Session: 12-06-02: Scientific Machine Learning (SciML) for Characterization, Modeling, and Design of Structures and Materials

Paper Number: 150160

150160 - A Reduced Order Model for Capturing Mechanical Interaction Phenomena in Woven Systems 

Weaves are hierarchical structures for which the arrangement of the weavers (i.e. warp and weft fibers) determines the mechanical properties of the overall structure. Understanding the mechanics of weaving is the first step in designing woven structures with complex geometries and programmable properties. Most existing engineering models of woven systems treat the weave as an anisotropic continuum with constitutive relations defining the directions of the weavers. This methodology assumes the individual weaver size is considerably smaller than the overall weave itself. Such homogenized models fail to capture weave-specific phenomena such as crimp interchange, slip, friction, locking, shear, and breakage. These effects determine how weaves behave under large strains and strain-rates and directly impact their performance for real-world applications like ballistic impact energy absorbers, three-dimensional housing structures, and shape morphing soft robots.

In this work, we present a discretized simulation model, based on reduced order geometric modeling techniques, that captures the mechanics of individual weaver interactions and their effect on the combined structure. The model is constructed for scale independent, linear elastic materials. We treat the weave as a collection of unit cells. Nodes represent the center lines of weaver cross-sections, bars represent both the weaver normal stiffness and axial stiffness, and rotational springs represent the shear stiffness. 1D elements are also included to govern lateral stiffness between contacting weavers. All elements are formulated in accordance with Hamilton’s principle and constructed in simulation using a finite element-like approach. The model elements are validated with analytical solutions for loading in both geometrically linear and nonlinear cases. A meshing algorithm was also devised to enable simulation of arbitrary woven geometries.

We show that the model gives anticipated weave deformations in various loading scenarios. Using eigenvalue analyses, we demonstrate that our model can capture global weave behaviors, like shear and anisotropic stiffness, as well as some weave-specific phenomena (crimp interchange, slip, etc.). By altering stiffness of individual elements, we show how the deformation modes of the weave change and can be tuned to achieve realistic weave performance. To illustrate the model’s utility, we simulate the deformations of arbitrary 3D woven shapes whose initial shape is generated using the meshing algorithm. The model’s simplicity lends itself to rapid woven structure analyses and inverse design implementations. The scale independence of the model makes it useful for a range of applications. Future work will seek to explore the inverse design problem and introduce more complexity, such as material nonlinearity and dynamic response.

Presenting Author: Anvay Pradhan University of Michigan

Presenting Author Biography: Pradhan is a third year PhD candidate in Mechanical Engineering & Scientific Computing at the University of Michigan

Authors:

Anvay Pradhan University of Michigan
Evgueni Filipov University of Michigan
Talia Moore University of Michigan