The theory of dislocation and generalized dislocation fields is developed within a second-order mechanical framework where the description of the internal state of the body and the balance equations involve the stress and hyper-stress tensors, work-conjugates to the strain and second-order distortion tensors. Consistently, the free energy density depends on the elastic strain and second-order distortion tensors. To obtain a continuous setting, the theory uses the duality between the discontinuity of the elastic displacement vector and distortion tensor fields and the incompatibility of the smooth second-order elastic distortion field. The conservation of these discontinuities across arbitrary patches provides transport relationships for the motion of dislocations and generalized disclinations serving as a kinematic basis for the description of plasticity and phase transformation. Closure of the theory derives from constitutive relationships for the mobility of dislocations and generalized disclinations compatible with the thermodynamic requirement of positive dissipation. In contrast with dislocations, the driving forces for generalized disclinations involve the hyper-stress tensor, not the stress tensor. The resulting theory is able to address boundary value problems for the elasto-plasticity of solids coupled with phase transformation along arbitrary loading paths. We provide examples showing generalized disclination distributions in plane state situations such as straight symmetrical tilt boundaries and symmetrical tilt boundaries involving steps and ledges.

位错理论和广义位错场是在二阶机械框架中发展的，其中对身体内部状态和平衡方程的描述涉及应力和超应力张量，应变的共轭和二阶变形张量。一致地，自由能密度取决于弹性应变和二阶变形张量。为了获得连续的设置，该理论使用了弹性位移矢量和变形张量场的不连续性与平滑二阶弹性变形场的不相容性之间的对偶性。这些不连续性在任意面片上的守恒提供了位错运动和广义错位的传输关系，这是描述可塑性和相变的运动学基础。该理论的封闭源于与正耗散的热力学要求兼容的位错迁移率和广义错位的本构关系。与位错相反，广义错位的驱动力包括高应力张量，而不是应力张量。由此产生的理论能够解决固体弹塑性与沿任意载荷路径发生相变的边界值问题。