  By investigating the benefits and shortcomings of the existing form of
continuous defect theory (CDT) and using recent advancements in size-dependent
continuum mechanics, we develop a fully coherent theoretical framework, denoted
as Consistent Continuous Defect Theory (C-CDT). Among several important
potential applications, C-CDT may provide a proper foundation to study the
continuum theory of crystal plasticity. The development presented here includes
an examination of the character of the bend-twist tensor, Weingarten's theorem,
Burgers and Frank vectors, continuous dislocation and disclination density
tensors, and the dualism between geometry and statics of CDT based on couple
stress theory (CST). Then, by using Consistent Couple Stress Theory (C-CST),
the new C-CDT is derived in a totally systematic manner. In this development,
the geometry of C-CDT is dual to the statics formulation in C-CST. Previously,
the fundamental step in the creation of C-CST was recognizing the
skew-symmetric character of the couple-stress tensor, which requires the
skew-symmetrical part of the bend-twist tensor to be the additional measure of
deformation in size-dependent continuum mechanics. Via Weingarten's theorem and
arguments from C-CST, we establish that in defect theory the dislocation
density tensor must be skew-symmetric and thus can be represented by an
equivalent dislocation density vector. In addition, we investigate the
character of a classical version of C-CDT with unexpected consequences. For
full consistency, there can be no continuous dislocation density tensor within
classical continuum mechanics, and the continuous disclination density tensor
becomes symmetric. This clearly is analogous to the absence of couple-stresses
and the symmetry of force-stresses in classical continuum mechanics.
