This study introduces a multiscale model for analyzing nonlinear thermo-viscoelastic responses of particulate composites. A simplified micromechanical model consisting of four sub-cells, i.e., one particle and three matrix sub-cells is formulated to obtain the effective thermal and mechanical properties and time-dependent response of the composites. The particle and matrix constituents are made of isotropic homogeneous viscoelastic bodies undergoing small deformation gradients. Perfect bonds are assumed along the sub-cell⁰́₉s interfaces. The coupling between the thermal and mechanical response is attributed to the dissipation of energy due to the viscoelastic deformation and temperature dependent material parameters in the viscoelastic constitutive model. The micromechanical relations are formulated in terms of incremental average field quantities, i.e., stress, strain, heat flux and temperature gradient, in the sub-cells. The effective mechanical properties and coefficient of thermal expansion are derived by satisfying displacement- and traction continuities at the interfaces during the thermo-viscoelastic deformations. The effective thermal conductivity is formulated by imposing heat flux- and temperature continuities at the subcells⁰́₉ interfaces. The expression of the effective specific heat at a constant stress is also established. A time integration algorithm for simultaneously solving the equations that govern heat conduction and thermoviscoelastic deformations of isotropic materials is developed. The algorithm is then incorporated within each sub-cell of the micromechanical model together with the macroscopic energy equation to determine the effective coupled thermoviscoelastic response of the particulate composite. The numerical formulation is implemented within the ABAQUS, general purpose displacement based FE software, allowing for analyzing coupled heat conduction and deformations of composite structures. Experimental data on the effective thermal properties and time dependent responses of particulate composites available in the literature are used to verify the micromechanical model formulation. The multiscale model capability is also examined by comparing the field variables, i.e., temperature, displacement, stresses and strains, obtained from heterogeneous and homogeneous composite structures, during the transient heat conduction and deformations. Examples of coupled thermoviscoelastic analyses of particulate composites and functionally graded structures are also presented. The present micromechanical modeling approach is found to be computationally efficient and shows good agreement with experiments in predicting the effective thermo-mechanical response of particulate composites and functionally graded materials. Our analyses forecast a better design for creep resistant and less dissipative structures using particulate composites and functionally graded materials.

<div>Polymer matrices present in composite materials are prone to have time-dependent behavior very sensitive to changes in temperature. The modeling of thermoviscoelasticity is fundamental for capturing the performance of anisotropic viscoelastic materials subjected to both mechanical and thermal loads, or for manufacturing simulation of composites. In addition, improved plate/shell and beam models are required to efficiently design and simulate large anisotropic composite structures. Numerical models have been extensively used to capture the linear viscoelasticity in composites, which can be generalized in integral or differential forms. The hereditary integral constitutive form has been adopted by many researchers to be implemented into finite element codes, but its formulation is complex and time consuming as it is function of the time history. The differential formulation provides faster computation times, but its applicability has been limited to capture the behavior of three-dimensional thermoviscoelastic orthotropic materials.</div><div><br></div><div>This work extends mechanics of structure genome (MSG) to construct linear thermoviscoelastic solid, plate/shell and beam models for multiscale constitutive modeling of three-dimensional heterogeneous materials made of time and temperature dependent constituents. The formulation derives the transient strain energy based on integral formulation for thermorheologically simple materials subject to finite temperature changes. The reduced time parameter is introduced to relate the time-temperature dependency of the anisotropic material by means of master curves at reference conditions. The thermal expansion creep is treated as inherent material behavior. Exact three-dimensional thermoviscoelastic homogenization solutions are also formulated for laminates modeled as an equivalent, homogeneous, anisotropic solid. The new model is implemented in SwiftComp, a general-purpose multiscale constitutive modeling code based on MSG, to handle real heterogeneous materials with arbitrary microstructures, mesostructures or cross-sectional shapes.</div><div><br></div><div>Three-dimensional representative volume element (RVE) analyses and direct numerical simulations using a commercial finite element software are conducted to verify the accuracy of the MSG-based constitutive modeling. Additionally, MSG-based plate/shell results are validated against thin-ply high-strain composites experimental data showing good agreement. Numerical cases with uniform and nonuniform cross-sectional temperature distributions are studied. The results showed that unlike MSG, the RVE method exhibits limitations to properly capture the long-term behavior of effective coefficients of thermal expansion (CTEs) when time-dependent constituent CTEs are considered. The analyses of the homogenized properties also revealed that despite the heterogeneous nature of the composite material, from a multiscale analysis perspective, the temperature dependencies of the effective stiffness and thermal stress properties are governed by the same shift factor as the polymer matrix. This conclusion remains the same for MSG-based solid, plate/shell and beam models with uniform temperature distributions.</div>

