Nonlinear continuum theory of dislocations

A multiscale gradient theory for single crystalline elastoviscoplasticity

“…(34) 2 and (35) as [3], Steinmann [32], Acharya and Bassani [33,73], Menzel and Steinmann [9], Bammann [34], Bassani [74], and Regueiro et al [39]. On the other hand, they are contradictory to the models of Teodosiu [1], Dillon and Kratochvil [5], Naghdi and Srinivasa [38,28], Le and Stumpf [30,31], Shizawa and Zbib [16,17], and Gurtin [13,36].…”

“…The last of (40) leads to symmetry of the Cauchy stress R, as defined in Eq. (31). Notice that inequality (39) is written in terms of two-point tensors S and F and the free energy per unit reference volume w 0 .…”

“…The coefficients C a bc of the ''crystal connection'' (cf. [31,67]) acquire the following form when referred to the current configuration:…”

“…In many cases the higher order gradients are associated, upon invocation of differential-geometric arguments, with the density of ''geometrically necessary dislocations'' (GNDs) in single crystals (cf. [28][29][30][31][32][33][34][35][36][37]) and in polycrystals (cf. [38,16,17,9,39]).…”

A geometric framework for the kinematics of crystals with defects

“…Methods from geometry on differentiable manifolds have come to the fore in recent years for describing the kinematics of elastoplasticity [1][2][3][4][5][6][7][8][9]. An understanding of the kinematics of defective crystals is central to constructing arguments related to nonlocal or gradient theories introducing scale effects in the description.…”