Development of constitutive laws for thermomechanical behaviors of composites containing multi-type ellipsoidal reinforcements

Composite materials are widely used in industrial applications because of their excellent properties and behaviors. While a composite material is defined as a mixture of two or more different materials, many research works in the literature dealt with composites of only two constituents, which are matrix and one type of particles. On the other hand, the theoretical research works that dealt with more than two constituents are rare. Using some additives affects the sintering behavior, the tribological behavior and the fracture mechanics behavior of composites. For example, a suitable amount of additives as sintering aids, in the sintering process, could lower the sintering temperature, enhance phase wettability and bonding strength and improve the interlaminar fracture resistance of a composite. Therefore, it is worthwhile to develop the constitutive laws that describe the behavior of such composite materials. Accordingly, the aim of this paper is to modify the previous paper, Shabana (2003) [Shabana, Y.M., 2003. Incremental constitutive equation for discontinuously reinforced composites considering reinforcement damage and thermoelastoplasticity. Computational Materials Science 28, 31–40], in order to propose constitutive laws that predict the thermomechanical behavior of composites containing multi-type ellipsoidal reinforcements. This includes reinforcements with different materials and/or different shapes that are represented by aspect ratios. These constitutive laws not only predict the macroscopic and microscopic thermoelastoplastic behaviors of composites containing multi-type ellipsoidal reinforcements, but also characterize their different overall effective properties such as modulus of elasticity, Poison’s ratio and thermal expansion coefficient in different directions. Beside this, they are applicable for porous materials and composites with multiple reinforcements and porosities of different shapes and distributions. In the present numerical analyses, composites with two, three and four constituents considering different materials and aspect ratios as well as reinforcement damage are discussed.