Homogenization of Composite Materials With Energetic Interfaces

Abstract eng:
This work proposes an appropriate homogenization framework for composites in which the material constituents in the microscale are separated by energetic interfaces. The energetic interfaces are considered material surfaces with their own constitutive behavior [1]. Our aim is to study the overall behavior of these composites under mechanical loading and assuming small deformations. The homogenization theory presented here is a two scale approach. In the microscale, both the bulk and the interface are characterized by appropriate equilibrium and constitutive equations [2]. The macroscale field variables (stress, strain) are correlated with their microscopic counterparts through appropriate averaging over the unit cell. The Hill's lemma allows us to identify several types of boundary conditions in the microscale that satisfy the Hill-Mandel conditions. Moreover, in the case of elastic material constituents and under periodic boundary conditions, we present a computational scheme for solving the unit cell problem and identifying the effective stiffness tensor. In the present study three special cases of composites with energetic interfaces are examined. In the first case we consider a multilayered material whose material constituents are orthotropic and are separated by a) a thin interphase layer and b) an energetic interface. Assuming that the two composite structures present the same effective behavior, we identify the correlation between the mechanical properties of the energetic interface and the thin layer. In the second example we examine isotropic fiber composites with thin interphase layers, which are substituted by energetic interfaces whose mechanical properties are provided through the relations obtained from the first example. The results obtained for very soft and very stiff interfaces indicate that there are bounds on the effective in-plane properties. The results of our approach are compared with existing analytical methods for small deformations [3]. In the third case we consider isotropic particle composites with thin interphase layers and we use existing analytical methods for small deformations [4]. It is shown that the thin interphase can be substituted by an energetic interface whose mechanical properties are provided through the relations obtained from the first example. The results obtained for very soft and very stiff interfaces indicate that there are bounds on the overall bulk and shear modulus.

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