Micro-displacement tensor

Abstract

We propose an extended kinematics of nominally elastic continuum solids allowing one to describe their mechanical interaction with micro-scale loading devices. The main new ingredient is the concept of a micro-displacement tensor which extends the conventional description of the deforming elastic solids in terms of macroscopic displacement vectors. We show that micro-displacement tensors are particularly useful in dealing with active incompatibility acquisition and its subsequent passive relaxation. We use the proposed approach to describe the energetics of surface deposition while accounting for the presence of micro-mechanical controls.To illustrate the effectiveness of the new conceptual scheme we present two case studies: crystallization from a melt resulting in pre-stress, and winding of a coil with controlled pre-stretch.