Combined Level-Set-XFEM-Density Topology Optimization of Four-Dimensional Printed Structures Undergoing Large Deformation

Author:

Geiss Markus J.1,Boddeti Narasimha2,Weeger Oliver2,Maute Kurt1,Dunn Martin L.3

Affiliation:

1. Ann and H. J. Smead Department of Aerospace Engineering Sciences, University of Colorado at Boulder, Boulder, CO 80309-0429 e-mail:

2. SUTD Digital Manufacturing and Design Centre, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372 e-mail:

3. College of Engineering and Applied Sciences, University of Colorado Denver, 1200 Larimer Street, Denver, CO 80217-3364 e-mail:

Abstract

Advancement of additive manufacturing is driving a need for design tools that exploit the increasing fabrication freedom. Multimaterial, three-dimensional (3D) printing allows for the fabrication of components from multiple materials with different thermal, mechanical, and “active” behavior that can be spatially arranged in 3D with a resolution on the order of tens of microns. This can be exploited to incorporate shape changing features into additively manufactured structures. 3D printing with a downstream shape change in response to an external stimulus such as temperature, humidity, or light is referred to as four-dimensional (4D) printing. In this paper, a design methodology to determine the material layout of 4D printed materials with internal, programmable strains is introduced to create active structures that undergo large deformation and assume a desired target displacement upon heat activation. A level set (LS) approach together with the extended finite element method (XFEM) is combined with density-based topology optimization to describe the evolving multimaterial design problem in the optimization process. A finite deformation hyperelastic thermomechanical model is used together with an higher-order XFEM scheme to accurately predict the behavior of nonlinear slender structures during the design evolution. Examples are presented to demonstrate the unique capabilities of the proposed framework. Numerical predictions of optimized shape-changing structures are compared to 4D printed physical specimen and good agreement is achieved. Overall, a systematic design approach for creating 4D printed active structures with geometrically nonlinear behavior is presented which yields nonintuitive material layouts and geometries to achieve target deformations of various complexities.

Funder

National Science Foundation

Air Force Office of Scientific Research

Publisher

ASME International

Subject

Computer Graphics and Computer-Aided Design,Computer Science Applications,Mechanical Engineering,Mechanics of Materials

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