Abstract:
To mimic biological systems capable of acquiring and manipulating elastic incompatibility we developed an extended kinematic framework allowing one to describe mechanical interactions of macro-scopic bodies with micro-scale mechanical "agents". A technologically relevant example of a surface related micro-mechanical "activity" is the interaction of a feeding head of a 3D printer with a deposited elastic material. At the center of the proposed approach is the notion of a micro-displacement tensor, a kinematic variable extending the conventional description of elastic deformation in terms of macro-displacement vectors. To illustrate the effectiveness of the model we present a fully quantitative analysis of two physically relevant examples: crystallization from a melt resulting in a pre-stress, and winding of a coil with a controlled pre-stretch.