Realizing the Willis equations with pre-stresses
arXiv:1411.0663 · doi:10.1016/j.jmps.2015.10.010
Abstract
This paper proves that the linear elastic behavior of the material with inhomogeneous pre-stresses can be described by the Willis equations. In this case, the additional terms in the Willis equations, compared with the classical linear elastic equations for homogeneous media, are related to the gradient of pre-stresses. In this way, the material length scale is naturally incorporated in the framework of continuum mechanics. All these findings also coincide with the results of transformation elastodynamics, so that they can meet the requirement of the principle of material objectivity and the principle of general invariance.
13 pages, 2 figures
References in corpus (4)
- Transformation elastodynamics and cloaking for flexural waves
- Hyperelastic cloaking theory: Transformation elasticity with pre-stressed solids
- Nonlinear pre-stress for cloaking from antiplane elastic waves
- The form-invariance of wave equations without requiring a priori relations between field variables
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- On static chiral Milton-Briane-Willis continuum mechanics
- Symmetry Breaking Creates Electro-Momentum Coupling in Piezoelectric Metamaterials
- An experimental verification of the one-dimensional static Willis-form equations
- Fundamental principles for generalized Willis metamaterials
- Modified 1D elastic wave equations that retain time synchronization under spatial coordinate transformations
- Understanding the First Order Inhomogeneous Linear Elasticity through Local Gauge Transformations
- Deeper understandings of the gauge theory for the first order inhomogeneous linear elasticity