Mechanics of damage, healing, damageability, and integrity of materials: A conceptual framework

2016 ◽  
Vol 26 (1) ◽  
pp. 50-103 ◽  
Author(s):  
George Z Voyiadjis ◽  
Peter I Kattan
Keyword(s):  
Damage Mechanics ◽  
Healing Process ◽  
Continuum Damage Mechanics ◽  
Damage Variable ◽  
Continuum Damage ◽  
Variable Section ◽  
Damage Healing ◽  
Characterization Of Materials ◽  
New Formulation

In this work several new and fundamental concepts are proposed within the framework of continuum damage mechanics. These concepts deal primarily with the nature of the two processes of damage and healing along with introducing a consistent and systematic definition for the concepts of damageability and integrity of materials. Toward this end, seven sections are presented as follows: “The logarithmic damage variable” section introduces the logarithmic and exponential damage variables and makes comparisons with the classical damage variable. In “Integrity and damageability of materials” section a new formulation for damage mechanics is presented in which the two angles of damage–integrity and healing–damageability are introduced. It is shown that both the damage variable and the integrity variable can be derived from the damage–integrity angle while the healing variable and damageability variable are derived from the healing–damageability angle. “The integrity field” section introduces the new concept of the integrity field while “The healing field” section introduces the new concept of the healing field. These two fields are introduced as a generalization of the classical concepts of damage and integrity. “Unhealable damage and nondamageable integrity” section introduces the new and necessary concept of unrecoverable damage or unhealable damage. In this section the concept of permanent integrity or nondamageable integrity is also presented. In “Generalized nonlinear healing” section generalized healing is presented where a distinction is clearly made between linear healing and nonlinear healing. As an example of nonlinear healing the equations of quadratic healing are derived. Finally in “Dissection of the healing process” section a complete and logical/mathematical dissection is made of the healing process. It is hoped that these new and fundamental concepts will pave the way for new, consistent, and holistic avenues in research in damage mechanics and characterization of materials.

scholarly journals A continuum damage mechanics framework for modeling micro-damage healing

2012 ◽  
Vol 49 (3-4) ◽  
pp. 492-513 ◽  
Author(s):  
Masoud K. Darabi ◽  
Rashid K. Abu Al-Rub ◽  
Dallas N. Little
Keyword(s):  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Damage Healing

scholarly journals On certain fundamental issues in continuum damage mechanics

2012 ◽  
Vol 21 (1-2) ◽  
pp. 33-36
Author(s):  
George Z. Voyiadjis ◽  
Peter I. Kattan
Keyword(s):  
Deformation Process ◽  
Damage Mechanics ◽  
Materials Science ◽  
Continuum Damage Mechanics ◽  
Damage Variable ◽  
Continuum Damage ◽  
Secondary Damage ◽  
Damage Process ◽  
Primary Damage ◽  
Definition Of

AbstractIn this article, we discuss three fundamental issues in continuum damage mechanics. First, we investigate the nature of the damage process. For this purpose, we dissect the expression of the effective stress into an infinite geometric series and introduce several stages of damage that we call primary damage, secondary damage, tertiary damage, etc. The second issue to be discussed is the problem of small damage. In this regard, we introduce a new definition of the damage variable that is suitable for small-damage cases. Finally, we discuss the new concept of undamageable materials. These are currently hypothetical materials that maintain a zero value of the damage variable throughout the deformation process. It is hoped that these proposed new types of materials will open the way to new areas of research in both damage mechanics and materials science.

scholarly journals Continuum damage mechanics modeling of composite laminates including transverse cracks

2017 ◽  
Vol 27 (6) ◽  
pp. 877-895 ◽  
Author(s):  
Tomonaga Okabe ◽  
Sota Onodera ◽  
Yuta Kumagai ◽  
Yoshiko Nagumo
Keyword(s):  
Composite Laminates ◽  
Damage Mechanics ◽  
Elastic Moduli ◽  
Crack Density ◽  
Continuum Damage Mechanics ◽  
Damage Variable ◽  
Continuum Damage ◽  
Transverse Cracks ◽  
Element Analysis ◽  
The Finite Element Analysis

