scholarly journals Reciprocity, passivity and causality in Willis materials

2016 ◽  
Vol 472 (2194) ◽  
pp. 20160604 ◽  
Author(s):  
Michael B. Muhlestein ◽  
Caleb F. Sieck ◽  
Andrea Alù ◽  
Michael R. Haberman
Keyword(s):  
Elastic Material ◽  
Time Domain ◽  
Material Properties ◽  
Constitutive Equations ◽  
Wave Motion ◽  
Constitutive Relations ◽  
Alternative Formulation ◽  
Elastic Materials ◽  
Order Dispersion ◽  
Insight Into

Materials that require coupling between the stress–strain and momentum–velocity constitutive relations were first proposed by Willis (Willis 1981 Wave Motion 3 , 1–11. ( doi:10.1016/0165-2125(81)90008-1 )) and are now known as elastic materials of the Willis type, or simply Willis materials. As coupling between these two constitutive equations is a generalization of standard elastodynamic theory, restrictions on the physically admissible material properties for Willis materials should be similarly generalized. This paper derives restrictions imposed on the material properties of Willis materials when they are assumed to be reciprocal, passive and causal. Considerations of causality and low-order dispersion suggest an alternative formulation of the standard Willis equations. The alternative formulation provides improved insight into the subwavelength physical behaviour leading to Willis material properties and is amenable to time-domain analyses. Finally, the results initially obtained for a generally elastic material are specialized to the acoustic limit.

On the Linear Constitutive Equations of Transversely Isotropic Incompressible Elastic Materials

1972 ◽  
Vol 45 (4) ◽  
pp. 1104-1110
Author(s):  
H. Demiray ◽  
M. Levinson
Keyword(s):  
Stress Concentration ◽  
Stress Analysis ◽  
Circular Hole ◽  
Elastic Material ◽  
Constitutive Equations ◽  
Transversely Isotropic ◽  
Elastic Materials ◽  
Rubber Composites ◽  
Limiting Case ◽  
Compressible Materials

Abstract The linear constitutive equations of a transversely isotropic, incompressible, elastic material are derived in this paper as a limiting case of the constitutive equations for the corresponding compressible materials. These equations should be appropriate for the stress analysis of products fabricated from certain laminated, reinforced rubber composites. Some details of a problem concerned with the stress concentration around a circular hole are also given.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

scholarly journals Direct measurement of Coulomb-laser coupling

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Doron Azoury ◽  
Michael Krüger ◽  
Barry D. Bruner ◽  
Olga Smirnova ◽  
Nirit Dudovich
Keyword(s):  
Coulomb Interaction ◽  
Time Domain ◽  
Coulomb Potential ◽  
Laser Field ◽  
Large Range ◽  
Extreme Ultraviolet ◽  
Strong Field ◽  
The Time Domain ◽  
First Time ◽  
Insight Into

AbstractThe Coulomb interaction between a photoelectron and its parent ion plays an important role in a large range of light-matter interactions. In this paper we obtain a direct insight into the Coulomb interaction and resolve, for the first time, the phase accumulated by the laser-driven electron as it interacts with the Coulomb potential. Applying extreme-ultraviolet interferometry enables us to resolve this phase with attosecond precision over a large energy range. Our findings identify a strong laser-Coulomb coupling, going beyond the standard recollision picture within the strong-field framework. Transformation of the results to the time domain reveals Coulomb-induced delays of the electrons along their trajectories, which vary by tens of attoseconds with the laser field intensity.

Theoretical Meso-Model of Al2O3/ZrO2 Ceramic Response under Compression

2014 ◽  
Vol 601 ◽  
pp. 92-95
Author(s):  
Tomasz Sadowski ◽  
Liviu Marsavina
Keyword(s):  
Grain Boundary ◽  
Material Properties ◽  
Mechanical Model ◽  
Constitutive Relations ◽  
Ceramic Composites ◽  
Theoretical Modeling ◽  
Polycrystalline Structure ◽  
Two Phase

This paper presents theoretical modeling of two-phase ceramic composites subjected to compression. The meso-mechanical model allows for inclusion of all microdefects in the polycrystalline structure that exists at the grain boundary interfaces and inside the grains. The constitutive relations for the Al2O3/ZrO2composite with the gradual degradation of the material properties due to different defects development were formulated.

Linear Anisotropic Elastic Materials

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Elastic Constants ◽  
Elastic Material ◽  
Positive Definite ◽  
Material Symmetry ◽  
Two Dimensional ◽  
Elastic Materials ◽  
Rectangular Coordinate System ◽  
Full Symmetry ◽  
Anisotropic Elastic ◽  
Anisotropic Elastic Material

The relations between stresses and strains in an anisotropic elastic material are presented in this chapter. A linear anisotropic elastic material can have as many as 21 elastic constants. This number is reduced when the material possesses a certain material symmetry. The number of elastic constants is also reduced, in most cases, when a two-dimensional deformation is considered. An important condition on elastic constants is that the strain energy must be positive. This condition implies that the 6×6 matrices of elastic constants presented herein must be positive definite. Referring to a fixed rectangular coordinate system x1, x2, x3, let σij and εks be the stress and strain, respectively, in an anisotropic elastic material. The stress-strain law can be written as . . . σij = Cijksεks . . . . . .(2.1-1). . . in which Cijks are the elastic stiffnesses which are components of a fourth rank tensor. They satisfy the full symmetry conditions . . . Cijks = Cjiks, Cijks = Cijsk, Cijks = Cksij. . . . . . .(2.1-2). . .

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