Mechanical behaviour of brittle matrix composites: a homogenization approach

A numerical model is developed with the aim of describing the macroscopic mechanical response of unidirectional brittle-matrix fiber-reinforced composites subjected to stresses acting in any plane transverse to the fibers. Finite element analyses of a representative unit cell are performed, with suitable boundary conditions ensuring continuity of the displacement field across adjacent cells and periodicity of the strain field over the cell. A strain-softening constitutive law is adopted for the matrix in tension to allow, for instance, for brittleness induced by possible defects in a polymeric matrix. The perfectly plastic case is also considered for sake of comparison. Results established for ductile composites are found to be inappropriate for brittle matrix composites: numerical analyses show that composites with softening matrix have transverse strength properties much poorer than perfectly plastic composites with matrix of equal strength, and even than the unreinforced matrix. An induced transverse anisotropy in the post-peak regime is also observed. A discussion on the proposed approach concludes the note