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.

Evaluation of a Strain Energy Equivalence Principle (SEEP)-Based Continuum Damage Model

2007 ◽  
Vol 353-358 ◽  
pp. 1199-1202
Author(s):  
Usik Lee ◽  
Deokki Youn ◽  
Sang Kwon Lee
Keyword(s):  
Strain Energy ◽  
Natural Frequencies ◽  
Damage Model ◽  
Elastic Stiffness ◽  
Constitutive Law ◽  
Mode Shapes ◽  
Continuum Damage ◽  
Energy Equivalence ◽  
Damage Theory ◽  
Square Plate

A new continuum damage theory (CDT) has been proposed by Lee et al. (1997) based on the SEEP. The CDT has the apparent advantage over the other related theories because the complete constitutive law can be readily derived by simply replacing the virgin elastic stiffness with the effective orthotropic elastic stiffness obtained by using the proposed continuum damage theory. In this paper, the CDT is evaluated by comparing the mode shapes and natural frequencies of a square plate containing a small line-through crack with those of the same plate with a damaged site replaced with the effective orthotropic elastic stiffness computed by using the CDT.

Notion of Continuum Damage Mechanics and its Application to Anisotropic Creep Damage Theory

1983 ◽  
Vol 105 (2) ◽  
pp. 99-105 ◽  
Author(s):  
S. Murakami
Keyword(s):  
Damage Mechanics ◽  
Creep Damage ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Damage State ◽  
Creep Theory ◽  
Damage Theory ◽  
Damaged Materials ◽  
Damage Tensor ◽  
Anisotropic Creep

After discussing the notion and the practical procedures of continuum damage mechanics, their utility is elucidated by applying them to formulate an anisotropic creep damage theory for nonsteady multiaxial states of stress. By taking account of the mechanisms of microstructural change of materials due to creep, it is shown that the creep damage state can be described by a second rank symmetric damage tensor, while the effects of material damage on creep deformation of damaged materials should be expressed by a fourth rank tensor formed from the damage tensor. Validity of the creep theory formulated in terms of these damage variables is examined by performing model tests. Specialization of the proposed theory is also discussed.

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.

Decomposition of Elastic Stiffness Degradation in Continuum Damage Mechanics

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
George Z. Voyiadjis ◽  
Peter I. Kattan
Keyword(s):  
Elastic Energy ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Elastic Stiffness ◽  
Stiffness Degradation ◽  
Continuum Damage ◽  
Energy Equivalence ◽  
The One ◽  
Special Case ◽  
Decomposition System

The degradation of elastic stiffness is investigated systematically within the framework of continuum damage mechanics. Consistent equations are obtained showing how the degradation of elastic stiffness can be decomposed into a part due to cracks and another part due to voids. For this purpose, the hypothesis of elastic energy equivalence of order n is utilized. In addition, it is shown that the hypothesis of elastic strain equivalence is obtained as a special case of the hypothesis of elastic energy equivalence of order n. In the first part of this work, the formulation is scalar and applies to the one-dimensional case. The tensorial formulation for the decomposition is also presented that is applicable to general states of deformation and damage. In this general case, one cannot obtain a single explicit tensorial decomposition equation for elastic stiffness degradation. Instead, one obtains an implicit system of three tensorial decomposition equations (called the tensorial decomposition system). Finally, solution of the tensorial decomposition system is illustrated in detail for the special case of plane stress.

Anisotropic (Continuum Damage Mechanics)-based multi-mechanism model for semi-crystalline polymer

2016 ◽  
Vol 27 (3) ◽  
pp. 357-386 ◽  
Author(s):  
Walid Ayadi ◽  
Lucien Laiarinandrasana ◽  
Kacem Saï
Keyword(s):  
Experimental Data ◽  
Shape Factor ◽  
Damage Mechanics ◽  
Crystalline Polymer ◽  
Continuum Damage Mechanics ◽  
Degree Of Crystallinity ◽  
Continuum Damage ◽  
Mechanism Model ◽  
Energy Equivalence ◽  
Proposed Model

In this work, the anisotropic damage of semi-crystalline polymers is investigated. The model, developed within a thermodynamic framework, includes the following features: (i) the degree of crystallinity; (ii) the hydrostatic pressure effect; and (iii) the damage anisotropy. The adopted tensorial damage variable is based on the Continuum Damage Mechanics approach under the energy equivalence assumption. For the quantification of the anisotropy, a parameter called “shape factor” is defined as the ratio between the void mean diameter and the void mean height. This parameter is linked to the main axial and the main radial damage components. Experimental data taken from the recent literature using the tomography technique were selected to assess the model capability. Finite element simulations of notched round bar specimens subjected to tensile test stopped at three key loading stages are systematically compared with experimental data. The proposed model was able not only to accurately simulate the macroscopic response of the material, but more interestingly, to reproduce the spatial distribution of the shape factor. This demonstrates the anisotropy effects of the material under study induced at different stages of the deformation.

Complex Damage Variables in Continuum Damage Mechanics

2015 ◽  
Vol 784 ◽  
pp. 3-10
Author(s):  
George Z. Voyiadjis ◽  
Peter I. Kattan
Keyword(s):  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Elastic Stiffness ◽  
Continuum Damage ◽  
Cross Sectional ◽  
Practical Applications ◽  
Area Reduction ◽  
Variable Approach ◽  
Energy Equivalence ◽  
Mathematical Equations

The concept of complex damage variables is introduced in this work. These damage variables have both real and imaginary parts. They are introduced not to use them in practical applications but to try to derive a direct relationship between the damage due to cross-sectional area reduction and the damage due to elastic stiffness degradation. In addition this concept can provide an insight in addressing the concept of healing that the authors have extensively published as well as the concept of undamageable materials. Toward this goal some success is achieved in the sense that some complicated relationships between the two damage processes are formulated. These relationships and the complex variable approach are novel ideas in Continuum Damage Mechanics. Throughout the formulation the hypothesis of strain equivalence is used in order to simplify the mathematical equations. This work can be extended and generalized by substituting the hypothesis of energy equivalence but this will complicate the equations unnecessarily.

New Tensors for Anisotropic Damage in Continuum Damage Mechanics

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
George Z. Voyiadjis ◽  
Mohammed A. Yousef ◽  
Peter I. Kattan
Keyword(s):  
Mechanical Behavior ◽  
Elastic Energy ◽  
Elastic Strain ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Damage Effect ◽  
Anisotropic Damage ◽  
Continuum Damage ◽  
Energy Equivalence ◽  
Scalar Invariant

In this work, new proposed damage tensors are studied in order to investigate the damage effect variables in the mechanical behavior of materials. All cases studied in this work are defined in terms of the elasticity of the material and based on the hypotheses of both elastic strain equivalence and elastic energy equivalence. Moreover, the new proposed damage tensors are anisotropically expressed in terms of the well-known damage effect tensor M. The principal-valued damage effect tensor is used to obtain the first scalar invariant of that tensor and its inverse, which are employed in expressing and verifying the new proposed damage tensors. The study demonstrates that most of the new proposed damage tensors are verified within the framework of continuum damage mechanics. In addition, new hybrid damage tensors are proposed which are defined in terms of the damage effect tensor and the new proposed damage tensors. The new hybrid damage tensors are eventually expressed in terms of the damage effect tensor.

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