(a) Elastic stress–strain relationship, (b) elastic-perfectly plastic stress–strain relationship. Initial elastic deformation occurs along line O–Y′ until stress exceeds the strength of the substrate, at which point failure occurs and deformation takes place along line Y′–P. If loading is halted at Y″, and then removed, elastic recovery occurs along line Y″–U, parallel to initial deformation O–Y′. (c) The effects of an elastic-perfectly plastic model distributed over a substrate volume, in which parts are in plastic failure, and others are in the elastic region. (d) The effects of Poisson's ratio on the overall form of the stress–strain relationship within a substrate; dotted line, v = 0.49; solid line, v = 0.3; dashed line, v = 0.1.