Wave Propagation through Lattice Materials

Lattice effective property and Bloch-wave homogenization

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G. U. Patil, K. H. Matlack, Effective property evaluation and analysis of three-dimensional periodic lattices and composites through Bloch-wave homogenization. The Journal of the Acoustical Society of America, vol. 145, 1259–1269 (2019) https://doi.org/10.1121/1.5091690.

Manipulating waves through elastic media has potential applications in cloaking, mode conversion, wave bending, and filtering, etc. The wave characteristics such as velocity, polarization, bandgaps, and directionality directly depend upon the effective mechanical properties of the periodic lattices. Here, we use the Bloch-wave homogenization approach to evaluate the effective static properties of the 3D periodic lattices: cubic, octet, Kelvin and bowtie. This approach lays the foundation for the nondestructive evaluation of the properties of the metamaterial using ultrasonic velocity measurements.


Elastic Anisotropy of Multimaterial Composite Lattices

Composites allow us to obtain unique properties by combining properties of two different materials. We apply the same principle to lattice materials and design composite lattices with two different materials and geometries. We parameterize the bulk material property of one of the lattice structure and show that the overall anisotropy of the lattice material can be tuned through the bulk material property. We use the Zener anisotropy index and the Universal anisotropy index to study the change in anisotropy behavior. These types of composite lattices are potentially multifunctional due to their higher energy absorption ability while being lightweight.

Composites of Cubic (left) and octet (right) lattices. Surrounding material is much softer than lattice bulk material.

Lattice effective property and Elastostatic Homogenization

Lattice materials possess properties that are a combination of bulk material properties and geometric configuration. Lattices with different geometric configurations will behave differently under static loading. In order to compare various lattices with each other and to facilitate lattice selection, evaluating the properties is essential. In this work, we study different configurations of lattice geometries and the effect of their geometric parameters on Young’s and Shear Modulus. We do finite element simulation of uniaxial and pure shear loading independently to evaluate uniaxial and shear modulus. We use the elastostatic homogenization approach along with periodic boundary conditions to model the equivalent elastic continuum.

Elastostatic boundary conditions for uniaxial stiffness (left) and shear stiffness (right)

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