Effective Material Properties of Damaged Elastic Solids

2006 ◽  
Vol 324-325 ◽  
pp. 1185-1188
Author(s):  
Usik Lee ◽  
Deokki Youn
Keyword(s):  
Elastic Properties ◽  
Material Properties ◽  
Equivalence Principle ◽  
Strain Energy ◽  
Damage Variable ◽  
Local Damage ◽  
Elastic Solids ◽  
Energy Equivalence ◽  
Effective Material Properties ◽  
Isotropic Solids

By using a continuum modeling approach based on the equivalent elliptical crack representation of a local damage and the strain energy equivalence principle, the effective elastic compliances and the effective engineering constants are derived in closed forms in terms of the virgin (undamaged) elastic properties and a scalar damage variable for damaged two- and threedimensional isotropic solids. It is shown that the effective Young’s modulus in the direction normal to the crack surfaces is always smaller than its intact value.

A Theory of Continuum Damage Mechanics for Anisotropic Solids

1999 ◽  
Vol 66 (1) ◽  
pp. 264-268 ◽  
Author(s):  
U. Lee
Keyword(s):  
Elastic Properties ◽  
Strain Energy ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Energy Equivalence ◽  
Damage Theory ◽  
Anisotropic Elastic ◽  
Isotropic Solids ◽  
Line Crack

This paper develops a fracture mechanics based continuum damage theory for initially anisotropic solids by extending the author’s previous damage theory for isotropic solids. The concepts of strain energy equivalence principle (SEEP) and equivalent line-crack modeling are used to develop the effective continuum elastic properties of a damaged solid in terms of the undamaged anisotropic elastic properties and a scalar damage variable.

Effects of Shear Deformation of Struts in Hexagonal Lattices on their Effective In-Plane Material Properties

2021 ◽  
Vol 1034 ◽  
pp. 193-198
Author(s):  
Pana Suttakul ◽  
Thongchai Fongsamootr ◽  
Duy Vo ◽  
Pruettha Nanakorn
Keyword(s):  
Shear Deformation ◽  
Material Properties ◽  
Strain Energy ◽  
Equivalent Strain ◽  
Homogenization Method ◽  
Two Dimensional ◽  
Engineering Applications ◽  
Large Numbers ◽  
Effective Material Properties ◽  
Unit Cells

Two-dimensional lattices are widely used in many engineering applications. If 2D lattices have large numbers of unit cells, they can be accurately modeled as 2D homogeneous solids having effective material properties. When the slenderness ratios of struts in these 2D lattices are low, the effects of shear deformation on the values of the effective material properties can be significant. This study aims to investigate the effects of shear deformation on the effective material properties of 2D lattices with hexagonal unit cells, by using the homogenization method based on equivalent strain energy. Several topologies of hexagonal unit cells and several slenderness ratios of struts are considered. The effects of struts’ shear deformation on the effective material properties are examined by comparing the results of the present study, in which shear deformation is neglected, with those from the literature, in which shear deformation is included.

On Formulas for the Velocity of Rayleigh Waves in Prestrained Incompressible Elastic Solids

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
Pham Chi Vinh
Keyword(s):  
Rayleigh Wave ◽  
Energy Function ◽  
Rayleigh Waves ◽  
Strain Energy ◽  
Hydrostatic Stress ◽  
Strain Energy Function ◽  
Elastic Solids ◽  
Algebraic Form ◽  
Cubic Equation ◽  
Isotropic Solids

In the present paper, formulas for the velocity of Rayleigh waves in incompressible isotropic solids subject to a general pure homogeneous prestrain are derived using the theory of cubic equation. They have simple algebraic form and hold for a general strain-energy function. The formulas are concretized for some specific forms of strain-energy function. They then become totally explicit in terms of parameters characterizing the material and the prestrains. These formulas recover the (exact) value of the dimensionless speed of Rayleigh wave in incompressible isotropic elastic materials (without prestrain). Interestingly that, for the case of hydrostatic stress, the formula for the Rayleigh wave velocity does not depend on the type of strain-energy function.

Universal deformations in inhomogeneous isotropic nonlinear elastic solids

2021 ◽  
Vol 477 (2253) ◽  
Author(s):  
Arash Yavari
Keyword(s):  
Strain Energy ◽  
Elastic Solid ◽  
Necessary Condition ◽  
Density Functions ◽  
Elastic Solids ◽  
Universal Deformations ◽  
Green Strain ◽  
The Right ◽  
Nonlinear Elastic ◽  
Isotropic Solids

Universal (controllable) deformations of an elastic solid are those deformations that can be maintained for all possible strain-energy density functions and suitable boundary tractions. Universal deformations have played a central role in nonlinear elasticity and anelasticity. However, their classification has been mostly established for homogeneous isotropic solids following the seminal works of Ericksen. In this article, we extend Ericksen’s analysis of universal deformations to inhomogeneous compressible and incompressible isotropic solids. We show that a necessary condition for the known universal deformations of homogeneous isotropic solids to be universal for inhomogeneous solids is that inhomogeneities respect the symmetries of the deformations. Symmetries of a deformation are encoded in the symmetries of its pulled-back metric (the right Cauchy–Green strain). We show that this necessary condition is sufficient as well for all the known families of universal deformations except for Family 5.

scholarly journals Broadband metamaterials and metasurfaces: a review from the perspectives of materials and devices

Nanophotonics ◽  
2020 ◽  
Vol 9 (10) ◽  
pp. 3165-3196 ◽  
Author(s):  
Joonkyo Jung ◽  
Hyeonjin Park ◽  
Junhyung Park ◽  
Taeyong Chang ◽  
Jonghwa Shin
Keyword(s):  
Material Properties ◽  
Frequency Bandwidth ◽  
Broad Bandwidth ◽  
Practical Applications ◽  
Effective Material Properties

AbstractMetamaterials can possess extraordinary properties not readily available in nature. While most of the early metamaterials had narrow frequency bandwidth of operation, many recent works have focused on how to implement exotic properties and functions over broad bandwidth for practical applications. Here, we provide two definitions of broadband operation in terms of effective material properties and device functionality, suitable for describing materials and devices, respectively, and overview existing broadband metamaterial designs in such two categories. Broadband metamaterials with nearly constant effective material properties are discussed in the materials part, and broadband absorbers, lens, and hologram devices based on metamaterials and metasurfaces are discussed in the devices part.

Elastic Properties of Steps at Interphase Boundaries

1991 ◽  
Vol 238 ◽  
Author(s):  
G. J. Shiflet
Keyword(s):  
Energy Density ◽  
Elastic Properties ◽  
Mathematical Analysis ◽  
Strain Energy ◽  
Chemical Processes ◽  
Diffusion Kinetics ◽  
Interphase Boundaries ◽  
Kinetics Of ◽  
Maximum Stresses

ABSTRACTStresses are introduced in crystals at interphase boundaries where steps improve the registry of atoms. A model and mathematical analysis based on an approach previously taken by van der Merwe and Shiflet1–4 of the problem incorporating a coherent step are presented. Computed distributions of stresses, strains, dilatation and energy density in the form of contours and nets are given for a coherent monatomic step. It is concluded that the maximum stresses are quite large and the fields decay fairly rapidly with distance from the steps, the gradient of dilatation around steps will significantly affect diffusion kinetics of impurities and the strain energy seems too low to significantly enhance chemical processes.

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