We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in R m×n , min(m, n) ≤ 2, then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit convexity assumptions on the quasiconvex (polyconvex) envelope.
Severe plastic deformation is one of the most effective methods of preparation of ultra-fine-structured materials with an extreaordinary combination of high strength and high ductility. The microstructure of these materials consists of sub-micrometer regions of misoriented crystal lattice. It is proposed that formation of the regions is a result of a tendency to decrease the internal energy opposed by a rearrangement of crystal lattice defects. The model of the structuralization process is formulated as an energy minimization problem.. and Obsahuje seznam literatury