An epithelium-inspired deformation modeling framework for responsive 4D materials

Joel Pepper

doi:10.17918/00011498

4D materials are a class of engineerable objects which change their shape and properties in response to external stimuli. Examples of this material type include 4D prints--3D prints that warp when heated--and certain configurations of epithelial tissue. 4D prints show promise in decreasing the need for shipping material and specialized molds during manufacturing as objects can be created flat then warped at their destination into their desired form. Epithelial tissue holds great potential to provide insights into the design of new and advanced configurations of 4D materials, and the simulation of epithelial structures may also lead to novel biological and medical insights. When working with 4D materials, one of the biggest challenges is designing the deformation process that takes them from their initial, simple configuration to the final target shape. 4D constructs must be designed via the specification and deployment of local deformations that aggregate to produce a specific macroscopic form. Targeted solutions to this problem exist throughout the literature, but most are either not extensible beyond the specific use case for which they were created, or do not include robust inverse design capabilities. To address the challenge of designing deformations that produce a specific shape, we turn to developmental biology for inspiration. This dissertation presents a generalized modeling framework for a design of 4D lattices which can produce a wide variety of complex curved surfaces via a directed deformation process, based on prescribed local geometry. The structure of the lattices and the deformations which they undergo are inspired by the morphological behavior of epithelial tissue in vivo. This framework takes as input target open surfaces and analyzes their conformations to determine the defining geometric properties which need to be replicated. Using this, it outputs flat, multi-layered grids made up of "responsive" nodes that, when their physics is simulated, warp into the target surface. The framework has been applied to develop three distinct material designs. The first is a novel configuration for 4D prints using stacked cuboidal grids, which shrink differentially at each layer to recreate the sizing and curvatures of the target surface. The second extends the framework to support bi-layer hexagonal grids modeled after epithelial tissue that have the capacity to recreate a wider variety of input surfaces. And the third explores a method to encode the shape changing behavior of the epithelium-inspired grids into a single machine learning model shared by all their constituent "cells" with the goal of having this shared agent iteratively drive the deformation of the "tissue" towards the target shape using only the local environmental information available to each individual cell. The overall modeling, simulation, and inverse design framework represents a novel method for the creation of 4D objects with a focus on using the basic geometric properties of local strains and curvatures to drive complex and varied deformations.

An epithelium-inspired deformation modeling framework for responsive 4D materials

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An epithelium-inspired deformation modeling framework for responsive 4D materials

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