A multi-scale model for coupled heat conduction and deformations of viscoelastic functionally graded materials

Khan, Kamran A.; Muliana, Anastasia

doi:10.1016/j.compositesb.2009.02.003

Cited by 40 publications

(14 citation statements)

References 30 publications

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“…Tsukamoto [11] analysed microstresses in FGMs on the basis of Eshelby's equivalent inclusion method and Mori-Tanaka's mean-field approximation; however, because this analysis evaluates volumetric average stresses in the matrix and dispersion phases, it cannot evaluate specific microstress distributions. Khan et al [12] performed coupled heat conduction and deformation analyses of viscoelastic FGMs using a simplified micromechanical model for particle reinforced composites; unfortunately, their micromechanical model also failed to incorporate the effect of stress concentration at the microscale. Note that these four studies did not consider the FGM microstructural morphology.…”

Section: Phase-a Particles With Phase-b Matrixmentioning

confidence: 99%

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Optimisation of material composition of functionally graded materials based on multiscale thermoelastic analysis

Chiba

Sugano

2012

Acta Mech

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This paper presents a method for optimisation of the material composition of functionally graded materials (FGMs) for thermal stress relaxation. This method consists of a multiscale thermoelastic analysis and a genetic algorithm. In the presented method, location-dependent unit cells representing the microstructures of two-phase FGMs are created using morphology description functions, and the homogenised material properties and microscale thermal stresses are computed using the asymptotic expansion homogenisation method. Thermal stress relaxation effects at the microscale in the FGMs are quantitatively evaluated, being reflected for the optimisation computation of the material composition. Numerical calculations are performed for a functionally graded infinite plate subjected to prescribed surface temperatures, and it is demonstrated that the optimisation with the knowledge of specific microstresses in FGMs results in not only a different trend of material composition distribution but also a different critical location for material failure from those obtained by conventional optimisation without the knowledge of the microstresses.

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Section: Phase-a Particles With Phase-b Matrixmentioning

confidence: 99%

“…The microscopic equations, Eqs. (11) and (12), are solved under periodic boundary conditions over the RME domain Y . To solve these equations for complex microstructures, a numerical method, e.g.…”

Section: Thermoelastic Problemmentioning

confidence: 99%

Optimisation of material composition of functionally graded materials based on multiscale thermoelastic analysis

Chiba

Sugano

2012

Acta Mech

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“…In order to analyze the heterogeneous structure in an efficient manner, it is necessary to have a homogenization scheme, which enables understanding of relationship between the effective properties of the FGMs and the microstructure (or distribution of volume factions of constituent phases). Many models have been developed to predict the effective properties of FGMs in two-dimensional domains for a specific volume fraction, including micromechanical models (Reiter, Dvorak, & Tvergaard, 1997;Yin, Sun, & Paulino, 2004;Zuiker, 1995), finite element methods (Chakraborty & Gopalakrishnan, 2003;Cho & Ha, 2001;Grujicic & Zhang, 1998;Kim & Paulino, 2002) and multi-scale approaches (Khan & Muliana, 2009;Tan et al, 2011). Recently, Wu, Meng, Liu, Li, and Huang (2014a) developed a homogenization method for random heterogeneous materials using Richardson extrapolation technique.…”

Section: Introductionmentioning

confidence: 99%

“…Wu, Nie, and Yang (2014b) proposed a semi-analytical, state-space method for surface instability study of elastic layers with varying properties in thickness direction. In these models (Chakraborty & Gopalakrishnan, 2003;Cho & Ha, 2001;Grujicic & Zhang, 1998;Khan & Muliana, 2009;Kim & Paulino, 2002;Reiter et al, 1997;Tan et al, 2011;Wu et al, 2014aWu et al, , 2014bYin et al, 2004;Zuiker, 1995), the material properties of each sub-layer need to be calculated and integrated into the model individually, which limits the computational efficiency and requires a convergence study to determine the minimum number of sub-layers that gives the required accuracy. Recently, Wang, Pan, Albrecht, and Feng (2009) proposed an efficient micromechanics approach, through which explicit expressions of the effective properties of magnetoelectric multiferroic multilayer composites can be obtained.…”

Section: Introductionmentioning

confidence: 99%

The effect of photodegradation on effective properties of polymeric thin films: A micromechanical homogenization approach

