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We develop a formal approach to design shaped microstructures from multilayer films with eigenstrains in the layers. The eigenstrains are inelastic strains that vary from layer to layer resulting in elastic misfit between the layers. Examples include thermal expansion mismatch between the layers, piezoelectric strains, and strains in shape memory alloys. In our approach, the eigenstrains are manipulated by spatially patterning the films to generate structures that, although fabricated by a conventional, planar thin film technology, deform into desired three-dimensional shaped surfaces. The material patterns in the individual layers are determined by topology optimization allowing the creation of arbitrarily complex, geometric layouts. In contrast to existing topology optimization methods for patterning plate structures, the goal of the proposed approach is to generate large deformations via eigenstrains, rather than to increase the stiffness of plate via reinforcement patterns. The optimization methodology is demonstrated by the design of two-and three-layer thin film structures. The performance of the optimized designs is verified by experiments showing the importance of accounting for a nonlinear kinematics in order to obtain the desired shape in the deformed configuration. While our approach is demonstrated in the context of the design of three-dimensional microstructures, it can be easily applied to a variety of problems where it is desired to control the complex shape of plate-like structures by spatial actuation-the spatial actuators are represented by eigenstrains.

We develop a computational approach to design 3-D structures that can be fabricated and then assembled and/or actuated by spatially tailoring the layout of multilayer films with eigenstrains. Eigenstrains are stress-free strains when they occur in an unconstrained solid. They are almost an inevitable companion, albeit often unwanted, of thin-film processes. When they vary through the thickness, the constraint of the layers leads to internal stresses and bending and buckling deformations can occur; when they additionally vary in the plane of the film, more complex deformations can result. To advantageously use this phenomenon, we build on relatively simple mechanics ideas in a continuum formulation and combine geometrically nonlinear finite-element analysis of arbitrary-shaped multilayer films with a topology optimization methodology to determine the material layout in each layer so the film deforms into a prescribed shape. We expand our previous experimentally validated approach to include initially curved films and anisotropic eigenstrains. Using an extended system formulation for directly computing instability points allows us to tailor postbuckling response while explicitly controlling the design at limit and bifurcation points. We demonstrate the potential and versatility of our approach by applying it to a series of problems of contemporary and emerging interest.[ 2008-0306]Index Terms-Design methodology, microelectromechanical devices, patterning, thin film.

Inspired by actuation mechanisms in plant structures and motivated by recent advances in electro-chemically driven micro-pumps, this paper is concerned with a novel concept for active materials based on distributed hydraulic actuation. Due to the similarity of the actuation principles seen in plants undergoing nastic motion, we refer to this class of active materials as nastic materials. We present a mechanical modeling approach for nastic materials representing the effects of pressure generation and fluid transport by incompressible eigenstrains. This model is embedded into a two-level macro/micro topology optimization procedure. On a macroscopic level, the integration of nastic material into a structural system is optimized. The placement and distribution of nastic material on a flexible substrate are optimized to generate target displacement and force distributions. On a microscopic level, the stress and strain generation is tailored to desired macroscopic material properties by optimizing the layout of vascular fluid channels embedded in an elastic matrix. For the layout optimization of vascular fluid channels, a novel topology optimization procedure is presented that models the effects of pressure along the fluid channels via an analogy with thermal conduction and convection. For this purpose an auxiliary heat transfer problem is solved. The macro-scale optimization procedure is studied for plate structures patterned by nastic materials in order to generate target bending and twist deformations. The results show the significant differences of the optimal distributions of active material depending on the strain model used for representing the actuation concept. The micro-scale vascular design methodology is verified with plane-stress examples. The results show that the layout of fluid channels can be optimized such that target strains are generated.