On the thermostatics of composite materials

Laws, Norman

doi:10.1016/0022-5096(73)90027-6

Cited by 164 publications

(96 citation statements)

References 9 publications

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“…Second, the pore pressure p is applied and the mean stresses σ ′′ Y and mean strains ε ′′ Y are developed. The application of Levin's theorem [44][45][46] provides the following relation:…”

Section: Localizationmentioning

confidence: 99%

Uncertainty propagation of a multiscale poromechanics-hydration model for poroelastic properties of cement paste at early-age

Venkovic¹,

Sorelli²,

Sudret³

et al. 2013

Probabilistic Engineering Mechanics

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The durability of concrete materials with regard to early-age volume changes and cracking phenomena depends on the evolution of the poroelastic properties of cement paste. The ability of engineers to control the uncertainty of the percolation threshold and the evolution of the elastic modulus, the Biot-Willis parameter and the skeleton Biot modulus is key for minimizing the vulnerability of concrete structures at early-age. This work presents original results on the uncertainty propagation and the sensitivity analysis of a multiscale poromechanics-hydration model applied to cement pastes of water-to-cement ratio of 0.40, 0.50 and 0.60. Notably, the proposed approach provides poroelastic properties required to model the behavior of partially saturated aging cement pastes (e.g. autogenous shrinkage) and it predicts the percolation threshold and undrained elastic modulus in good agreement with experimental data. The development of a stochastic metamodel using polynomial chaos expansions allows to propagate the uncertainties of kinetic parameters of hydration, cement phase composition, elastic moduli and morphological parameters of the microstructure. The presented results show that the propagation does not magnify the uncertainty of the single poroelastic properties although, their correlation may amplify the variability of the estimates obtained from poroelastic state equations. In order to reduce the uncertainty of the percolation threshold and that of the poroelastic properties at early-age, engineers need to assess more accurately the apparent activation energy of calcium aluminate and, later on, of the elastic modulus of low density calcium-silicate-hydrate.

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Section: Localizationmentioning

confidence: 99%

Uncertainty propagation of a multiscale poromechanics-hydration model for poroelastic properties of cement paste at early-age

Venkovic¹,

Sorelli²,

Sudret³

et al. 2013

Probabilistic Engineering Mechanics

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“…In this form, the problem can be solved by using the classical Levin's theorem [16] (see also [13]). This yields the following constitutive equation (see [7] in a general context of poroelasticity):…”

Section: Principle Of the Modeling Including Initial Stressesmentioning

confidence: 99%

“…We are ready now for the replacement of summation in (13) by the integration on the surface of unit sphere. For simplicity, only opened microcracks are considered here.…”

mentioning

confidence: 99%

A two scale anisotropic damage model accounting for initial stresses in microcracked materials

Levasseur

Collin

Charlier

et al. 2011

Engineering Fracture Mechanics

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a b s t r a c tIn a recent study [15], we proposed a class of isotropic damage models which account for initial stresses. The present paper extends this approach to anisotropic damage due to growth of an arbitrarily penny-shaped microcracks system. The basic principle of the upscaling technique in the presence of initial stress is first recalled. Then, we derive a closed-form expression of the elastic energy potential corresponding to a system of arbitrarily oriented microcracks. It is shown that the coupling between initial stresses and damage is strongly dependent of the microcracks density and orientation. Predictions of the proposed model are illustrated through the investigation of the influence of initial stresses on the material response under non monotonous loading paths. Finally, by considering a particular distribution of microcracks orientation, described by a second order damage tensor, it is shown that the model is a generalization of the macroscopic damage model of Halm and Dragon [9], for which a physically-based interpretation is then proposed.

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“…However, neglecting the interaction of particles is an unrealistic assumption of Eshelby for materials with randomly dispersed particulate microstructure, even at a few percent volume fraction [89]. Further proposed models such as Mori-Tanaka [90][91][92], the self-consistent scheme [93][94][95][96][97][98], the generalized self-consistent scheme [99][100][101][102][103], and the differential method [104,105] are mainly based on the mean-field approximation [106] and approximate the interaction between the phases. The extension of these models to account for the electroelastic behavior of composite materials was addressed by Dunn and Taya [107].…”

Section: Introductionmentioning

confidence: 99%

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

185

138

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The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill-Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE 2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two-and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

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On the thermostatics of composite materials

Cited by 164 publications

References 9 publications

Uncertainty propagation of a multiscale poromechanics-hydration model for poroelastic properties of cement paste at early-age

Uncertainty propagation of a multiscale poromechanics-hydration model for poroelastic properties of cement paste at early-age

A two scale anisotropic damage model accounting for initial stresses in microcracked materials

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

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