Fully coupled heat conduction and deformation analyses of nonlinear viscoelastic composites Kamran A. Khan a,⇑ , Anastasia H. Muliana b a Computational Solid Mechanics Laboratory (CSML), Division of Physical Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia b Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA article info Article history: Available online 16 January 2012 Keywords: Coupled thermoviscoelasticity Particulate composites Dissipation in composites Heat generation Conduction Cyclic loading abstract This study presents an integrated micromechanical model-finite element framework for analyzing coupled heat conduction and deformations of particle-reinforced composite structures. A simplified micromechan- ical model consisting of four sub-cells, i.e., one particle and three matrix sub-cells is formulated to obtain the effective thermomechanical properties and micro–macro field variables due to coupled heat conduc- tion and nonlinear thermoviscoelastic deformation of a particulate composite that takes into account the dissipation of energy from the viscoelastic constituents. A time integration algorithm for simulta- neously solving the equations that govern heat conduction and thermoviscoelastic deformations of isotro- pic homogeneous materials is developed. The algorithm is then integrated to the proposed micromechanical model. A significant temperature generation due to the dissipation effect in the visco- elastic matrix was observed when the composite body is subjected to cyclic mechanical loadings. Heat con- duction due to the dissipation of the energy cannot be ignored in predicting the factual temperature and deformation fields within the composite structure, subjected to cyclic loading for a long period. A higher creep resistant matrix material or adding elastic particles can lower the temperature generation. Our anal- yses suggest that using particulate composites and functionally graded materials can reduce the heat gen- eration due to energy dissipation. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Polymer matrix composites have been utilized in various engi- neering applications due to their light weight characteristics and low cost manufacturing; however they exhibit significant time- dependent behaviors when exposed to coupled mechanical and non-mechanical effects, such as diffusion of a fluid, heat conduc- tion, chemical reactions that affect their overall mechanical proper- ties. To reduce complexity in analyzing the response of composites, the interactions of the different field variables are often ignored and the governing equations of the diffusion and deformation are solved independently. This approach can lead to sensible response predic- tions when the effect of field coupling on the overall performance of composites is insignificant. Viscoelastic materials are considered as dissipative materials and during the deformation significant heat could be generated, increasing the temperature of the viscoelastic bodies, and elevated temperatures accelerate creep deformation and/or stress relaxation in the body, leading to a fully coupled thermo-mechanical response. For example, under dynamics and impact loadings polymer composites experiences pronounced heat generation. When a quasi-static cyclic loading is applied to a visco- elastic body over a long period of time a considerable amount of heat is generated. This proposition has been supported by the experimental results of Schapery and Cantey [32], Tauchert [35], Rittel [31], Luukkonen et al. [23], and Weng et al. [36]. In designing composite structures, it is necessary to determine the macroscopic effective properties of the composite and under- stand responses of the constituents when the composite are sub- jected to various external stimuli. Conducting experiments to obtain the effective response of composites under various loading histories and at different compositions and properties of the constit- uents is often costly and time consuming. In some cases it is chal- lenging or impractical to perform experiments on determining coupled thermoviscoelastic behavior of composite structures. Mod- eling response of composites that include detailed microstructural characteristics allows obtaining macroscopic response of the struc- tural components and detailed response of the constituents. Thus, several micromechanical models with simplified microstructural morphologies have been developed to predict the effective response of composites and their microstructural behaviors. Examples are: linear thermoelasticity [11,13]; linear viscoelastic responses of composites, e.g. Brinson and co-authors [6], Brinson and Lin [7], Li 0263-8223/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2012.01.010 ⇑ Corresponding author. E-mail address: kamran.khan@kaust.edu.sa (K.A. Khan). Composite Structures 94 (2012) 2025–2037 Contents lists available at SciVerse ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct