Degenerate Torque Materials for Perfect Cloaking in Elastic Media
Abstract
Research Problems: Cloaking for various wave phenomena is an issue of fundamental importance both practical and theoretical. However, little to no work succeeded in probing the problem of cloaking for elastic waves, the major obstacle being that the corresponding equations are not form-invariant. The lack of form-invariance is in its essence a problem in material design meaning that there is a class of theoretical constitutive behaviors that no known materials satisfy. The ultimate purpose of the proposed research is to model, design and fabricate materials that will fill in this Òbehavioral gapÓ. The suggested Òcloaking materialsÓ will have a generalized form-invariant constitutive behavior, making them excellent candidates for the design of elastic wave control devices in general, and of elastic cloaks in particular. The central object of this proposal is the study of cloaking materials within the framework of a new class of elastic materials termed ÒDegenerate Torque MaterialsÓ (DTMs) and characterized as materials admitting a set of collapse mechanisms and torque-induced non-symmetric stress states. The research will establish a theoretical framework for the modelling of DTMs and will tackle the inverse problem of design of specific DTMs targeting particular macroscopic constitutive parameters, typical of those required by elastic cloaks. The necessity in elastic cloaking of a material with engineered collapse mechanisms and torque distributions, as well as modern advances in additive manufacturing technology, all encourage the use of truss- or lattice-based design paradigms. The research will accordingly explore paths towards the design and fabrication as well as dynamic modeling and homogenization of specific degenerate mechanical trusses and lattices admitting collapse mechanisms and exhibiting aptitude for the support of torque densities and non-symmetric stresses. Broad Impact: On a fundamental level, the findings of this research should have lasting impact on the theory of elasticity by suggesting a solution to the long-standing problem of transformation-invariance. On the other hand, it brings new insight to another fundamental problem in elasticity, that of the closure of constitutive laws under homogenization. The technological impact of the novel DTM functionalities that we will explore will be felt across multiple engineering fields and allow for the creation of some seriously outlandish devices for civil and defense applications. Our material fabrication and experimental characterization of DTMs will allow assessing (and possibly stretching) the capabilities of 3D printing and laser acquisition systems against challenging problems due to the coexistence of small and large scales and to the presence of geometrically complex internal features.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 14, 2019
- Source ID
- W911NF1810031
Entities
People
- Guoliang Huang
Organizations
- Army Contracting Command
- United States Army
- University of Missouri