This thesis deals with two aspects of the mechanics of symmetry-breaking defects such as phase boundaries, inclusions and free surfaces, and their role in the macroscopic response of active materials. We first examine the problem of kinetics using a nonlocal theory, and then study the role of geometry in active materials with fields that are not confined to the material.; 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. Our analysis shows that kinetics is inherent to the theory. Viewing nucleation as a dynamic instability at small times, we obtain interesting scaling results and insight into nucleation in regularized theories. We also exploit the computational ease of this theory to study an unusual mechanism that allows a phase boundary to bypass an inclusion.; Shifting focus to problems of an applied nature, we consider issues in the design of ferroelectric optical/electronic circuit elements. Free surfaces and electrodes on these devices generate electrical fields that must be resolved over all space, and not just within the body. These fields greatly enhance the importance of geometry in understanding 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 electromechanical loading.
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