Academic literature on the topic 'Ellipsoidal viscoelastic inclusion'

The self-consistent (SC) micromechanical model of a composite containing coated micro-inclusions, originally proposed in the static regime by Cherkaoui et al. (1994, J. Eng. Mater. Technol., 116, 274–278), is implemented in the quasistatic regime by the introduction of frequency dependent complex moduli for the matrix material. The original model is improved by using dilute strain concentration tensor (DSCT) formulation. It is shown that these concentration tensors can be used to approximate effective composite behavior of composites containing ellipsoidal inclusions having a known orientation distribution or of composites containing multiple types of coated inclusions. The DSCT formulation is also shown to be capable of modeling the effects of multiple scales (submicron-meso-macro), as well as that of a distribution of inclusion coating thicknesses. Various potential material modeling applications are verified through comparison with experimental data in the literature. Notably, the DSCT SC model is applied in the quasistatic regime for calculation of acoustic transmission loss of a slab of viscoelastic composite submerged in water for the range of frequencies between 0-100kHz and compared with experimental data of Baird et al. (1999, J. Acoust. Soc. Am., 105, 1527–1538).

Approximations for frequency-dependent and complex-valued effective stiffness tensors of cracked porous media (saturated with a single fluid) are developed on the basis of an inclusion-based model (the T-matrix approach to rock physics) and a unified treatment of the global-flow and squirt-flow mechanisms. Essentially, this study corrects an inconsistency or error related to fluid-mass conservation in an existing expression for the t-matrix (wave-induced deformation) of a communicating cavity, a cavity that is isolated with respect to stress propagation (through the solid matrix) but that can exchange fluid mass with other cavities because of global and/or local pressure gradients associated with passage of a long viscoelastic wave. An earlier demonstration of Gassmann consistency remains valid because the new theory of global flow and squirt flow (which also takes into account solid mechanical effects of stress interaction by us-ing products of communicating t-matrices associated with two-point correlation functions of ellipsoidal symmetry) only differs from an earlier version by a correction term that goes to zero in the low-frequency limit. If the unified model is applied to the special case of a model involving a single set of spheroidal cavities (having the same aspect ratio and orientation), the results become identical with those obtained using a special theory of global flow that predicts that at zero frequency the cavities will behave as though they are isolated with respect to wave-induced fluid flow (in accordance with Gassmann’s formulas) and that at high frequencies, they will behave as though they are dry. Our theory predicts that there will be a continuous transition from a global-flow-dominated system (characterized by a negative velocity dispersion) to a squirt-flow-dominated system (characterized by a positive velocity dispersion) if one begins with a single set of cavities and then introduces a distribution of shapes and/or orientations that gradually becomes wider (more realistic).

Study on viscoelastic properties of the multi-layered coarse-grained soil (CGS) is very important for safety assessment and disaster prevention of subgrade engineering. Current research work is mainly focused on the one-layered CGS and the actual pebble inclusion of irregular polyhedron is usually simplified as an ideal shape of sphere or ellipsoid. Very few studies are available for predicting viscoelastic parameters of the multi-layered CGS. In this paper, a new method is proposed to predict viscoelastic parameters of multi-layered CGS based on the homogenization method and elastic–viscoelastic corresponding principle, in which the interface-layer viscoelasticity and the actual shape of pebble inclusion are firstly taken into account. Research results show the creep deformation is decreased with the increase of the shape factor (ρ) of pebble inclusion, and the interface-layer height (h) and numbers (N). ρ is in the range of 1–1.8 and the suitable interface-layer height is 20–30% as much as the height of one-layered CGS. The tested creep curves of the multi-layered CGS agree well with the predicted ones and can prove the existence of the interface-layer (considering at least one interface-layer) and verify the validity of this new interface-layer method.

