Mathematical simulation of brittle fracture for thin-walled solids

A model of brittle materials is proposed. The model allows one to describe the processes of initiation and growth of cracks in thin-walled constructions up to their fracture. The model is included into the library of material models of shell finite element of program PIONER. The solutions of some problems obtained with this program are presented (in particular, several test problems of quasistatic deformation with analytical solutions: the deformation and fracture of plates under homogeneous stress-strain states and the beam fracture under pure bending). The dynamic deformation and fracture of a plate by a concentrated mass with different initial velocities are studied. This problem simulates the impact of an arrow on a bronze plate as an element of protective weaponry of Central Asia nomads. A range of initial velocities at which a concentrated mass is capable to destroy such a plate is specified. It is shown that the fracture of a part of the plate's material causes the dynamic loss of its stability.