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.

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.

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.

Investigation of the super healing theory in continuum damage and healing mechanics

2018 ◽  
Vol 28 (6) ◽  
pp. 896-917 ◽  
Author(s):  
Chahmi Oucif ◽  
George Z Voyiadjis ◽  
Peter I Kattan ◽  
Timon Rabczuk
Keyword(s):  
Plane Stress ◽  
Elastic Energy ◽  
Elastic Strain ◽  
Elastic Stiffness ◽  
Continuum Damage ◽  
Self Healing ◽  
Energy Equivalence ◽  
Stiffness Variation ◽  
Damage Healing ◽  
Definition Of

Self-healing is the capability of a material to heal (repair) damages autogenously and autonomously. New theoretical investigation extended from the healing material which represents a strengthening material was recently proposed. It concerns the theory of super healing. The healing in this case continues beyond what is necessary to recover the original stiffness of the material, and the material becomes able to strengthen itself. In the present work, the definition of the super healing theory is extended and defined based on the elastic stiffness variation. It concerns the degradation, recovery, and strengthening of the elastic stiffness in the case of damage, healing, and super healing materials, respectively. Comparison of the healing and super healing efficiencies between the hypotheses of the elastic strain and elastic energy equivalence is carried out. The classical super healing definition is also extended to generalized nonlinear and quadratic super healing based on elastic stiffness strengthening, and comparison of the super healing behavior in each theory is performed. It is found that the hypothesis of the elastic energy equivalence overestimates both the generalized nonlinear and quadratic super healed elastic stiffness strengthening. In addition, the generalized nonlinear super healing theory gives a high strengthening of the super healed elastic stiffness compared to the quadratic super healing theory in both equivalence hypotheses. It is also demonstrated that both the generalized nonlinear and quadratic super healing theories can be applied in the case of plane stress.

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.

Fatigue Life of the Human Teeth: A Continuum Damage Approach

2019 ◽  
Vol 43 ◽  
pp. 1-19
Author(s):  
Theddeus Tochukwu Akano
Keyword(s):  
Fatigue Life ◽  
Damage Mechanics ◽  
Stress Amplitude ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Elastoplastic Model ◽  
Human Teeth ◽  
Proposed Model ◽  
Number Of Cycles ◽  
Cycles To Failure

Normal oral food ingestion processes such as mastication would not have been possible without the teeth. The human teeth are subjected to many cyclic loadings per day. This, in turn, exerts forces on the teeth just like an engineering material undergoing the same cyclic loading. Over a period, there will be the creation of microcracks on the teeth that might not be visible ab initio. The constant formation of these microcracks weakens the teeth structure and foundation that result in its fracture. Therefore, the need to predict the fatigue life for human teeth is essential. In this paper, a continuum damage mechanics (CDM) based model is employed to evaluate the fatigue life of the human teeth. The material characteristic of the teeth is captured within the framework of the elastoplastic model. By applying the damage evolution equivalence, a mathematical formula is developed that describes the fatigue life in terms of the stress amplitude. Existing experimental data served as a guide as to the completeness of the proposed model. Results as a function of age and tubule orientation are presented. The outcomes produced by the current study have substantial agreement with the experimental results when plotted on the same axes. There is a notable difference in the number of cycles to failure as the tubule orientation increases. It is also revealed that the developed model could forecast for any tubule orientation and be adopted for both young and old teeth.

Modelling the asymmetric tension–compression properties of additively manufactured alloys using continuum damage mechanics

2021 ◽  
pp. 146442072110134
Author(s):  
A Nayebi ◽  
H Rokhgireh ◽  
M Araghi ◽  
M Mohammadi
Keyword(s):  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Element Model ◽  
Continuum Damage ◽  
Compression Tests ◽  
Compression Properties ◽  
Mechanics Model ◽  
Stress Components ◽  
Tension And Compression ◽  
Closure Effect

Additively manufactured parts often comprise internal porosities due to the manufacturing process, which needs to be considered in modelling their mechanical behaviour. It was experimentally shown that additively manufactured parts’ tensile and compressive mechanical properties are different for various metallic alloys. In this study, isotropic continuum damage mechanics is used to model additively manufactured alloys’ tension and compression behaviours. Compressive stress components can shrink discontinuities present in additively manufactured alloys. Therefore, the crack closure effect was employed to describe different behaviours during uniaxial tension and compression tests. A finite element model embedded in an ABAQUS’s UMAT format was developed to account for the isotropic continuum damage mechanics model. The numerical results of tension and compression tests were compared with experimental observations for additively manufactured maraging steel, AlSi10Mg and Ti-6Al-4V. Stress–strain curves in tension and compression of these alloys were obtained using the continuum damage mechanics model and compared well with the experimental results.

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