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Controlling Displacement Fields in Polar Willis Solids via Gauge Transformations
Yangyang Chen1, Michael R Haberman2
1Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.
Physical Review Letters
|April 21, 2023
Summary
Researchers developed novel polar Willis metamaterials capable of precisely controlling both rigid-body displacement and material deformation. This breakthrough enables advanced shape-morphing capabilities and arbitrary displacement control functions through inverse design.
Area of Science:
- Solid Mechanics
- Metamaterials Science
- Linear Elasticity
Background:
- Total displacement in solids comprises rigid-body motion and deformation.
- Controlling deformation enables shape-morphing materials, but simultaneous control of both is challenging.
- Polar Willis solids offer a potential avenue for novel displacement control.
Purpose of the Study:
- To demonstrate simultaneous control of rigid-body displacement and deformation in solids.
- To introduce a method for realizing such solids using lattice metamaterials.
- To provide an analytical framework for inverse design of these materials.
Main Methods:
- Exploiting gauge transformations within linear transformation elasticity.
- Developing a displacement gauge to induce polarity and Willis coupling.
- Designing lattice metamaterials with tailored geometries, grounded springs, and coupled gears.
Main Results:
- Elastostatic polar Willis solids exhibiting simultaneous control of displacement and deformation were realized.
- The developed solids break minor symmetries of the stiffness tensor and show cross-coupling between stress and displacement.
- Numerical demonstrations confirmed a range of displacement control functions, including peculiar ones.
Conclusions:
- A novel analytical framework for the inverse design of grounded polar Willis metamaterials is presented.
- These metamaterials offer unprecedented control over arbitrary displacement functions.
- The findings open new possibilities for advanced material design and applications.
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