Kinematic Description of Damage

1998 ◽  
Vol 65 (1) ◽  
pp. 93-98 ◽  
Author(s):  
Taehyo Park ◽  
G. Z. Voyiadjis
Keyword(s):  
Fourth Order ◽  
Damage Mechanics ◽  
Effective Strain ◽  
Continuum Damage Mechanics ◽  
Second Order ◽  
Finite Strains ◽  
Damage Effect ◽  
Energy Equivalence ◽  
Simple Mapping ◽  
Damage Tensor

In this paper the kinematics of damage for finite elastic deformations is introduced using the fourth-order damage effect tensor through the concept of the effective stress within the framework of continuum damage mechanics. However, the absence of the kinematic description of damage deformation leads one to adopt one of the following two different hypotheses. One uses either the hypothesis of strain equivalence or the hypothesis of energy equivalence in order to characterize the damage of the material. The proposed approach in this work provides a relation between the effective strain and the damage elastic strain that is also applicable to finite strains. This is accomplished in this work by directly considering the kinematics of the deformation field and furthermore it is not confined to small strains as in the case of the strain equivalence or the strain energy equivalence approaches. The proposed approach shows that it is equivalent to the hypothesis of energy equivalence for finite strains. In this work, the damage is described kinematically in the elastic domain using the fourth-order damage effect tensor which is a function of the second-order damage tensor. The damage effect tensor is explicitly characterized in terms of a kinematic measure of damage through a second-order damage tensor. The constitutive equations of the elastic-damage behavior are derived through the kinematics of damage using the simple mapping instead of the other two hypotheses.

Anisotropic Damage Effect Tensors for the Symmetrization of the Effective Stress Tensor

1997 ◽  
Vol 64 (1) ◽  
pp. 106-110 ◽  
Author(s):  
G. Z. Voyiadjis ◽  
T. Park
Keyword(s):  
Stress Tensor ◽  
Effective Stress ◽  
Fourth Order ◽  
Damage Mechanics ◽  
Continuum Theory ◽  
Continuum Damage Mechanics ◽  
Damage Effect ◽  
Anisotropic Damage ◽  
Tensor Algebra ◽  
Physical Description

Based on the concept of the effective stress and on the description of anisotropic damage deformation within the framework of continuum damage mechanics, a fourth order damage effective tensor is properly defined. For a general state of deformation and damage, it is seen that the effective stress tensor is usually asymmetric. Its symmetrization is necessary for a continuum theory to be valid in the classical sense. In order to transform the current stress tensor to a symmetric effective stress tensor, a fourth order damage effect tensor should be defined such that it follows the rules of tensor algebra and maintains a physical description of damage. Moreover, an explicit expression of the damage effect tensor is of particular importance in order to obtain the constitutive relation in the damaged material. The damage effect tensor in this work is explicitly characterized in terms of a kinematic measure of damage through a second-order damage tensor. In this work, tensorial forms are used for the derivation of such a linear transformation tensor which is then converted to a matrix form.

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.

scholarly journals A bi-dissipative damage model for concrete

2015 ◽  
Vol 8 (1) ◽  
pp. 49-65
Author(s):  
J. J. C. Pituba ◽  
W. M. Pereira Júnior
Keyword(s):  
Reinforced Concrete ◽  
Structural Engineering ◽  
Damage Mechanics ◽  
Damage Model ◽  
Continuum Damage Mechanics ◽  
Concrete Material ◽  
Framed Structures ◽  
Energy Equivalence ◽  
Proposed Model ◽  
Damage Processes

This work deals with an improvement of an anisotropic damage model in order to analyze reinforced concrete structures submitted to reversal loading. The original constitutive model is based on the fundamental hypothesis of energy equivalence between real and continuous media following the concepts of the Continuum Damage Mechanics. The concrete is assumed as an initial elastic isotropic medium presenting anisotropy, permanent strains and bimodularity induced by damage evolution. In order to take into account the bimodularity, two damage tensors governing the rigidity in tension or compression regimes are introduced. However, the original model is not capable to simulate the influence of the previous damage processes in compression regimes. In order to avoid this problem, some conditions are introduced to simulate the damage unilateral effect. It has noted that the damage model is agreement with to micromechanical theory conditions when dealing to unilateral effect in concrete material. Finally, the proposed model is applied in the analyses of reinforced concrete framed structures submitted to reversal loading. These numerical applications show the good performance of the model and its potentialities to simulate practical problems in structural engineering.

