Shear-Normal Coupled Deformations in Anisotropic Structured Materials

Citation

Boddapati, Purna Chandra Jagannadh Kumar (2025) Shear-Normal Coupled Deformations in Anisotropic Structured Materials. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/k1t8-4t34. https://resolver.caltech.edu/CaltechTHESIS:08142024-070224435

Abstract

The advent of additive manufacturing has allowed the design and engineering of a new class of materials known as metamaterials, or structured/architected materials. These metamaterials exhibit unique functionalities, such as ultrahigh strength-to-density ratios, which their base materials cannot achieve. Often designed to exhibit near-isotropic behavior, metamaterials derive their special properties from the distinctive deformation, dynamic motion, and elastic energy distribution of their micro- and meso-architectures. However, designing metamaterials for anisotropy, despite their ability to attain unique properties, is challenging. Fully characterizing anisotropic stiffness in planar loading requires six independent elastic tensor moduli. This high number of independent elastic stiffness parameters also expands the design space of structured materials and leads to unusual phenomena, such as materials that can shear under uniaxial compression. This direction-dependent shear-axial coupling is crucial for many applications such as shape-morphing, elastic wave manipulation devices and impact redirection.

This thesis aims to understand the fundamental limits of shear-normal coupled deformations in anisotropic structured materials. Currently, there are no established upper and lower bounds on anisotropic moduli achieving extreme elastic anisotropy, similar to the Hashin-Shtrikman bounds in isotropic composites. This range is known as G-closure and provides limits for the achievable tensors. To date, there are no experimental methods that can measure the stiffness parameters of fully anisotropic structured materials from a single experiment. To address these challenges, we first introduce a method to generate two-phase periodic anisotropic unit cell geometries and construct a database of unit cells with a diverse range of effective elasticity tensors. The constructed database is compared with the properties achieved by hierarchical laminates and identify the regions where hierarchical designs are necessary to reach a specific extreme elasticity tensor.

We then propose an experimental methodology to evaluate the anisotropic material properties. Our technique, which utilizes the virtual fields method, allows for the determination of six separate stiffness tensor parameters of two-dimensional structured materials using just one tension test. This method thus eliminates the need for multiple experiments as is typical in traditional methods. We show the accuracy of our method using synthetic data generated from finite element simulations as well as by conducting experiments on four additively manufactured specimens. The approach requires no stress data and uses the full-field displacement data measured using digital image correlation and global force data.

We present a method for creating functionally graded anisotropic structures that smoothly transition between unit cells with distinct patterns. Isotropic materials with spatially varying density gradients have been shown to exhibit unique characteristics such as superior energy absorption. However, achieving smooth spatial gradients in the anisotropic mechanical properties while ensuring the connectivity of adjacent meso-architectures is non-trivial. This method allows for independent control of several functional gradients, such as porosity, anisotropic moduli, and symmetry. We show that certain nonlinearly graded structures when designed with unit cells positioned at distinct corners of the property space boundary exhibit novel mechanical behaviors. We conclude by designing specific functionally graded structures that demonstrate peculiar behaviors such as selective strain energy localization, localized rotations, compressive strains under tension, and longitudinal-shear wave mode conversion.

Thesis Files