In this study, the continuum damage mechanics model for predicting the stiffness reduction of composite laminates including transverse cracks is formulated as a function of crack density. To formulate the model, first the damage variable in the direction normal to the fiber of a ply including transverse cracks is derived. The damage variable is derived by the model assuming a plane strain field in the isotropic plane and using the Gudmundson–Zang model for comparison. The effective compliance based on the strain equivalent principle proposed by Murakami et al. and classical laminate theory are then used to formulate the elastic moduli of laminates of arbitrary lay-up configurations as a function of the damage variable. Finally, the results obtained from this model are compared to the finite-element analysis reported in previous studies. The model proposed in this paper can predict the stiffness of laminates containing damage due to transverse cracks (or surface crack) from just the mechanical properties of a ply and the lay-up configurations. Furthermore, this model can precisely predict the finite-element analysis results and experiment results for the elastic moduli of the laminate of arbitrary lay-up configuration, such as cross-ply, angle ply, and quasi-isotropic, including transverse cracks. This model only considers the damage of the transverse crack; it does not consider damage such as delamination. However, this model seems to be effective in the early stage of damage formation when transverse cracking mainly occurs. The model assuming plane strain field in the isotropic plane which is proposed in this paper can calculate the local stress distribution in a ply including transverse cracks as a function of crack density. The damage evolution of transverse cracks can thus be simulated by determining the fracture criterion.

scholarly journals Conceptual thoughts on continuum damage mechanics for shallow ice shelves

2014 ◽  
Vol 60 (222) ◽  
pp. 685-693 ◽  
Author(s):  
Arne Keller ◽  
Kolumban Hutter
Keyword(s):  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Damage Variable ◽  
Continuum Damage ◽  
Zeroth Order ◽  
Ice Dynamics ◽  
Ice Shelves ◽  
Rough Approximation ◽  
Isotropic Damage ◽  
Consistent Treatment

AbstractWe consider a theory for shallow ice shelves that includes an isotropic damage variable. A zeroth-order shallow-shelf approximation allows a simple yet consistent treatment of both ice dynamics and damage evolution. We find that the damage variable (like temperature) has, in general, to vary with depth; a purely two-dimensional membrane theory can only be considered a rough approximation for isothermal ice shelves.

Fundamental aspects for characterization in continuum damage mechanics

2018 ◽  
Vol 28 (2) ◽  
pp. 200-218 ◽  
Author(s):  
George Z Voyiadjis ◽  
Peter I Kattan
Keyword(s):  
Damage Mechanics ◽  
Conceptual Modeling ◽  
Continuum Damage Mechanics ◽  
Mean Value ◽  
Complete Analysis ◽  
Mean Value Theorem ◽  
Continuum Damage ◽  
Interfacial Damage ◽  
True Nature ◽  
Characterization Of Materials

New issues, derivations, and remarks are presented for the subject of continuum damage mechanics. Emphasis is placed on the fundamental and basic aspects of damage mechanics. This work is a continuation of a previous work of the authors and provides for a complete analysis of the issues discussed previously. The topics discussed include: (1) the true nature of the damage–integrity angle, (2) modeling damaged solids as composite systems, (3) hypothesis of strain equivalence as a special case of the hypothesis of elastic energy equivalence, (4) mechanics of damaged beams, (5) a mean value theorem for damage mechanics, (6) partial damage mechanics characterization, (7) micro-damage or nano-damage, (8) crack and void mechanics, and (9) conceptual modeling of interfacial damage. It is hoped that these new and fundamental concepts will pave the way for new, consistent, and holistic avenues in research in damage mechanics and characterization of materials.

Microstructure Based Formability Characterization of Multi Phase Steels Using Damage Mechanics

2007 ◽  
Vol 348-349 ◽  
pp. 217-220
Author(s):  
Vitoon Uthaisangsuk ◽  
Ulrich Prahl ◽  
Wolfgang Bleck
Keyword(s):  
Metal Forming ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Failure Behavior ◽  
Continuum Damage ◽  
Structural Components ◽  
Multiphase Microstructure ◽  
Multi Phase ◽  
Multiphase Steels

Due to the coexistence of different micro structural components and their interactions, multiphase steels offer an excellent combination between high formability and strength. On the micro-scale, the fracture examination shows large influence of different phases and their distributions on the mechanical properties and failure mechanisms. Considering the influence of multiphase microstructure, an approach is presented using representative volume elements (RVE) in combination with continuum damage mechanics (CDM). Herein, the influence of the material properties of individual phases and the local states of stress on the material formability as well as the failure behavior can be examined. By means of the RVE-CDM approach, a precise criterion for the deformability characterization in sheet metal forming of multi phase steels is presented.

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