Analysis of unbalanced laminate composites with imperfect interphase: Effective properties via asymptotic homogenization method

This work addresses the Asymptotic Homogenization Method (AHM) to find all the non-zero independent constants of the fourth-order elasticity tensor of a theoretically infinite periodically laminated composite. The concept of Unit Cell describes the domain, comprised of two orthotropic composite plies separated by an isotropic interphase. A general case with an unbalanced composite is considered. Thus, the coupled components of the tensor are expected. Both analytical and numerical solutions are derived. In addition, an interphase degradation model is proposed to evaluate its effect on the effective properties of the media. Two different stacking sequences are considered with five degrees of interphase imperfection each. The results show good agreement between the analytical and numerical solutions. In addition, it is clear that the more imperfect the interphase is, the more affected the effective properties of the media are, especially those dependent on the stacking direction.

MODELING OF MECHANICAL BEHAVIOUR OF A 1D, LINEAR AND MICROPERIODIC COMPOSITE, WITH FAILURE, VIA THE ASYMPTOTIC HOMOGENIZATION METHOD

In this paper the Asymptotic Homogenization Method is combinedwith a model of Hyperelasticity with softening (wich models the mechanical failureof the material), with the purpose of estimating the mechanical behaviour ofmicroperiodic composites in the way to reproduces better the behaviour obtainedin experiments, found in the literature. This hybrid approach brings somesatisfactory results, showing that the (hypothetical)composite studied presentseffective behaviour very close to the expected from the Hyperelasticity model. Thatis a very important fact because can be used as a tool to predict the failure ofcomposite materials, trough its constituent materials informations. This evaluatingneeds more steps, to be possible much bigger and strong conclusions, however theresults obtained until now seems like very promissory.

Magneto-electric coupling constants in piezoelectric/piezomaganetic layered composite

During the last few years, piezoelectric/piezomagnetic composites have been studied due to the numerous applications related to the coupling between these materials and the fields. In the present work, two theoretical models for calculating the magneto/electric coupling factor of the composite with 2-2 connectivity, are presented. Using the asymptotic homogenization method, the effective coefficients of a periodic magneto–electro–elastic layered composite can be obtained in matrix form. By using this matrix, a two-layered composite formed by BaTiO3 and CoFe2O4 are studied, and expressions for the effective coefficients are obtained. The effective magneto/electric coupling factor as a function of the piezoelectric volumetric fraction are found from these particular coefficients. In addition, a dynamic model of the multilayer piezoelectric/piezomagnetic composite is discussed. The dynamical model has been used to determinate the magnetoelectric coupling constants.

Effective Behavior of Nonlinear Microperiodic Composites with Imperfect Contact Via the Asymptotic Homogenization Method.

The asymptotic homogenization method is applied here to one-dimensional boundary-value problems for nonlinear differential equations with rapidly oscillating piecewise-constant coefficients which model the behavior of nonlinear microperiodic composites, in order to assess the influence of interfacial imperfect contact on the effective behavior. In particular, a nonlinear power-law flux on the gradient of the unknown was considered. Several calculations were performed and are discussed at the end of this work, including a comparison of some results with variational ounds, which is also an important approach of this work.

Size effects of mechanical metamaterials: a computational study based on a second-order asymptotic homogenization method

In this paper, size effects exhibited by mechanical metamaterials have been studied. When the sizescale of the metamaterials is reduced, stiffening or softening responses are observed in experiments. In order to capture both the stiffening and softening size effects fully, a second-order asymptotic homogenization method based on strain gradient theory is used. By this method, the metamaterials are homogenized and become effective strain gradient continua. The effective metamaterial parameters including the classical and strain gradient stiffness tensors are calculated. Comparisons between a detailed finite element analysis and the effective strain gradient continua model have been made for metamaterials under different boundary conditions, different aspect ratios, different unit cells (closed or open cells) and different topologies. It shows that both stiffening and softening size effects can be captured by using the effective strain gradient continua models.

Simple Implementation of Asymptotic Homogenization Method for Periodic Composite Materials

In this paper, a simple implementation method of Asymptotic homogenization (AH) method is developed with the aid of commercial FEM software as a tool box. Then, abundant structural elements (like beam, shell and solid elements) in commercial software can be used to model unit cell with various complex substructures of periodic materials, while simultaneously reducing the model to a small scale with less amount of calculation. During the implementation, a set of simple displacement boundary conditions are assumed for unit cell, and final effective elastic constant can be directly calculated after several static analysis. Two representative examples of applications are chosen and discussed to verify the validity and applicability of the new implementation method by comparing with other methods. The proposed method is expected to become an effective benchmark for assessing other homogenization theories and extended to other homogenization problems (such as thermal expansion coefficient) in the future.