Homogenization of linear viscoelastic materials is possible using the viscoelastic correspondence principle (VCP) and homogenization solutions obtained for linear elastic materials. The VCP involves a Laplace-Carson Transform (LCT) of the material phases constitutive theories and in most cases, the time domain solution must be obtained through numerical inversion of the LCT. The objective of this paper is to develop and test numerical algorithms to invert LCT which are encountered in the context of homogenization of linear viscoelastic materials. The homogenized properties, as well as the stress concentration and strain localization tensors, are considered. The algorithms suggested have the following two key features: (1) an acceptance criterion which allows to reject solutions of unacceptable accuracy and (2) some algorithms lead to solutions for the homogenized properties where the thermodynamics restrictions imposed on linear viscoelastic materials are M. Lévesque (B) CREPEC, encountered. These two features are an improvement over the previous algorithms. The algorithms are tested on many examples and the accuracy of the inversion is excellent in most cases.

Digital image correlation is a photomechanical technique utilized to measure displacement fields. Although the method has been used successfully in a variety of applications, there is a need for guidelines to choose correlation parameters and for an understanding of their link with the analyzed texture and their effect on the uncertainty of measured quantities. In this paper, two criteria are proposed from a texture study to evaluate the best compromise between measurement uncertainty and spatial resolution prior to any mechanical test. These criteria are then validated on a priori uncertainty evaluations with different textures, and on a real experiment when comparing image correlation results with strain gauge data.

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a b s t r a c tThe interaction between humid air and transversely isotropic fiber-reinforced composites with swelling polymeric matrix is considered. A model is proposed for the water saturation level in a polymer when stresses are applied, that uses directly obtainable material parameters only. In a composite, the reinforcements modify the water uptake of the polymer matrix because of the internal stresses that are induced by its restricted swelling, and this effect is evaluated. As a consequence of the coupling between stresses and absorption capacity, the sorption isotherm of a composite is ruled by the (non-linear) Langmuir equation when the unreinforced matrix obeys the (linear) Henry's law.