A three-dimensional damage percolation model, which captures the effect of microstructural heterogeneity on damage evolution, has been developed to model damage initiation and propagation in materials containing second phase particles. It considers the three phenomena preceding ductile rupture of the material: void nucleation, growth, and coalescence. Three-dimensional X-ray tomography is used to obtain measured three-dimensional second phase particle distributions in aluminum alloy sheet. Material damage evolution is studied within a tensile test simulation and compared to measured damage from an in situ tensile test utilizing X-ray tomography. Experimental and simulation results for material damage initiation and evolution are in good agreement.

An exact analytic solution is obtained for the problem of light propagation in a three-core nonlinear directional coupler with identical parallel fibres in the geometry of a regular triangle for an arbitrary dependence of the propagation constant on the light intensity.