Shakedown Limit In Brittle-Matrix Composites With Plastic Crack Bridging Fibers Under Combined Traction-Flexure

The behaviour of a composite beam with multiple reinforcing fibers under periodic tractionflexure is analysed through a fracture mechanics-based model. In more detail, an edgecracked beam under external loads is also subjected to the crack bridging reactions due to the fibers. Assuming a rigid-perfectly plastic bridging law for the fibers and a linear-elastic law for the matrix, the statically indeterminate bridging forces are obtained from compatibility conditions. Under assigned load paths, shakedown conditions are explored by making use of the Melan’s theorem, here reformulated for the discrete problem under consideration, where crack opening displacement at the fiber level plays the role of plastic strain in the counterpart problem of an elastic-plastic solid. The limit of shakedown is determined through an optimization procedure based on a linear programming technique.