Homogenization analysis method for composites considering geometrical nonlinearity and fracture of microstructure

For the design and production of new advanced composite materials and structures, the need for numerical simulations of their mechanical behaviors is increasing. There are two requirements for the simulation. First, microstructural architectures must be considered. The homogenization analysis method, which is an applied mathematical method developed from late 1970's to early 1980's, seems to be the most appropriate method for modelling microstructures in current literature. The second requirement is the solution of nonlinear problems. Therefore, we have developed a nonlinear homogenization method where both geometrical nonlinearity due to large deformation of microstructures and material nonlinearity due to microscopic fractures are considered. The new formulation of the nonlinear homogenization method is based on a stepwise linear algorithm with initial stresses. Two examples, i.e., biomechanical problem and fracture behavior of woven fabric composite material, were solved.