  The continuum mechanics of line defects representing singularities due to
terminating discontinuities of the elastic displacement and its gradient field
is developed. The development is intended for application to coupled phase
transformation, grain boundary, and plasticity-related phenomena at the level
of individual line defects and domain walls. The continuously distributed
defect approach is developed as a generalization of the discrete, isolated
defect case. Constitutive guidance for equilibrium response and dissipative
driving forces respecting frame-indifference and non-negative mechanical
dissipation is derived. A differential geometric interpretation of the defect
kinematics is developed, and the relative simplicity of the actual adopted
kinematics is pointed out. The kinematic structure of the theory strongly
points to the incompatibility of dissipation with strict deformation
compatibility.
