Abstract
Inspired by crystallography, the periodic assembly of trusses into architected materials has enjoyed popularity for more than a decade and produced countless cellular structures with beneficial mechanical properties. Despite the successful and steady enrichment of the truss design space, the inverse design has remained a challenge: While predicting effective truss properties is now commonplace, efficiently identifying architectures that have homogeneous or spatially varying target properties has remained a roadblock to applications from lightweight structures to biomimetic implants. To overcome this gap, we propose a deep-learning framework, which combines neural networks with enforced physical constraints, to predict truss architectures with fully tailored anisotropic stiffness. Trained on millions of unit cells, it covers an enormous design space of topologically distinct truss lattices and accurately identifies architectures matching previously unseen stiffness responses. We demonstrate the application to patient-specific bone implants matching clinical stiffness data, and we discuss the extension to spatially graded cellular structures with locally optimal properties.
Highlights
Opportunities for selecting materials in the engineering design process have fundamentally changed over the past decade due to innovation in materials systems with tailored properties
Our framework to smoothly transition between different unit cells enables the design of lightweight structures with spatially varying, locally optimized properties, for applications from wave guiding to artificial bone
We start by defining a large, structured design space of truss lattices by drawing inspiration from the truss descriptors proposed by Zok et al [45]
Summary
We start by defining a large, structured design space of truss lattices by drawing inspiration from the truss descriptors proposed by Zok et al [45]. Of seven elementary lattice topologies as fundamental building blocks (details provided in SI Appendix, Fig. S1) These comprise both well-studied topologies (like the octet) and nonstandard ones to admit a wide range of anisotropic responses with a relatively small number of beam elements. To expand the achievable stiffness space in a continuous manner, we enlarge the design space by applying a series of affine geometric transformations to the obtained lattice topology, which transforms every vertex at a location X j to its new location x j as follows: Assuming that the UC aligns with the Cartesian coordinate axes {e1, e2, e3}, we first stretch the UC with a stretch tensor U = diag(U1, U2, U3) with principal stretches U1, U2, U3 > 0, followed by a rigid-body rotation RI ∈ SO[3]. Our design parameterization is not unique (there is flexibility in the selection of elementary lattices and the parameterization of the affine transformations); the main idea is to offer an elegant and, most importantly, sufficiently rich design space that covers a sufficiently large anisotropic stiffness space
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