Abstract
In this article, a multi-scale computational homogenization scheme is proposed for the study of composite materials. A classical unilateral contact law has been incorporated in the microscopic level, for the investigation of the contact between the constitutive materials. The either-or decision resulting from the contact-no contact condition in the microscopic scale, makes the problem non-linear. This change in the contact state of the microscopic level, is taken into account by the proposed approach. Debonding between the matrix and the surrounding fibers and its impact on the macroscopic structure, are depicted. In addition, a change in the direction of the macroscopic load during analysis, results in a non-linear behavior due to the alteration of the microscopic contact state. The distribution of the displacement jump is influenced in this case, as well.
Highlights
In the present work a multi-scale, computational homogenization scheme is proposed for the study of composite materials
The main idea of this article is related to the investigation of the contact state between the matrix and the fibers, in the microscopic level of a composite material, within a multi-scale framework
A multi-scale computational homogenization approach is proposed for the study of composite materials
Summary
In the present work a multi-scale, computational homogenization scheme is proposed for the study of composite materials. A unit cell is explicitly solved and the resulting average quantities are used for the determination of the parameters of a macroscopic constitutive law [4,5] From another point of view, multi-scale computational homogenization incorporates a concurrent analysis of both the macro and the microstructure in a nested multi-scale approach, [6–14]. Within this method, the macroscopic constitutive behavior is determined during simulation, after solving the microscopic problem and transferring the necessary information on the macroscopic scale. A continuous macroscopic model is considered in the macro scale and an overall multi-scale contact computational homogenization scheme is developed With this numerical scheme, several phenomena related to the microscopic contact conditions and its impact on the macroscopic model, have been investigated. Among them are included the influence of the jump of displacements on the macroscopic response, as well as the alteration of the macroscopic load direction during analysis resulting in a microscopic contact change and its impact on the macroscopic structural behavior
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