scholarly journals On continuum damage mechanics

2019 ◽  
Vol 52 (3) ◽  
pp. 125-147
Author(s):  
Kari Juhani Santaoja
Keyword(s):  
Stress Tensor ◽  
Effective Stress ◽  
Elastic Strain ◽  
Damage Mechanics ◽  
Volume Fraction ◽  
Strain Tensor ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
The Matrix ◽  
Elastic Strain Tensor

A material containing spherical microvoids with a Hookean matrix response was shown to take the appearance usually applied in continuum damage mechanics. However, the commonly used variable damage D was replaced with the void volume fraction f , which has a clear physical meaning, and the elastic strain tensor \Bold {ε}^e with the damage-elastic strain tensor \Bold {ε}^{de}. The postulate of strain equivalence with the effective stress concept was reformulated and applied to a case where the response of the matrix obeys Hooke’s law. In contrast to many other studies, in the derived relation between the effective stress tensor \Bold {\Tilde{σ}} and the stress tensor \Bold {σ}, the tensor \Bold {\Tilde{σ}} is symmetric. A uniaxial bar model was introduce for clarifying the derived results. Other candidates for damage were demonstrated by studying the effect of carbide coarsening on creep rate.

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.

Evaluation of the Effects of Inclusion Distribution on the Local Ductility of DP Steel

2012 ◽  
Vol 706-709 ◽  
pp. 1527-1532 ◽  
Author(s):  
Y. Suwa ◽  
T. Matsuno ◽  
S. Hirose ◽  
N. Fujita ◽  
A. Seto
Keyword(s):  
Finite Element ◽  
Damage Mechanics ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Element Analysis ◽  
Dp Steel ◽  
The Difference ◽  
Inclusion Distribution

In the present study, the effects of inclusions on the local ductility of DP steel are investigated using finite element analysis (FEA). In order to evaluate local ductility, a continuum damage mechanics (CDM) model has been incorporated into the Abaqus/Explicit® commercial finite element code. Furthermore, three-dimensional representative volume elements (RVEs) with ferrite, martensite, and inclusion phases have been used to evaluate the stress-strain response. Simulation results show that the volume fraction of the martensite as well as the difference in hardness between the ferrite and the martensite phases dominates the effect of inclusions on local ductility.

A precipitate evolution-based continuum damage mechanics model of creep behaviour in welded 9Cr steel at high temperature

2018 ◽  
Vol 233 (1) ◽  
pp. 39-51
Author(s):  
C Ó Murchú ◽  
SB Leen ◽  
PE O’Donoghue ◽  
RA Barrett
Keyword(s):  
Damage Mechanics ◽  
Volume Fraction ◽  
Creep Behaviour ◽  
Continuum Damage Mechanics ◽  
Time To Failure ◽  
Continuum Damage ◽  
State Variable ◽  
9Cr Steel ◽  
Mechanics Model ◽  
Physically Based

A multiaxial, physically based, continuum damage mechanics methodology for creep of welded 9Cr steels is presented, incorporating a multiple precipitate-type state variable, which simulates the effects of strain- and temperature-induced coarsening kinematics. Precipitate volume fraction and initial diameter for carbide and carbo-nitride precipitate types are key microstructural variables controlling time to failure in the model. The heat-affected zone material is simulated explicitly utilising measured microstructural data, allowing detailed investigation of failure mechanisms. Failure is shown to be controlled by a combination of microstructural degradation and Kachanov-type damage for the formation and growth of creep cavities. Comparisons with experimental data demonstrate the accuracy of this model for P91 material.

scholarly journals On Continuum Damage Modeling of Fiber Reinforced Viscoelastic Composites with Microcracks in terms of Invariants

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Melek Usal
Keyword(s):  
Damage Mechanics ◽  
Transverse Isotropy ◽  
Matrix Material ◽  
Damage Model ◽  
Viscoelastic Behavior ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Symmetric Tensors ◽  
The Matrix ◽  
Linear Viscoelastic Behavior