The present work extends the multicoated micromechanical model of Lipinski et al. (2006, “Micromechanical Modeling of an Arbitrary Ellipsoidal Multi-Coated Inclusion,” Philos. Mag., 86(10), pp. 1305–1326) in the quasistatic domain to compute the effective material moduli of a viscoelastic material containing multicoated spherical inclusions displaying elastic or viscoelastic behavior. Losses are taken into account by introducing the frequency-dependent complex stiffness tensors of the viscoelastic matrix and the multicoated inclusions. The advantage of the micromechanical model is that it is applicable to the case of nonspherical multicoated inclusions embedded in anisotropic materials. The numerical simulations indicate that with proper choice of material properties, it is possible to engineer multiphase polymer system to have a high-loss modulus (good energy dissipation characteristics) for a wide range of frequencies without substantially degrading the stiffness of the composite (storage modulus). The numerical analyses show also that with respect to the relative magnitudes of the loss factors and the storage moduli of the matrix, inclusion and coating, the overall properties of the viscoelastic particulate composite are dominated by the properties of the matrices in some frequency ranges. The model can thus be a suitable tool to explore a wide range of microstructures for the design of materials with high capacity to absorb acoustic and vibrational energies.

L'objectif principal de la thèse consiste à développer une approche micromécanique pour prédire le comportement viscoélastique macroscopique des matériaux hétérogènes à partir des propriétés locales des constituants et de leur microstructure. Les propriétés viscoélastiques effectives sont obtenues par l'utilisation des méthodes d'homogénéisation à champ moyen appropriées. L'approche micromécanique proposée est basée sur une loi constitutive fonctionnelle ayant la forme d'une intégrale de Volterra. Dans un premier temps, nous obtenons une formulation micromécanique à variables internes développée avec le module de relaxation. Dans un autre temps, nous développons une deuxième approche micromécanique cette fois-ci écrite avec le module de fluage, consistant à la formulation duale à la première. À l'aide des techniques des fonctions de Green, nous établissons, dans les deux cas, une équation intégrale décrivant le problème viscoélastique hétérogène. Cette équation principale fait apparaître un terme intégral de volume difficile à évaluer directement, ce qui nous amène à construire une deuxième équation intégrale complémentaire venant s'ajouter à la première. Cette formulation générale définie par ces deux équations intégrales est appliquée au problème classique de l'inclusion viscoélastique d'Eshelby. La solution exacte du problème est obtenue dans le cas d'une morphologie ellipsoïdale arbitraire de l'inclusion ayant un comportement viscoélastique anisotrope et plongée dans une matrice viscoélastique isotrope. Nous utilisons une méthode à variables internes qui considère que l'histoire du matériau est contenue dans son état interne. La résolution de l'approche directement dans l'espace-temps nous conduit à une solution exacte avec un gain appréciable de temps de calcul, en comparant avec les résultats obtenus par les approches héréditaires, traitées dans l'espace de Laplace-Carson. Les deux formulations proposées permettent d'évaluer l'effet du comportement anisotrope et de la morphologie ellipsoïdale des inclusions, tout en permettant également d'étudier l'influence du vieillissement sur le comportement mécanique du composite. Les deux modèles obtenus présentent des résultats cohérents avec ceux disponibles dans la littérature, en permettant un gain de calcul intéressant par rapport aux méthodes existantes
The primary aim of this thesis is to devise a novel micromechanical approach for predicting the macroscopic viscoelastic response of heterogeneous materials. The behavior is achieved through micromechanical modeling that is based on local properties and microstructure. The effective viscoelastic properties are obtained by the use of appropriate mean-field homogenization methods. The mechanical approach is based on a Volterra integral-form functional constitutive law. Firstly, a new internal variable micromechanical formulation is obtained by utilizing the relaxation modulus. Secondly, a second micromechanical approach is developed, which employs the creep modulus and consists to the dual formulation. Using Green's function techniques, we derive integral equations that describe the heterogeneous viscoelastic problem for both cases. The main equation contains a challenging volume integral term, which necessitates the development of a second complementary integral equation. These two integral equations form the general formulation that we apply to the classical Eshelby viscoelastic inclusion problem. We employ an internal variable method that considers the material's history to be contained in its internal state. The approach is solved directly in the time domain, resulting in an exact solution with reduced computation time compared to hereditary approaches processed in the Laplace-Carson space. Our model enables us to evaluate the impact of anisotropic inclusions and to examine the influence of aging behavior on the composite viscoelastic properties. Both approaches proposed in this thesis deliver results that are consistent with those reported in the literature and offer a significant computational advantage over existing methods