Odd Elasticity in Chiral Active Solids
Abstract
Active materials are composed of microscopic constituents each endowed with motors or other internal sources of energy. When many active components are held together by interactions in a solid structure, the resulting non-equilibrium medium displays emergent mechanical properties that lie at the interface between dynamical systems and solid mechanics. This project aims to develop a generalization of the time-honored formalism of continuum mechanics capable of predicting the properties of active solids in which internal torques are switched on when the microscopic elastic constituents are under tension. In recent years, a growing understanding has emerged of hydrodynamic theories of active matter and how they differ from their equilibrium counterparts. By contrast, elastic theories of active matter must confront a fundamental difficulty: the elastic free energy, the starting place for elastic theory, is not well defined far from equilibrium . The overall scientific objective of this proposal is to construct an elastic theory of active continua by revisiting the fundamental notion of the elastic tensor K_ijkl, the coefficient that relates stress and strain in the constitutive equations of elastic media. Our hypothesis is that certain classes of active solids are described by elastic theories with an odd elastic coefficient, i.e. one which is antisymmetric (or odd) under an exchange of indices across the major axis: K_ijkl=-K_klij. This term is explicitly forbidden in standard elasticity because it does not conserve energy. Preliminary work shows that this apparently small modification implies that one can draw energy out of the system after a cycle of mechanical deformation which implies that such a theory must describe an active solid. As a first goal of this research, we plan to build a theoretical blueprint to design and operate active elastic engines and characterize their efficiency. The second goal is to construct concrete microscopic models and explicit coarse graining procedures that give rise to odd elasticity starting from an elastic network composed of active meta-beams that respond to applied compression (or elongation) with a clockwise (or counterclockwise) torque. The third goal is to perform a rigorous symmetry analysis that classifies all allowed terms in such theories, especially time-reversal and chiral symmetries that must be broken to generate such an odd elastic response. Our forth goal is to study the odd mechanical response of an elastic medium as a function of activity, including specific topics such as the Poisson ratio, elastodynamics, extreme mechanics of thin sheets and rods as well as activity induced instabilities.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Apr 29, 2019
- Source ID
- W911NF1910268
Entities
People
- Vincenzo Vitelli
Organizations
- Army Contracting Command
- United States Army
- University of Chicago