
Highly Nonlinear ◽  
Transformation Field Analysis ◽  
High Stress Triaxiality

This study presents a family of estimates for effective potentials in nonlinear polycrystals. Noting that these potentials are given as averages, several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields. Two of these quadrature formulae reduce to known schemes, including a recent proposition (Ponte Castañeda 2015 Proc. R. Soc. A 471 , 20150665 ( doi:10.1098/rspa.2015.0665 )) obtained by completely different means. Other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments. These quadrature formulae are applied to the estimation of effective potentials in polycrystals governed by two potentials, by means of a reduced-order model proposed by the authors (non-uniform transformation field analysis). It is shown how the quadrature formulae improve on the tangent second-order approximation in porous crystals at high stress triaxiality. It is found that, in order to retrieve a satisfactory accuracy for highly nonlinear porous crystals under high stress triaxiality, a quadrature formula of higher order is required.

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