Design of patterned multilayer films with eigenstrains by topology optimization

Abstract

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.

A Computational Design Methodology for Assembly and Actuation of Thin-Film Structures via Patterning of Eigenstrains

“…It includes the following important features: multilayer films with eigenstrains; spatial patterning of material and eigenstrains in each layer; possible anisotropy; nonlinear geometric effects, including buckling and postbuckling; and both flat and curved film systems. The latter three features are extensions from our previous work [11]. After describing our approach, we demonstrate its potential and versatility by applying it to three classes of problems of contemporary and emerging interest: initially flat films with predominately bending deformations, curved films with predominately bending deformations, and initially flat films with buckling deformations.…”

“…We model the deformation of such a layered plate using standard Kirchhoff thin-plate kinematics. We recognize that these may lead to inaccuracies due to thick-plate effects that exist locally near patterned features with characteristic in-plane dimensions on the order of the plate thickness, but numerical tests and measurements suggest that this approximation is reasonable in the description of the overall deformation behavior of the plate [11]. In this paper, we use three-node 18-DOF layered composite finite-elements [14] that consist of a combination of a membrane triangle with drilling degrees of freedom and an assumed quadratic rotation bending triangle [15], [16].…”

“…The objective function is then formulated as the minimization of the difference of each nodal displacement component from its target displacement. This so-called displacement leveling function has proven to be effective for similar optimization problems [11]. Applying a mass constraint to improve the clarity of the eigenstrain distribution, the optimization problem is written as follows:…”

“…In this paper, we further develop and demonstrate an experimentally validated computational analysis and design approach [11], [12] that, with proper interpretation of the physical mechanisms, is applicable to a wide variety of fabrication techniques, as well as actuation schemes. Specifically, we consider the analysis and then design of 3-D structures that can be obtained from multilayer films with controlled spatial distributions of eigenstrains, both through-the-thickness and in-plane.…”

Patterned bilayer plate microstructures subjected to thermal loading: Deformation and stresses

“…The latter can result from Joule heating during current flow (Shen, 2001;Kim and Lin, 2005;Keller et al, 2007). Furthermore, film patterns can be designed to yield specific device performance due to the interaction of misfit strains and pattern geometry (Pajot et al, 2006). Finally we note that technological trends are continually resulting in thinner and thinner films which make issues of dimensional stability due to misfit strains increasingly important.…”