Efficient Reformulation of the Thermoelastic Higher-Order Theory for Functionally Graded Materials

Bansal, Yogesh; Pindera, Marek‐Jerzy

doi:10.1080/714050872

Cited by 65 publications

(16 citation statements)

References 32 publications

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“…Then, using (81), (76), (78), (11), (77), we obtain (4), (5), (6), where g is defined by (7). We assume that the material is non-homogeneous, in the sense that all material parameters depend on the coordinates x and y.…”

Section: Appendix Amentioning

confidence: 99%

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Biaxial Loading of Continuously Graded Thermoviscoplastic Materials

2006

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In this paper we study the problem of biaxial loading of a sheet made of a continuously graded thermoviscoplastic material. The material phases are supposed to exhibit thermal softening, strain-rate sensitivity and strain hardening, continuously varying along all directions. First we formulate the plane stress problem of a non-homogeneous material and study the behavior of temperature, strain and strain-rate related to inhomogeneities of thermomechanical parameters and geometrical defects. Next we present the "effective" instability analysis of Dudzinski and Molinari (Int J Solids Struc 1991), adapted to the non-homogeneous case, to define the critical conditions and select the localization modes by studying the overall strains for which a certain level of instability growth is developed. Finally, we present the numerical simulation of the fully non-linear dynamical problem. Several aspects of the deformation process and the related role of non-homogeneities are analyzed: onset of strain and temperature localization, ductility, contours of temperature increase as detectors of instability, interplay with initial defects, multiple necking, decrease of thinning-rate, variation of the multiple necking due to boundary conditions.

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Section: Appendix Amentioning

confidence: 99%

“…Recently, Bansal and Pindera [6,7] have shown that the "higher-order theory", introduced in [2,3] for functionally graded materials, is in fact a simple finite-volume direct averaging micromechanics approach. These materials are expected to show superior properties for high temperature resistance.…”

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confidence: 99%

Biaxial Loading of Continuously Graded Thermoviscoplastic Materials

2006

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“…An attractive alternative to the finite-element method in the solution of periodic repeating unit cell (RUC) problems is the parametric finite-volume theory developed by Cavalcante et al 7 having as basis the original version constructed by Bansal and Pindera 8 . In that parametric version the heterogeneous material microstructure is discretized using quadrilateral subvolumes which are mapped into corresponding reference square subvolumes.…”

Section: Introductionmentioning

confidence: 99%

A model for evaluation of effective thermal conductivity of periodic composites with poorly conducting interfaces

Filho

Marques

2014

Mat. Res.

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This paper presents a new micromechanical extension of the parametric finite-volume theory for evaluation of effective thermal conductivities of periodic unidirectional fiber reinforced composites. Such materials are assumed as composed of repeating unit cells with arbitrary internal architectural arrangements of fiber coated by thin interphase with low thermal conductivity. The parametric homogenization approach uses quadrilateral subvolumes for discretization of the repeating unit cell microstructure, thereby allowing an efficient modeling of the details of fibers with arbitrarily shaped cross sections. The interphases are replaced by imperfect interface elements with continuity in normal heat flux and discontinuity in temperature. The performance of the homogenization model is demonstrated for several numerical examples, including two-and three-phase composites with regular squared and hexagonal arrays of fibers. The ability of the model to accurately predict the effective thermal conductivity of those composites is demonstrated by means of comparisons of results obtained using finite-element and analytical solutions.

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“…This method can of course be used to "tailor" (design) new materials with enhanced properties by averaging in a clever (but very heterogeneous) way simple phases. It has been often described (and sometimes revisited) in the mechanical literature and here again giving a complete list is impossible; let us mention Suquet (1982), Francfort, Leguillon and Suquet (1983), Francfort, Nguyen andSuquet (1983), Hashin (1983), Suquet (1983), Maugin (1992), Aboudi et al (1999), Ghosh et al (2001), Bansal and Pindera (2003), Michel and Suquet (2004), Alshirts and Maugin (2005), Bansal and Pindera (2005), Bardzokas and Zobnin (2005), Guinovart-Diaz et al (2005), Suquet (2005), Idiart et al (2006)). In particular, the concept of "homogeneous equivalent continuum" (Maugin (1992)) has been used to predict the macroscopic response from microscopic analyses by replacing the macroscopic heterogeneous medium, represented by an element called "representative volume element", by a continuum model (see Van der Sluis et al (1999), where a numerical homogenization technique has been proposed, which offers the possibility to determine the effective properties of a viscoplastic constitutive model).…”

Section: Introductionmentioning

confidence: 99%

Stability by Homogenization of Thermoviscoplastic Problems

Charalambakis

Murat

2010

Math. Models Methods Appl. Sci.

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Abstract.In this paper we study the homogenization of the system of partial differential equations describing the quasistatic shearing of heterogeneous thermoviscoplastic materials. We first prove the existence and uniqueness of the solution of the system for the general model. We then define "stable by homogenization" models as the models where the equations in both the heterogeneous problems and the homogenized one are of the same form.Finally we show that three types of models, all three with non oscillating strain-rate sensitivity, are stable by homogenization: the viscoplastic model, the thermoviscous model and the thermoviscoplastic model under steady boundary shearing and body force. In these three models, the homogenized (effective) coefficients depend on the initial conditions, and, in the case of the thermoviscoplastic model, also on the boundary shearing and body force. Ces résultats théoriques sont illustrés par des exemples numériques.

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Efficient Reformulation of the Thermoelastic Higher-Order Theory for Functionally Graded Materials

Cited by 65 publications

References 32 publications

Biaxial Loading of Continuously Graded Thermoviscoplastic Materials

Biaxial Loading of Continuously Graded Thermoviscoplastic Materials

A model for evaluation of effective thermal conductivity of periodic composites with poorly conducting interfaces

Stability by Homogenization of Thermoviscoplastic Problems

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