Conselho Nacional de Desenvolvimento Científico e Tecnológico / In the present work, a methodology for numerical simulation of self-heating phenomenon in viscoelastic materials has been developed, with the aim of proposing and validating finite element models that can be applied to predict the thermomechanical behaviour of structures including viscoelastic materials. The model takes into account the dependence of the mechanical characteristics of the viscoelastic material with respect to frequency and temperature and allows to obtain the transient temperature field. For this purpose, the heat source calculation is computed based on the dissipated energy obtained from the harmonic response calculation as the structure is submitted to cyclic loading. The validation of the model and the adjustment of two initially unknown parameters, namely the film coefficient for natural heat convection and the ratio of the heat source over the mechanical power dissipated through viscoelastic effects, were carried out by comparison of the model-predicted responses to experimental results counterparts, the latter being obtained by the application of a cyclic load to a sample specimen by means of a universal test machine, and measuring the temperatures within the viscoelastic material of the dispositive using thermocouples. A curve-fitting procedure was developed using an optimization routine, in order to identify optimal set of values of h and b. For each test, the experimental results were compared to those obtained from the numeric model after the identification, thus allowing the evaluation of the accuracy and limitations of the proposed model procedure. / Neste trabalho foi desenvolvida uma metodologia de simulação numérica do fenômeno de auto-aquecimento, tendo como objetivo a realização e a validação de um modelo a ser aplicado à predição do comportamento termomecânico de estruturas incluindo materiais viscoelásticos. O modelo de elementos finitos proposto leva em conta a dependência das propriedades mecânicas do material viscoelástico com relação à frequência e temperatura, e permite a obtenção do campo de temperatura em regime transitório. O cálculo da fonte de calor é baseado na energia de dissipação viscoelástica obtida por meio da resposta em regime harmônico da estrutura submetida a um carregamento cíclico. A validação do modelo proposto e o ajuste de dois parâmetros inicialmente desconhecidos, a saber, o coeficiente de transferência de calor por convecção natural e a razão da fonte de calor pela energia decorrente da dissipação viscoelástica, foram efetuados via confrontação com resultados experimentais, estes sendo obtidos aplicando-se cargas cíclicas sobre um corpo de prova por meio de uma máquina universal de ensaios e registrando a temperatura no material viscoelástico do dispositivo com auxílio de termopares. Um procedimento de ajuste de curvas via uma rotina de otimização foi desenvolvido para a identifição dos parâmetros. Para cada ensaio, os resultados experimentais e os correspondentes obtidos com o modelo numérico após a identificação foram comparados, permitindo avaliar a precisão e as limitações do procedimento de modelagem proposto. / Mestre em Engenharia Mecânica

Fundação de Amparo a Pesquisa do Estado de Minas Gerais / This work is dedicated to the development of a strategy for numerical-computational modeling and experimental verification of the self-heating phenomenon in viscoelastic materials with emphasis on the thermal runaway phenomenon taking into account the combined effects of dynamic loads and static preloads. The methodology of modeling by finite element allows us to consider the influence of frequency, temperature and static preload on the self-heating phenomenon of the linear viscoelastic materials. For this purpose, modifications are made that allow thermomechanical analysis of more complex viscoelastic structures, in addition the evaluation of introducing metal inserts in bulk material for reducing effects of self-heating. The validation of the proposed model and the identification of the physical parameters of thermal efficiency and heat transfer by natural convection, initially unknown, are obtained by comparison of the results of numerical simulations with the corresponding obtained through experimental tests for a specimen formed by a translational viscoelastic joint. The curve-fitting procedure is formulated as an inverse optimization problem through use of the Firefly Algorithm for minimizing the objective function defined as the square difference between the temperatures obtained from the simulations and the corresponding generated by the tests for each time instant. The accuracy and limitations of the model are evaluated by comparing the