Modeling of the Mechanical Behavior of Composites Showing Nonlinear Material Behavior Using the Embedded Element Method

Abstract

Composite materials are heterogeneous materials that are composed of two or more different materials. They are used in numerous applications, such as, automotive, aerospace, biomechanics application. Accurate and realistic modeling of these materials are important to ensure a high-quality production and obtaining a durable material. Finite element method is the most common choice to model these types of materials. Usual approach in modeling composites is the homogenization of the material properties. However, this approach is only valid under many assumptions. Apart from this limitation, this approach does not allow evaluation of stresses and strains in component materials. In order to achieve more realistic modeling, components should be modeled separately. This approach also has problems with meshing, since continuity between meshes of components should be provided. On the other hand, if component materials have complex shapes, many elements come to existence, which makes the analysis difficult. In order to resolve these issues, embedded element method was developed. In this method, component materials are meshed separately, as embedded and host regions. Constraint equations are defined between these regions such that they behave as a unified material. Continuity of meshes is not needed in this method, hence proper and fewer elements can be used. Besides, modeling of mechanical behavior is not limited to assumptions, and stresses and strains on the components can be investigated. However, in order to achieve realistic results, relative size of embedded regions should be smaller than host region, and host materials should show linear-elastic material behavior. In addition to these limitations, the host material in the embedded region still exists in this method and this redundant volume affects the mechanical behavior. Most common composite host (matrix) materials are thermo-elastic and thermo-plastic materials, and also muscles and tissues show non-linear mechanical behavior. When the embedded region ratio increases, this non-linearity and effect of the redundant volume should be taken into consideration. The aim of this study is to develop a method to use embedded element method for elasto-plastic and inelastic materials. This aim is achieved by developing a custom user subroutine that can be used to define proper material behavior, such that the effect of the redundant volume is eliminated. A single fiber model with single element and multiple elements and a randomly distributed fibers model with a volume fraction of 0.6 is used to test the proposed approach. Obtained results are compared with a continuously meshed version of this model. As it comes out, the proposed model can provide reliable results on S11 and S12 components of stress on a two-dimensional model. Accuracy of these results improves as expected, when the fiber volume fraction decreases from 0.6 to 0.4.