Rotational Degrees of Freedom in Modeling Materials with Intrinsic Length Scale

Engineering materials are non-homogeneous and even discrete, yet standard continuum descriptions of such materials are admissible, provided that the size of the non-homogeneities is much smaller than the characteristic length of the deformation pattern. If this is not the case, either the individual non-homogeneities have to be described explicitly or the range of applicability of the continuum concept is extended by including additional variables or degrees of freedom. We review models dealing with the discrete nature of granular materials and with layered materials with sliding layers. Both cases require the introduction of rotational degrees of freedom; for layered materials it is the layer bending that represents a rotational degree of freedom. We consider the effects of the rotational degrees of freedom from apparent strain localization in simple shearing to new fracture modes.