experimental and simulated temperature profile, allowing to verify the numerical evidence and the qualitative consistence of the results obtained with reported in the literature for the thermal runaway phenomenon for simple devices without effect preload. / Este trabalho é dedicado ao desenvolvimento de uma estratégia de modelagem numéricocomputacional e verificação experimental do fenômeno do autoaquecimento de materiais viscoelásticos com ênfase no fenômeno da fuga térmica levando-se em conta os efeitos combinados de cargas dinâmicas e pré-cargas estáticas. A metodologia de modelagem por elementos finitos permite considerar a influência da frequência, da temperatura e da pré-carga estática no fenômeno do autoaquecimento de materiais viscoelástico lineares. Para tanto, são feitas modificações que permitem a análise termomecânica de estruturas viscoelásticas mais complexas, além da avaliação da introdução de insertos metálicos no volume do material para a redução dos efeitos do autoaquecimento. A validação do modelo proposto e a identificação dos parâmetros físicos de rendimento térmico e de transferência de calor por convecção natural incialmente desconhecidos, são obtidos através da confrontação dos resultados das simulações numéricas com os correspondentes obtidos via ensaios experimentais para um corpo de prova formado por uma junta viscoelástica translacional. O procedimento de ajuste de curvas é formulado como um problema inverso de otimização via emprego da técnica Colônia de Vagalumes para a minimização da função objetivo definida como sendo a diferença quadrática entre as temperaturas obtidas das simulações e as correspondentes geradas pelos ensaios para cada instante de tempo. A precisão e as limitações do modelo são avaliadas pela comparação dos perfis simulados e experimentais de temperatura, possibilitando confirmar as evidências numéricas e a consistência qualitativa dos resultados obtidos com o reportado na literatura para o fenômeno da fuga térmica para dispositivos mais simples e sem o efeito da pré-carga. / Mestre em Engenharia Mecânica

L’apparition massive de nids de poule sur chaussées bitumineuses a été observée en cours d’hiver sur de très courtes périodes de temps, caractérisées par l’alternance entre températures positives et fortement négatives accompagnée de précipitations pluvieuses. Ceci a conduit à rechercher un mécanisme spécifique de dégradation de couches d’enrobés bitumineux (EB) lié au comportement au gel des EB partiellement saturés en eau. Celui-ci a été étudié en laboratoire à partir d’essais à déformation libre ou empêchée, avec ajout de chaux pour certaines formules d’EB.Ces essais ont montré l’apparition de déformations de gonflement ou contraintes importantes induites lors du gel de l’eau interstitielle. D’autres essais utilisant l’IRM ont permis de visualiser le phénomène au sein du matériau. Sur la base de ces essais, nous proposons une loi de comportement thermoviscoélastique avec changement de phase pour EB. Un programme aux éléments finis a été développé (Free Fem++)pour intégrer cette loi dans le calcul de structures ; ce code couple les équations mécaniques et de diffusion de la chaleur prenant également en compte le changement de phase à travers la chaleur latente de solidification de l’eau interstitielle.Après validation du logiciel, celui-ci a été appliqué au calcul de structures bitumineuses bicouches représentatives des couches supérieures d’une chaussée. Les résultats mettent alors en évidence l’apparition de contraintes d’arrachement élevées à l’interface entre couches générées par le gel,susceptibles d’expliquer la formation de nids de poule. Un essai de laboratoire sur bicouche a confirmé la fragilisation de l’interface induite dès le premier cycle de gel. / Massive development of potholes occurring in bituminous pavements was observed during winters over short time laps characterized by temperature alternating between positive and highly negative values along with rainfalls. This led us to seek for a specific mechanism of degradation of asphalt concrete (AC) layers, related to the behavior of partially saturated AC subjected to freeze. Two types of laboratory tests were performed under traction free and restrained strain conditions to study the behavior of AC within this context, incorporating lime additive in some mix design formulations. These tests showed the development of large swelling strains or stresses induced by the phase change of pore water into ice. Additional tests using MRI allowed us to visualize this phenomenon from inside the material specimens. Based on these tests, we developed a thermoviscoelastic constitutive law including phase change for partially saturated AC. A Finite Element (FE) program was implemented (FreeFem++) to introduce the developed law instructural calculations; this FE code handles the coupling between mechanics and the heat equation, also taking into account the phase change through the latent heat of crystallization of pore water. After validating the software, this numerical tool was utilized to compute the response of bilayer bituminous structures representative of the upper layers of a pavement. The results obtained show the development of highfrost-induced pull-out stresses located at the interface between the layers, likely to explain the formation of potholes. A test carried out on a bilayer sample confirmed the weakening of the interface right after the first frost cycle.

