Variational Bounds for Multiphase Transversely Isotropic Composites

A general algorithm for the calculation of variational bounds for any type of anisotropic linear elastic composite is presented. Analytical expressions for the bounds are derived using this general approach. Bounds for multiphase, linear, transversely isotropic, elastic composites are reported. Bounds for the two-dimensional case are calculated. Some comparisons with other models are shown

An approach for modeling non-ageing linear viscoelastic composites with general periodicity

International audienceThe present work deals with the modeling of non-ageing linear viscoelastic composite materials and quasi-periodic microstructure. The stratified functions and the curvilinear coordinates play an important role in the design of different geometrical shapes. The main objective focuses on the application of two-scales Asymptotic Homogenization Method (AHM) to obtain the overall behavior of the viscoelastic composite materials. Although the whole process is based on the analysis of laminated configurations, a multi-step homogenization scheme to estimate the effective properties of a structure reinforced with long rectangular fibers and wavy effects is used. The associated local problems, the homogenized problem and the analytical expressions for the effective coefficients are obtained by using the correspondence principle and the Laplace-Carson transform. Also, the inter-connection between the effective relaxation modulus and the effective creep compliance is performed. Finally, the inversion to the original temporal space is calculated. Some comparisons between the proposed approach and Finite Elements Method (FEM) results are displayed

Prevalence of Age-Related Macular Degeneration in Europe: The Past and the Future

Purpose Age-related macular degeneration (AMD) is a frequent, complex disorder in elderly of European ancestry. Risk profiles and treatment options have changed considerably over the years, which may have affected disease prevalence and outcome. We determined the prevalence of early and late AMD in Europe from 1990 to 2013 using the European Eye Epidemiology (E3) consortium, and made projections for the future. Design Meta-analysis of prevalence data. Participants A total of 42 080 individuals 40 years of age and older participating in 14 population-based cohorts from 10 countries in Europe. Methods AMD was diagnosed based on fundus photographs using the Rotterdam Classification. Prevalence of early and late AMD was calculated using random-effects meta-analysis stratified for age, birth cohort, gender, geographic region, and time period of the study. Best-corrected visual acuity (BCVA) was compared between late AMD subtypes; geographic atrophy (GA) and choroidal neovascularization (CNV). Main Outcome Measures Prevalence of early and late AMD, BCVA, and number of AMD cases. Results Prevalence of early AMD increased from 3.5% (95% confidence interval [CI] 2.1%–5.0%) in those aged 55–59 years to 17.6% (95%

Soft and hard anisotropic interface in composite materials

For a large class of composites, the adhesion at the fiber-matrix interface is imperfect i.e. the continuity conditions for displacements and often for stresses is not satisfied. In the present contribution, effective elastic moduli for this kind of composites are obtained by means of the Asymptotic Homogenization Method (AHM). Interaction between fiber and matrix is considered for linear elastic fibrous composites with parallelogram periodic cell. In this case, the contrast or jump in the displacements on the boundary of each phase is proportional to the corresponding component of the tension on the interface. A general anisotropic behavior of the interphase is assumed and the interface stiffnesses are explicitly given in terms of the elastic constants of the interphase. The constituents of the composites exhibit transversely isotropic properties. A doubly periodic parallelogram array of cylindrical inclusions is considered. Comparisons with theoretical and experimental results verified that the present model is efficient for the analysis of composites with presence of imperfect interface and parallelogram cell. The present method can provide benchmark results for other numerical and approximate methods

Micro–macro asymptotic approach applied to heterogeneous elastic micropolar media. Analysis of some examples

International audienc

Effective predictions of heterogeneous flexoelectric multilayered composite with generalized periodicity

International audienceIn this work, the general mathematical statements for flexoelectric heterogeneous equilibrium boundary value problems are reported. A methodology to find the local problems and the effective properties of flexoelectric composites with generalized periodicity is presented, using the two-scales asymptotic homogenization method. The statement of the homogenized boundary values problem is given. A procedure to solve the local problems of stratified multilayered composites with complex geometry and perfect contact at the interface is proposed. Consequently, the analytical expressions of the effective coefficients are obtained. The piezoelectric limit case for rectangular bi-laminated composites is validated. Finally, numerical analysis to illustrate the behavior of the effective properties for rectangular and wavy flexoelectric bi-layered structures are shown

Computation of the relaxation effective moduli for fibrous viscoelastic composites using the asymptotic homogenization method

International audienceA two-phase parallel fibre-reinforced periodic viscoelastic composite is considered wherein the constituents are isotropy. Simple closed-form formulae are obtained for the effective properties of composites with square and hexagonal cells by means of the two-scale asymptotic homogenization method. The computation of the effective properties of non-ageing linear viscoelastic composites with periodic structure containing long cylindrical fibres of circular cross-section is performed. The local problems and overall viscoelastic properties are obtained in explicit form using the elastic-viscoelastic correspondence principle and assuming perfect contact conditions at the interface between constituents. Comparison with different viscoelastic models allowing explicit inverse Laplace transforms such as, traditional Maxwell and Kelvin models and Rabotnov-Scott Blair fractional exponential model are shown. The analytical results are verified by comparison with computational ones

Antiplane magneto-electro-elastic effective properties of three-phase fiber composites

International audienceIn the present work, applying the asymptotic homogenization method (AHM), the derivation of the antiplane effective properties for three-phase magneto-electro-elastic fiber unidirectional reinforced composite with parallelogram cell symmetry is reported. Closed analytical expressions for the antiplane local problems on the periodic cell and the corresponding effective coefficients are provided. Matrix and inclusions materials belong to symmetry class 6mm. Numerical results are reported and compared with the eigenfunction expansion-variational method (EEVM) and other theoretical models. Good agreements are found for these comparisons. In addition, with the herein implemented solution, it is possible to reproduce the effective properties of the reduced cases such as piezoelectric or elastic composites obtain- ing good agreements with previous reports