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.

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.

Shakedown-Ratcheting Analysis of a Spherical Pressure Vessel by Anisotropic Continuum Damage Mechanics

2018 ◽  
Author(s):  
Ali Nayebi ◽  
Azam Surmiri ◽  
Hojjatollah Rokhgireh
Keyword(s):  
Pressure Vessel ◽  
Damage Mechanics ◽  
Kinematic Hardening ◽  
Continuum Damage Mechanics ◽  
Mapping Method ◽  
Anisotropic Damage ◽  
Continuum Damage ◽  
Interaction Diagram ◽  
Plastic Shakedown ◽  
Spherical Pressure

In cyclic loading and when plastic flow occurs, discontinuities grow. In this research, interaction diagram of Bree has been developed when the spherical pressure vessel contains discontinuities such as voids and microcracks. Bree’s diagram is used for ratcheting assessment of pressurized equipment in ASME III NH. Nature of these defects leads to an anisotropic damage. Anisotropic Continuum Damage Mechanics (CDM) is considered to account effects of these discontinuities on the behavior of the structure. Shakedown – ratcheting response of a hollow sphere under constant internal pressure and cyclic thermal loadings are studied by using anisotropic CDM theory coupled with nonlinear kinematic hardening of Armstrong-Frederick m’s model (A-F). Return mapping method is used to solve numerically the developed relations. Elastic, elastic shakedown, plastic shakedown and ratcheting regions are illustrated in the modified Bree’s diagram. Influence of anisotropic damage due to the plastic deformation is studied and it was shown that the plastic shakedown region is diminished because of the developed damage.

An Anisotropic Creep Damage Model for Anisotropic Weld Metal

2007 ◽  
Author(s):  
S. Peravali ◽  
T. H. Hyde ◽  
K. A. Cliffe ◽  
S. B. Leen
Keyword(s):  
Weld Metal ◽  
Test Data ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Isotropic Case ◽  
Anisotropic Damage ◽  
Secondary Creep ◽  
Continuum Damage ◽  
Anisotropic Creep

Past studies from creep tests on uniaxial specimens and Bridgman notch specimens, for a P91 weld metal, showed that anisotropic behaviour (more specifically transverse isotropy) occurs in the weld metal, both in terms of creep (steady-state) strain rate behaviour and rupture times (viz. damage evolution). This paper describes the development of a finite element (FE) continuum damage mechanics methodology to deal with anisotropic creep and anisotropic damage for weld metal. The method employs a second order damage tensor following the work of Murakami and Ohno [1] along with a novel rupture stress approach to define the evolution of this tensor, taking advantage of the transverse isotropic nature of the weld metal, to achieve a reduction in the number of material constants required from test data (and hence tests) to define the damage evolution. Hill’s anisotropy potential theory is employed to model the secondary creep. The theoretical model is implemented in a material behaviour subroutine within the general-purpose, non-linear FE code ABAQUS [2]. The validation of the implementation against established isotropic continuum damage mechanics solutions for the isotropic case is described. A procedure for calibrating the multiaxial damage constants from notched bar test data is described for multiaxial implementations. Also described is a study on the effect of uniaxial specimen orientation on anisotropic damage evolution.

THE FOUNDATIONS OF CONTINUUM DAMAGE MECHANICS

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Siamak Yazdani ◽  
Sevenn Borgersen ◽  
Asli Pelin Gurgun ◽  
Hossein Nazari
Keyword(s):  
Damage Mechanics ◽  
Nonlinear Behavior ◽  
Continuum Damage Mechanics ◽  
Uniaxial Stress ◽  
Internal Variable ◽  
Continuum Damage ◽  
Damage Potential ◽  
Variable Theory ◽  
Wide Range ◽  
The Many

Damage Mechanics has become a useful theory in describing the nonlinear behavior of solids driven by the nucleation and growth of cracks and microcracks. This approach, based on the first principles of mechanics and thermodynamics, has also been combined with classical theories of plasticity to address a wide range of loading applications. In spite of the many different damage mechanics models and representations that are proposed, the foundation of damage mechanics is not well understood or at least not thoroughly published giving rise to the many inaccurate definitions and formulations. The intent of this paper is to provide the background of the continuum damage mechanics outlining the fundamentals on which this field theory is set up. The internal variable theory of continuum thermodynamics is reviewed and is shown that with Legendre transformation technique, various potential functions can be developed for damage mechanics formulation in either stress or strain space. The concept of constrained or neighboring equilibrium state is also introduced and is explained. The paper will conclude with the derivation of the general damage potential and a suggestion is given for the isotropic damage formulation with the resulting uniaxial stress-strain relation.

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.

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.

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.

An Elastoplastic-anisotropic Damage Model for Concrete

2011 ◽  
Vol 261-263 ◽  
pp. 371-375
Author(s):  
Jun Liu ◽  
Gao Lin
Keyword(s):  
Effective Stress ◽  
Damage Mechanics ◽  
Damage Model ◽  
Nonlinear Behavior ◽  
Continuum Damage Mechanics ◽  
Anisotropic Damage ◽  
Softening Effect ◽  
Damage Constitutive Model ◽  
Structural Levels ◽  
Damage Tensor

An elastoplastic-anisotropic damage constitutive model for the description of nonlinear behavior of concrete is presented. The yield surface is developed in effective stress spaces, which takes into account the hardening effect and better match the experimental data. The stiffness degradation and softening effect are considered in the framework of continuum damage mechanics formulation. The second-order damage tensor is used to characterize the anisotropy induced by the orientation of microcracks. In order to simulate the unilateral effect, the elastic Helmholtz free energy is decomposed into a volumetric part and a deviatoric part. The different behavior under tensile and compressive loadings is modeled by using different variables in effective stress and damage tensor. Numerical results of the model accord well with experimental results at the material and structural levels.

A homogenisation-based continuum damage mechanics model for cyclic damage in 3D composites

2009 ◽  
Vol 113 (1144) ◽  
pp. 371-383 ◽  
Author(s):  
S. Ghosh ◽  
J. R. Jain
Keyword(s):  
Fourth Order ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Constitutive Law ◽  
Model Parameters ◽  
Zone Model ◽  
Continuum Damage ◽  
Proposed Model ◽  
Micromechanical Damage ◽  
Cyclic Damage

Abstract This paper develops a 3D homogenisation based continuum damage mechanics (HCDM) model for fibre-reinforced composites undergoing micromechanical damage under cyclic loading. Micromechanical damage in a representative volume element (RVE) of the material occurs by fibre-matrix interfacial debonding, which is incorporated in the model through a hysteretic bilinear cohesive zone model. The proposed model expresses a damage evolution surface in the strain space in the principal damage co-ordinate system or PDCS. PDCS enables the model to account for the effect of non-proportional load history. The material constitutive law involves a fourth order orthotropic tensor with stiffness characterised as a macroscopic internal variable. Cyclic damage parameters are introduced in the monotonic HCDM model to describe the material degradation due to fatigue. Three dimensional damage in composites is accounted for through functional forms of the fourth order damage tensor in terms of components of macroscopic strain and elastic stiffness tensor. The HCDM model parameters are calibrated from homogenisation of micromechanical solutions of the RVE for a few representative cyclic strain histories. The proposed model is validated by comparing results of the HCDM model with pure micromechanical analysis results followed by homogenisation. Finally, the potential of cyclic HCDM model as a design tool is demonstrated through macro-micro analysis of cyclic damage progression in composite structures.

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