Nonlocal Microstructural Mechanics of Active Materials

This works deals with two problems in the mechanics§of active materials with long-range interactions.§Classical PDE continuum models of active materials§are not closed, and require nucleation and kinetic§information or regularization as additional§constitutive input. We examine this problem in the§peridynamic formulation, a nonlocal continuum model§that uses integral equations to account for§long-range forces that are important at small scales,§and allows resolution of the structure of interfaces.§We then consider the design of ferroelectric§optoelectronic circuit elements. Free surfaces and§electrodes on these devices generate electrical§fields that must be resolved over all space. These§fields enhance the role of geometry in the§electromechanical response of these materials, and§give rise to strong size and shape dependence. We§describe a computational method that transforms this§problem into a local setting in an accurate and§efficient manner. We apply it to three examples:§closure domains, a ferroelectric slab with segmented§electrodes and a notch subjected to§electro-mechanical loading.