Damage Deactivation

1995 ◽  
Vol 62 (2) ◽  
pp. 450-458 ◽  
Author(s):  
N. R. Hansen ◽  
H. L. Schreyer
Keyword(s):  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Uniaxial Stress ◽  
Projection Operators ◽  
Continuum Damage ◽  
Order Tensor ◽  
Smooth Functions ◽  
One Dimensional ◽  
Opening And Closing ◽  
Damage Tensor

A phenomenological algorithm, motivated by the “mode I” microcrack opening and closing mechanism, is developed for the deactivation and reactivation of the damage effects as modeled by certain continuum damage mechanics theories. One-dimensional formulations with and without coupled plasticity are used to elucidate concepts associated with damage deactivation and to suggest multidimensional deactivation formulations applicable to continuum damage theories that employ a second-order tensor as the damage measure. Strain-based projection operators are used to deactivate the damage effects in the damage tensor. Motivated by observations from one-dimensional coupled formulations, both the total and elastic strains must be compressive for the damage to be rendered inactive. By introducing smooth functions to represent the transition from the active to the inactive state, discontinuities in the response are avoided. To illustrate the aspects associated with deactivation, a consistent set of examples using a strain-controlled one-cycle uniaxial stress loading is given for each formulation.

Bridging the macro to mesoscale: Evaluating the fourth-order anisotropic damage tensor parameters from ultrasonic measurements of an isotropic solid under triaxial stress loading

2018 ◽  
Vol 28 (2) ◽  
pp. 219-232 ◽  
Author(s):  
Louise Olsen-Kettle
Keyword(s):  
Fourth Order ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Uniaxial Stress ◽  
Anisotropic Damage ◽  
Internal Damage ◽  
Isotropic Solid ◽  
Selection Of Variables ◽  
Transverse Isotropic ◽  
Selection Of

One of the most challenging problems which arises in continuum damage mechanics is the selection of variables to describe the internal damage. Many theories have been proposed and various types of damage variables ranging from scalar to vector to tensor quantities have been used. In this paper we consider anisotropic damage and the most general form for damage by using a fourth-order tensor for the damage variables. We demonstrate how experimentally measured quantities can be related to the internal tensorial damage variables. We apply this analysis to experiments of an initially isotropic solid becoming transverse isotropic under triaxial or uniaxial stress loading.

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.

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.

Homogenization Based 3D Continuum Damage Mechanics Model for Composites Undergoing Microstructural Debonding

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
Jayesh R. Jain ◽  
Somnath Ghosh
Keyword(s):  
Fourth Order ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Interfacial Debonding ◽  
Material Behavior ◽  
Constitutive Law ◽  
Continuum Damage ◽  
Loading History ◽  
Model Framework ◽  
Mechanics Model

This paper develops a microscopic homogenization based continuum damage mechanics (HCDM) model framework for fiber reinforced composites undergoing interfacial debonding. It is an advancement over the 2D HCDM model developed by Raghavan and Ghosh (2005, “A Continuum Damage Mechanics Model for Unidirectional Composites Undergoing Interfacial Debonding,” Mech. Mater., 37(9), pp. 955–979), which does not yield accurate results for nonproportional loading histories. The present paper overcomes this shortcoming through the introduction of a principal damage coordinate system (PDCS) in the HCDM representation, which evolves with loading history. The material behavior is represented as a continuum constitutive law involving a fourth order orthotropic tensor with stiffness characterized as a macroscopic internal variable. The current work also extends the model of Raghavan and Ghosh to incorporate damage in 3D composites through functional forms of the fourth order damage tensor in terms of macroscopic strain components. The model is calibrated by homogenizing the micromechanical response of the representative volume element (RVE) for a few strain histories. This parametric representation can significantly enhance the computational efficiency of the model by avoiding the cumbersome strain space interpolations. The proposed model is validated by comparing the CDM results with homogenized micromechanical response of single and multiple fiber RVEs subjected to arbitrary loading history.

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.

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