Modélisation micromécanique des matériaux composites multifonctionnels

Abstract

The issue of accurately predicting the effective behavior of composite materials has taken the attention of many researchers in the last few decades and continues to be in the forefront of material research. Micromechanics have proven to be very powerful in analyzing and predicting the effective behavior of composite materials. In the frame of this thesis, various micromechanical models have been elaborated in order to investigate the effective behavior of different kinds of smart composites such as: piezoelectric, piezomagnetic, magnetoelectroelastic, viscoelectroelastic, viscomagnetoelectroelastic as well as shape memory alloys. The effective properties of multi-phase magnetoelectroelastic composites have been investigated using different micromechanical models. An N-phase Incremental Self Consistent model is developed to circumvent the limitation of the Self Consistent predictions. The Self Consistent shows limitation for the prediction of some coupling coefficients. Also, the prediction of the Self Consistent model is very limited when the void inclusions are considered. The modeling is based on the solution of integral equations. The effective N-phase magnetoelectroelastic moduli are expressed as a function of magnetoelectroelastic concentration tensors based on the considered micromechanical models. The effective properties are obtained for various types, shapes and volume fractions of inclusions and compared with the existing results. Note that the effective properties of magnetoelectroelastic composites might be greatly affected by the presence of an interphase between the matrix and inclusions. To take this effect into account, accurately, a micromechanical modeling is developed to investigate the effective properties of magnetoelectroelastic composite with multi-coated inclusions and functionally graded interphases. The modeling is based on the solution of the integral equations that take into account the multi-coated and functionally graded effects and on the magnetoelectroelastic interfacial operators that allow expressing the generalized strain jump through the interphase. Taking into account the multi-coated and functionally graded effects in the modeling help in the design of new smart composites with higher coupling coefficients. Piezoelectric and magnetoelectroelastic composites that contain a polymer phase show a significant time dependent behavior and particularly at elevated temperature. A micromechanical modeling is developed to investigate the viscoelectroelastic and viscomagnetoelectroelastic behaviors of heterogeneous piezoelectric and magnetoelectroelastic composite materials. The modeling is based on generalizing the correspondence principle of linear viscoelasticity to the case of viscoelectroelasticity and viscomagnetoelectroelasticity. The viscoelastic correspondence principle is combined with Mori-Tanaka micromechanical model. The effective properties are predicted in the frequency and time domains based on Carson and Laplace transforms. To investigate the nonlinear behavior of smart composites, the shape memory alloys are considered. The effective transformation behavior of this kind of composites is investigated based on the Mori-Tanaka model that takes the coating effects around the inclusions combined with the constitutive equations describing the transformation behavior of shape memory alloy materials. The obtained results are compared with one predicted based on the classical Mori-Tanaka model that does not consider the effect of the coating layer around the inclusion and also with the obtained ones based on the finite element method. It is shown that the developed model captures the effective transformation behavior better than the one that is based on the classical Mori-Tanaka model. As the obtained results do not agree well with the ones predicted based on the finite element method the developed methodological approaches need more refinement for this kind of nonlinear materials