Limit analysis of periodic composites by a kinematic approach

The efficient evaluation of strength domains for metal-matrix composite (MMC) materials with unidirectional periodic fibers is the objective pursued in this paper. The analyses presented are based on the kinematic limit theorem and on the finite element method in its displacement formulation. The resulting nonlinear mathematical programming problems are solved by an iterative procedure. The limit analysis method developed and implemented for MMCs takes the strain-periodicity of the microscopic displacement field into account and directly leads to an upper bound of the collapse multiplier and to a collapse mechanism. The numerical tests performed so far exhibit fast convergence and show excellent agreement with experimental and numerical results arising from different approaches