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

Effective transport properties for periodic multiphase fiber-reinforced composites with complex constituents and parallelogram unit cells

[EN] The two-scale asymptotic homogenization method is used to find closed-form formulas for effective properties of periodic multi-phase fiber-reinforced composites where constituents have complexvalued transport properties and parallelogram unit cells. An antiplane problem relevant to linear elasticity is formulated in the frame of transport properties. The application of the method leads to the need of solving some local problems whose solution is found using potential theory and shear effective coefficients are explicitly obtained for nphase fiber-reinforced composites. Simple formulae are explicitly given for three- and four-phase fiber-reinforced composites. The broad applicability, accuracy and generality of this model is determined through comparison with other methods reported in the literature in relation to shear elastic moduli and several transport problems of multi-phase fiber-reinforced composites in their realm, such as conductivity in a biological context and permittivity leading to gain and loss enhancement of dielectrics. Also, the example of gain enhancement of inertial mass density is looked into. Good agreement with other theoretical approaches is obtained. The formulas may be useful as benchmarks for checking experimental and numerical results.YE gratefully acknowledges the Program of Postdoctoral Scholarships of DGAPA from UNAM, Mexico. RG and RR would like to thank to COIC/STIA/9042 and COIC/STIA/9045/2019. RR thanks the International Research Training Group GRK 2078 "Integrated engineering of continuous-discontinuous long fiber reinforced polymer structures"(CoDiCoFRP) funded by German Research Foundation (DFG) for inviting him as a guest scientist, parts of the manuscript were written during this stay. JB and FJS acknowledge the funding of PAPIIT-DGAPA-UNAM IA100919. TB acknowledges the support by DFG under the grant GRK 2078/2. Thanks to the Department of Mathematics and Mechanics, IIMAS-UNAM, for its support and Ramiro Chavez Tovar and Ana Perez Arteaga for computational assistance.Sabina, FJ.; Guinovart-Díaz, R.; Espinosa-Almeyda, Y.; Rodríguez-Ramos, R.; Bravo-Castillero, J.; López-Realpozo, JC.; Guinovart-Sanjuán, D.... (2020). Effective transport properties for periodic multiphase fiber-reinforced composites with complex constituents and parallelogram unit cells. International Journal of Solids and Structures. 204:96-113. https://doi.org/10.1016/j.ijsolstr.2020.08.001S9611320