A continuum damage model is developed for the linear viscoelastic behavior of composites with microcracks consisting of an isotropic matrix reinforced by two arbitrarily independent and inextensible fiber families. Despite the fact that the matrix material is isotropic, the model in consideration bears the characteristic of directed media included in the transverse isotropy symmetry group solely due to its fibers distributions and the existence of microcracks. Using the basic laws of continuum damage mechanics and equations belonging to kinematics and deformation geometries of fibers, the constitutive functions have been obtained. It has been detected as a result of the thermodynamic constraints that the stress potential function is dependent on two symmetric tensors and two vectors, whereas the dissipative stress function is dependent on four symmetric tensors and two vectors. To determine arguments of the constitutive functionals, findings relating to the theory of invariants have been used as a method because of the fact that isotropy constraint is imposed on the material. As a result the linear constitutive equations of elastic stress, dissipative stress, and strain energy density release rate have been written in terms of material coordinate description. Using these expressions, total stress has been found.

scholarly journals Characterization of Discontinuity and Mechanical Anisotropy of Shale Based on Continuum Damage Mechanics

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Qinglin Shan ◽  
Peng Yan ◽  
Hengjie Luan ◽  
Yujing Jiang ◽  
Sunhao Zhang
Keyword(s):  
Mechanical Properties ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Element Model ◽  
Degradation Process ◽  
Fracture Network ◽  
Mechanical Anisotropy ◽  
Model Parameters ◽  
Continuum Damage ◽  
The Matrix

The effect of the bedding structure on the mechanical properties of layered shale was studied by means of experiment and numerical simulation. Based on continuum damage theory and discrete fracture network modeling method (D-DFN), a finite element model describing structural discontinuity and mechanical anisotropy of shale is established. In this model, the degradation process of stiffness and strength of shale after failure is described based on the stress-displacement relationship of elements. In order to distinguish the mechanical properties between the bedding and the matrix, a nonzero initial damage variable is set in bedding elements to show initial lower elastic modulus and strength of bedding elements compared with initially nondamaged matrix elements. The calibration of model parameters is discussed, and the simulation results are compared with the experimental results. The results show that the D-DFN method can effectively simulate the anisotropic characteristics of shale deformation and strength, which verifies the effectiveness of the method.

Elasto-Plastic Analysis of a Functionally Graded Rotating Disk Under Cyclic Thermo-Mechanical Loadings Considering Continuum Damage Mechanics

2015 ◽  
Vol 07 (02) ◽  
pp. 1550026 ◽  
Author(s):  
Ali Nayebi ◽  
Ali Tirmomenin ◽  
Mohsen Damadam
Keyword(s):  
Damage Mechanics ◽  
Volume Fraction ◽  
Yield Criterion ◽  
Kinematic Hardening ◽  
Numerical Procedure ◽  
Rotating Disk ◽  
Continuum Damage Mechanics ◽  
Back Stress ◽  
Functionally Graded ◽  
Continuum Damage

The goal of this work is to study the influence of continuum damage mechanics on a functionally graded rotating disk subjected to cyclic temperature gradient loading through nonlinear kinematic hardening rule employed to model the back stress. The formulations have been developed on the basis of von Mises' yield criterion. The material properties are assumed to be independent of temperature and vary according to a power law volume fraction relation but Poisson's ratio is assumed to be constant. Return mapping algorithm (RMA), an incremental method, has been used in the numerical procedure. Material behaviors such as elastic shakedown, plastic shakedown and ratcheting were specified in the existence of continuum damage mechanics to obtain the Bree's interaction diagram for different temperatures and angular velocities.

Evaluating Fracture Toughness of Ductile Materials: A Critical Indentation Energy Model Based on Continuum Damage Mechanics

2005 ◽  
Author(s):  
Jung-Suk Lee ◽  
Eui-Hyun Kim ◽  
Dongil Kwon
Keyword(s):  
Fracture Toughness ◽  
Damage Mechanics ◽  
Volume Fraction ◽  
Continuum Damage Mechanics ◽  
Fracture Toughness Test ◽  
Continuum Damage ◽  
Test Results ◽  
Ductile Materials ◽  
Good Agreement ◽  
Critical Void

A new model for determining fracture toughness of ductile materials is presented that uses indentation and is based on continuum damage mechanics (CDM) and the concept of critical void volume fraction. Fracture toughness evaluated using the model showed good agreement with standard fracture toughness test results.

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.

Sign in / Sign up

Export Citation Format

Share Document