Plasticity of polycrystal

Constitutive relations for polycrystal in elastic-plastic range were derived where plastic strains are produced by slips in crystallites. The slip criterion and strain-hardening law for monocrystal in the given crystallographic class in particular, Schmid's law was applied and the relevant plastic yield hypersurface analysed. The geometry was described by probabilistic methods. The fields of stress and strain produced by plastic distortions were taken into account without any simplifications and this is the essential of the generalisation towards previous methods. The solution was based on variational theorems of plasticity. A numerical procedure was outlined using nonlinear programming methods the grains being divided in subregions of approximately homogeneous distortions; thus consecutive points of sigma-epsilon curve were determined.