Zhang

Waksmanski

Wheeler

et al. 2015

International Journal of Engineering Science

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a b s t r a c tAn analytical model is developed to study the impact of photodegradation on the elastic properties of polymeric thin films. The multi-phase heterogeneous aged polymer material is considered as a two-phase functionally graded material with varying volume ratios as functions of both time and depth. The concentration gradations are obtained using a three-species chemical kinetic model with the kinetics being driven by light that is absorbed as it passes through the film. Concentration gradations are connected to the elastic stiffness through volume averaging and a micromechanics approach is employed to find effective properties of functionally graded composites. Concise matrix expressions of the effective properties are presented. The derived formulas are applied to study the effective responses of an aged simply-supported polymer film under surface loads. The obtained results are then compared with and validated by those from a multi-layer analytical model. The present formulas are also applied to predict the evolution of effective properties of a polymer thin film under photodegradation, and the variation of effective responses under surface loads. The present solution could be useful in studying the relation between polymer molecular structure and mechanical properties, and in the evaluation of long-term mechanical responses of polymeric structures.

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“…Though, there is no analytical solution for complicated constitutive models. In most researches, micro-macro approach is assumed to determine the homogenized viscoelastic response of a composite (Khan and Muliana, 2009), and then the deformation in the composite is measured at multiple length scales. There is no analytical and/or homogenization technique for studying complex geometries that is governed by advanced constitutive models.…”

Section: Introductionmentioning

confidence: 99%

Microstructure-Based Computational Modeling of Mechanical Behavior of Polymer Micro/Nano Composites

Tehrani¹

2013

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The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Lightweight advanced materials are critical in the manufacturing of many Army vehicles. Recently, numerical tools have been utilized to customize experiments to achieve optimized behavior of micro/nano polymer composites (MNPCs). Most numerical studies are based on characterizing the MNPCs through simple microstructures, as circular particles or straight fibers embedded in a specific polymer matrix. Although these geometries are effective in virtually modeling some types of composite material behavior, they fail to address some critical key Names of Under Graduate students supportedPERCENT_SUPPORTED NAME FTE Equivalent:Total Number:The number of undergraduates funded by this agreement who graduated during this period with a degree in science, mathematics, engineering, or technology fields:The number of undergraduates funded by your agreement who graduated during this period and will continue to pursue a graduate or Ph.D. degree in science, mathematics, engineering, or technology fields:Number of graduating undergraduates who achieved a 3.5 GPA to 4.0 (4.0 max scale): Number of graduating undergraduates funded by a DoD funded Center of Excellence grant for Education, Research and Engineering:The number of undergraduates funded by your agreement who graduated during this period and intend to work for the Department of DefenseThe number of undergraduates funded by your agreement who graduated during this period and will receive scholarships or fellowships for further studies in science, mathematics, engineering or technology fields: Student Metrics This section only applies to graduating undergraduates supported by this agreement in this reporting periodThe number of undergraduates funded by this agreement who graduated during this period: 0.00 ...... Names of Personnel receiving masters degrees Inventions (DD882) Scientific ProgressBecause the mechanical responses of polymers and many types of polymer composites are in the large deformation range, the Eulerian or Lagrangian concept is required for measuring the stress and strain. On the other hand, developing a large deformation based constitutive model requires a number of considerations, and should be performed from a thermodynamics point of view to study the motion of each component of the material. Even though such approach is precise and physically sound, it is limited to just one type of material. Furthermore, polymers show high dependency to the rate and time of the applied load; hence, employing viscoelastic, viscoplastic and viscodamage models is necessary. To address these issues, a consistent framework is developed to generalize elastic/viscoelastic and plastic/viscoplastic models from small strain to the large deformation range. The developed continuum based app...

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A multi-scale model for coupled heat conduction and deformations of viscoelastic functionally graded materials

Cited by 40 publications

References 30 publications

Optimisation of material composition of functionally graded materials based on multiscale thermoelastic analysis

Optimisation of material composition of functionally graded materials based on multiscale thermoelastic analysis

The effect of photodegradation on effective properties of polymeric thin films: A micromechanical homogenization approach

Microstructure-Based Computational Modeling of Mechanical Behavior of Polymer Micro/Nano Composites

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