The equations of dislocation transport at finite crystal deformation were developed, with a special emphasis on a vector density representation of dislocations. A companion thermodynamic analysis yielded a generalized expression for the driving force of dislocations that depend on Mandel (Cauchy) stress in the reference (spatial) configurations and the contribution of the dislocation core energy to the free energy of the crystal. Our formulation relied on several dislocation density tensor measures linked to the incompatibility of the plastic distortion in the crystal. While previous works develop such tensors starting from the multiplicative decomposition of the deformation gradient, we developed the tensor measures of the dislocation density and the dislocation flux from the additive decomposition of the displacement gradient and the crystal velocity fields. The two-point dislocation density measures defined by the referential curl of the plastic distortion and the spatial curl of the inverse elastic distortion and the associate dislocation currents were found to be more useful in deriving the referential and spatial forms of the transport equations for the vector density of dislocations. A few test problems showing the effect of finite deformation on the static dislocation fields are presented, with a particular attention to lattice rotation. The framework developed provides the theoretical basis for investigating crystal plasticity and dislocation patterning at the mesoscale, and it bears the potential for realistic comparison with experiments upon numerical solution.

建立了有限晶体变形时的位错输运方程，特别着重于位错的矢量密度表示。伴随的热力学分析得出了位错的驱动力的广义表达式，该位错的驱动力取决于参考（空间）构型中的曼德尔应力（Cauchy）以及位错核心能量对晶体自由能的贡献。我们的配方依赖于几种位错密度张量测量，这些测量与晶体中塑性变形的不相容性有关。虽然先前的工作是从变形梯度的乘法分解开始的，但这种张量是 我们根据位移梯度和晶体速度场的加性分解，开发了位错密度和位错通量的张量测量。发现由塑性变形的参考卷曲和逆弹性变形的空间卷曲以及相关的位错电流定义的两点位错密度测量在推导矢量的输运方程的参考和空间形式方面更有用位错密度。提出了一些测试问题，这些问题显示了有限变形对静态位错场的影响，并特别关注晶格旋转。开发的框架为研究中尺度的晶体可塑性和位错图案提供了理论基础，