Dans cette thèse, tout d’abord, nous faisons l’Analyse Mathématique du modèle exact du chauffage radiatif d’un corps semi-transparent $\Omega$ par une source radiative noire qui l’entoure. Il s’agit donc d’étudier le couplage d’un système d’Equations de Transfert Radiatif avec condition au bord de réflectivité indépendantes avec une équation de conduction de la chaleur non linéaire avec condition limite non linéaire de type Robin. Nous prouvons l’existence et l’unicité de la solution et nous démontrons des bornes uniformes sur la solution et les intensités radiatives dans chaque bande de longueurs d’ondes pour laquelle le corps est semi-transparent, en fonction de bornes sur les données, Deuxièmement, nous considérons le problème du contrôle optimal de la température absolue à l’intérieur du corps semi-transparent $\Omega$ en agissant sur la température absolue de la source radiative noire qui l’entoure. À cet égard, nous introduisons la fonctionnelle coût appropriée et l’ensemble des contrôles admissibles $T_{S}$, pour lesquels nous prouvons l’existence de contrôles optimaux. En introduisant l’espace des états et l’équation d’état, une condition nécessaire de premier ordre pour qu’un contrôle $T_{S}$ : t ! $T_{S}$ (t) soit optimal, est alors dérivée sous la forme d’une inéquation variationnelle en utilisant le théorème des fonctions implicites et le problème adjoint. Ensuite, nous considérons le problème de l’existence et de l’unicité d’une solution faible des équations de la thermoviscoélasticité dans une formulation mixte de type Hellinger- Reissner, la nouveauté par rapport au travail de M.E. Rognes et R. Winther (M3AS, 2010) étant ici l’apparition de la viscosité dans certains coefficients de l’équation constitutive, viscosité qui dépend dans ce contexte de la température absolue T(x, t) et donc en particulier du temps t. Enfin, nous considérons dans ce cadre le problème du contrôle optimal de la déformation du corps semi-transparent $\Omega$, en agissant sur la température absolue de la source radiative noire qui l’entoure. Nous prouvons l’existence d’un contrôle optimal et nous calculons la dérivée Fréchet de la fonctionnelle coût réduite. / This thesis begins with a rigorous mathematical analysis of the radiative heating of a semi-transparent body made of glass, by a black radiative source surrounding it. This requires the study of the coupling between quasi-steady radiative transfer boundary value problems with nonhomogeneous reflectivity boundary conditions (one for each wavelength band in the semi-transparent electromagnetic spectrum of the glass) and a nonlinear heat conduction evolution equation with a nonlinear Robin boundary condition which takes into account those wavelengths for which the glass behaves like an opaque body. We prove existence and uniqueness of the solution, and give also uniform bounds on the solution i.e. on the absolute temperature distribution inside the body and on the radiative intensities. Now, we consider the temperature $T_{S}$ of the black radiative source S surrounding the semi-transparent body $\Omega$ as the control variable. We adjust the absolute temperature distribution (x, t) 7! T(x, t) inside the semi-transparent body near a desired temperature distribution Td(·, ·) during the time interval of radiative heating ]0, tf [ by acting on $T_{S}$. In this respect, we introduce the appropriate cost functional and the set of admissible controls $T_{S}$, for which we prove the existence of optimal controls. Introducing the State Space and the State Equation, a first order necessary condition for a control $T_{S}$ : t 7! $T_{S}$ (t) to be optimal is then derived in the form of a Variational Inequality by using the Implicit Function Theorem and the adjoint problem. We come now to the goal problem which is the deformation of the semi-transparent body $\Omega$ by heating it with a black radiative source surrounding it. We introduce a weak mixed formulation of this thermoviscoelasticity problem and study the existence and uniqueness of its solution, the novelty here with respect to the work of M.E. Rognes et R. Winther (M3AS, 2010) being the apparition of the viscosity in some of the coefficients of the constitutive equation, viscosity which depends on the absolute temperature T(x, t) and thus in particular on the time t. Finally, we state in this setting the related optimal control problem of the deformation of the semi-transparent body $\Omega$, by acting on the absolute temperature of the black radiative source surrounding it. We prove the existence of an optimal control and we compute the Fréchet derivative of the associated reduced cost functional.