A DYNAMICAL THEORY OF STRUCTURED SOLIDS .1. BASIC DEVELOPMENTS

Based on the well-accepted notion of a Bravais lattice of a crystal at the atomic scale and with particular reference to inelastic behaviour of materials, this paper is concerned with the construction of a macr oscopic dynamical theory of solids which incorporates the effect of th e presence of the atoms and their arrangements. The theory incorporate s a wide variety of microstructural processes occurring at various phy sical scales and has a range approaching the atomic scale. These proce sses include the effect of the motion of individual dislocations, whic h are modeled here as continuous distributions at the macroscopic scal e. The formulation of the basic theory, apart from the kinematical and kinetical variables employed in classical continuum mechanics, utiliz es a triad of independent vector-valued variables - called directors - (or an equivalent tenser-valued variable) which represent the lattice vectors and are determined by additional momentum-like balance laws a ssociated with the rate of change of lattice deformation in the spirit of a Cosserat (or directed) continuum. A suitable composition of the triad of directors and the ordinary deformation gradiednt is identifie d as a measure of permanent or plastic deformation, the referential gr adient of which plays a significant role in the kinematics of lattice defects. In particular, a uniquely defined skew-symmetric part of the gradient of plastic deformation is identified as a measure of the dens ity of dislocations in the crystal. The additional momentum-like balan ce laws associated with the rate of lattice deformation include the ef fect of forces necessary to maintain the motion of dislocations, as we ll as the inertia effects on the microscopic and submicroscopic scales arising from the director fields. The basic theoretical developments also provide important clarifications pertaining to the structure of t he constitutive response functions for both viscoplasticity and (the m ore usual) rate-independent plasticity.