Approximation of the effective moduli of particulate composite with the fixed grid finite element method

• The fixed grid finite element method is introduced to approximate the effective moduli of particulate composite.
• A simple scheme is proposed to calculate the volume fraction of the constituents in every element.
• The validity of the method is verified for composites both with soft conclusions and with hard conclusions.
• The availability of the method for composite with multiple irregular inclusions is presented.

The fixed grid finite element method is introduced to approximate the effective moduli of particulate composite. The difficulty of domain discretization induced by the inclusions is avoided in the fixed grid finite element method, as the discretization is independent of the inclusions. The elastic properties of every finite element are approximated by a weighted function, and the volume fractions of the constituents in the element are taken as the weights. A simple scheme is proposed to approximate the volume fractions in every element. The validities of the fixed grid finite element method are verified, by comparing the effective moduli obtained from the fixed grid finite element method with those obtained from finite element method. The anisotropy of particulate composite is discussed with the fixed grid finite element, and the applicability of the fixed grid finite element method for composite with multiple irregular inclusions is illustrated.