Unified Theory of the Mechanical Behavior of Matter

anholonomic object Ax¹ b₁ base vectors body boundary of Figure boundary shown Burgers circuit Burgers vector associated chapter closure failure associated coincidence site lattice configuration shown considered coordinate system corresponds crack dislocations crystal lattice dislocations curvature tensor Dirac delta function dislocation content dislocation density tensor dislocations in Figure dotted arrows double shear dx² elastic and plastic elastic strain equation Figure 6.1a follows given by Eq grain boundary dislocation Heaviside function interface leftmost line integral linear approximation linearized form M. J. Marcinkowski metric tensor nonvanishing components obtain parallel displacement particular plane plastic rotation plastic strain pure plastic respect result rightmost S₁₂ S₁₂² screw dislocations shown in Figure similar to Eq simple shear strain tensor stress field stress-free substituted into Eq surface dislocation array surface integral tensor associated tensor quantities tion torsion tensor twist disclination vanish view of Eq wedge disclination write written yields буу бху