A mechanical reduced order model for elastomeric 3D printed architectures
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Ward Small, Jeremy M. Lenhardt, Robert S. Maxwell, and Thomas S. Wilson Materials Science Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA (Received 4 October 2017; accepted 13 December 2017)
Direct ink writing of silicone elastomers enables printing with precise control of porosity and mechanical properties of ordered cellular solids, suitable for shock absorption and stress mitigation applications. With the ability to manipulate structure and feedstock stiffness, the design space becomes challenging to parse to obtain a solution producing a desired mechanical response. Here, we derive an analytical design approach for a specific architecture. Results from finite element simulations and quasi-static mechanical tests of two different parallel strand architectures were analyzed to understand the structure-property relationships under uniaxial compression. Combining effective stiffness-density scaling with least squares optimization of the stress responses yielded general response curves parameterized by resin modulus and strand spacing. An analytical expression of these curves serves as a reduced order model, which, when optimized, provides a rapid design capability for filament-based 3D printed structures. As a demonstration, the optimal design of a face-centered tetragonal architecture is computed that satisfies prescribed minimum and maximum load constraints.
I. INTRODUCTION
Additive manufacturing (AM), or 3D printing, provides unprecedented spatial control over feature geometry and material composition.1,2 In direct ink writing (DIW), a filament-based 3D printing process, a shear-thinning fluid is extruded from a nozzle onto a substrate using a multiaxis printing system, producing a 3D structure in a layer-by-layer fashion.3 With custom silicone elastomeric ink formulations, we have developed a printing capability to fabricate cushions for stress mitigation, vibration isolation, and impact absorption.4 Direct ink writing can reliably manufacture ordered architectures with highly uniform and reproducible geometric, material, and mechanical properties which are far superior to traditional stochastic foams, from both a design and lifetime performance standpoint.5 These ordered cellular solids are a subset of mechanical metamaterials, typically structures consisting of arrays of unit cells with unique properties, including large strength to weight ratios6,7 and negative thermal expansion.8 While many of these lattice networks only consider static feedstock material properties, Contributing Editor: Katia Bertoldi a) Address all correspondence to this author. e-mail: [email protected] b) This author was an editor of this journal during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http://www.mrs. org/editor-manuscripts/. DOI: 10.1557/jmr.2017.483
the introduction of soft materials with functional, dynamic properties enable even more complex behaviors. Lattices and foams comprised of two elastomers can e
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