Cloaking in two-dimensional elastic solids (Conference Presentation)

2020 ◽  
Author(s):  
Hussein Nassar ◽  
Yangyang Chen ◽  
Guoliang Huang
Keyword(s):  
Two Dimensional ◽  
Elastic Solids

scholarly journals Frequency-Dependent Tensile and Compressive Effective Moduli of Elastic Solids With Randomly Distributed Two-Dimensional Microcracks

2015 ◽  
Vol 82 (8) ◽  
Author(s):  
Youxuan Zhao ◽  
Yanjun Qiu ◽  
Laurence J. Jacobs ◽  
Jianmin Qu
Keyword(s):  
Wave Attenuation ◽  
Two Dimensional ◽  
Effective Moduli ◽  
The Finite Element Method ◽  
Elastic Solids ◽  
Frequency Dependent ◽  
Micromechanics Models ◽  
Dynamic Case ◽  
Crack Faces ◽  
Analytical Expressions

This paper develops micromechanics models to estimate the tensile and compressive elastic moduli of elastic solids containing randomly distributed two-dimensional microcracks. The crack faces are open under tension and closed under compression. When the crack faces are closed, they may slide against one another following the Coulomb's law of dry friction. The micromechanics models provide analytical expressions of the tensile and compressive moduli for both static and dynamic cases. It is found that the tensile and compressive moduli are different. Further, under dynamic loading, the compressive and tensile moduli are both frequency dependent. As a by-product, the micromechanics models also predict wave attenuation in the dynamic case. Numerical simulations using the finite element method (FEM) are conducted to validate the micromechanics models.

Two-dimensional stress wave analysis in incompressible elastic solids

1989 ◽  
Vol 10 (8) ◽  
pp. 701-712 ◽  
Author(s):  
Tang Zhi-jing ◽  
T. C. T. Ting ◽  
Li Yong-chi
Keyword(s):  
Stress Wave ◽  
Two Dimensional ◽  
Wave Analysis ◽  
Elastic Solids ◽  
Stress Wave Analysis

scholarly journals Material Point Method Investigations of Trauma to Fluids and Elastic Solids Due to Finite Barriers

2009 ◽  
Vol 7 (4) ◽  
Author(s):  
J Dean ◽  
M Roth ◽  
Paul Gray
Keyword(s):  
Eddy Currents ◽  
Material Point Method ◽  
Elastic Solid ◽  
Material Point ◽  
Point Method ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Elastic Solids ◽  
Point Particles ◽  
Large Building

A Material Point Method (MPM) algorithm is developed and utilized to investigate how the dynamics of (Langrangian) Navier-Stokes fluids as well as that of elastic solids is affected by trauma due to finite barriers. For the fluid simulations, material point particles are placed in a two dimensional pipe with various initial and boundary conditions and stationary perturbations to fluid flow. Results show that eddy currents are present not only in the wake of the perturbing object but are also responsible for disruption of laminar flow upstream from the barrier. An unfortunately relevant application for sudden finite trauma to an elastic solid involves simulations of an aircraft striking a large building under varying system conditions. The work presented here is introductory in nature; the potential ramifications and importance of continued study is discussed and emphasized.

Capillarity with solids

2017 ◽  
Author(s):  
S. Mora ◽  
Y. Pomeau
Keyword(s):  
Theoretical Analysis ◽  
Variational Approach ◽  
General Framework ◽  
Deep Understanding ◽  
The Self ◽  
Two Dimensional ◽  
Elastic Solids ◽  
Comprehensive Review ◽  
Capillary Phenomena ◽  
Physical Phenomena

Capillary phenomena occurring on soft solid interfaces are discussed over this lecture. The main goal is to show how a variational approach provides a deep understanding of the static effects coming from the self-capillarity of elastic solids. After an introduction, the general framework is introduced and then various situations are discussed. In each case, the physical phenomena are first briefly introduced, a theoretical analysis is presented, and then the predictions are compared with experiments when available. This lecture is intended as an introduction rather than as a comprehensive review. Demonstrations are simplified as much as possible thanks to physically relevant assumptions (symmetric problems, two-dimensional problems, etc.). The aim is to highlight the main physical ingredients. References are included throughout the text for readers desiring a more in-depth treatment.

Deformation of Inhomogeneous Elastic Solids With Two-Dimensional Damage

2001 ◽  
Vol 68 (4) ◽  
pp. 528-536
Author(s):  
J. J. Luo ◽  
I. M. Daniel
Keyword(s):  
Periodic Structures ◽  
Elastic Behavior ◽  
Two Dimensional ◽  
Elastic Solids ◽  
Inhomogeneous Materials ◽  
Linear Elastic ◽  
Reinforced Composite ◽  
Macroscopic Deformation ◽  
Microscopic Damage ◽  
Microscopic Deformation

A general correlation is derived between macroscopic stresses/strains and microscopic deformation on the damage surfaces for inhomogeneous elastic solids with two-dimensional damage. Assuming linear elastic behavior for the undamaged materials, the macroscopic deformation associated with nonlinear strains, or damage strains, is shown to be the weighted sum of the microscopic deformations on the damage surfaces. For inhomogeneous materials with periodic structures (laminated composites, for example) and various identifiable damage modes, simple relations are derived between the macroscopic deformation and microscopic damage. When the number of identifiable damage modes is less than or equal to the number of relevant measurable macroscopic strains, the correlation can be used to evaluate the damage progression from simple macroscopic stress and strain measurements. The simple case of a unidirectional fiber-reinforced composite under longitudinal load is used to show how the results can help detect and characterize the damage using macroscopic measurements, without resorting to assumptions of detailed microscopic deformation mechanisms.

Three-Dimensional Deformations

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Anisotropic Elasticity ◽  
Two Dimensional ◽  
Elastic Solids ◽  
Elastic Materials ◽  
Dimensional Solution ◽  
Line Integral ◽  
Isotropic Elasticity ◽  
Anisotropic Elastic

There appears to be very little study, if any, on the extension of Stroh's formalism to three-dimensional deformations of anisotropic elastic materials. In most three-dimensional problems the analyses employ approaches that are remotely related to Stroh's two-dimensional formalism. This is not unexpected, since this has been the situation between two-dimensional and three-dimensional isotropic elasticity. However it needs not be the case for three-dimensional anisotropic elasticity. Much can be gained if a connection to the Stroh formalism can be established. Barnett and Lothe (1975a) appeared to be the only ones who made a connection between a three-dimensional solution and Stroh's two-dimensional formalism. Earlier, several investigators obtained the Green's function for the infinite anisotropic medium in term of a line integral on an oblique plane in the three-dimensional space. That line integral, as we will see here, is one of Barnett-Lothe tensors on an oblique plane. We propose in this chapter extensions and applications of Stroh's two-dimensional formalism to certain three-dimensional deformations of anisotropic elastic solids.

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