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.

scholarly journals Nonlocal Theories in Continuum Mechanics

10.14311/610 ◽  
2004 ◽  
Vol 44 (5-6) ◽  
Author(s):  
M. Jirásek
Keyword(s):  
Damage Mechanics ◽  
Continuum Theory ◽  
Nonlinear Behavior ◽  
Continuum Damage Mechanics ◽  
Internal Variable ◽  
Continuum Damage ◽  
Hardening Modulus ◽  
Wide Range ◽  
Discrete Media ◽  
Dynamic Phenomena

The purpose of this paper is to explain why the standard continuum theory fails to properly describe certain mechanical phenomena and how the description can be improved by enrichments that incorporate the influence of gradients or weighted spatial averages of strain or of an internal variable. Three typical mechanical problems that require such enrichments are presented: (i) dispersion of short elastic waves in heterogeneous or discrete media, (ii) size effects in microscale elastoplasticity, in particular with the size dependence of the apparent hardening modulus, and (iii) localization of strain and damage in quasibrittle structures and with the resulting transitional size effect. Problems covered in the examples encompass static and dynamic phenomena, linear and nonlinear behavior, and three constitutive frameworks, namely elasticity, plasticity and continuum damage mechanics. This shows that enrichments of the standard continuum theory can be useful in a wide range of mechanical problems. 

A UNIFIED INELASTICITY AND DAMAGE MECHANICS FOR RUBBER-LIKE MATERIALS

2018 ◽  
Vol 5 (2) ◽  
Author(s):  
Siamak Yazdani ◽  
Ashkan Saboori
Keyword(s):  
Damage Mechanics ◽  
Soft Tissues ◽  
Strain Tensor ◽  
Nonlinear Behavior ◽  
Polymeric Materials ◽  
Internal Variable ◽  
Damage Potential ◽  
Variable Theory ◽  
Strain Energy Density Function ◽  
Internal Variable Theory

The nonlinearities observed in the behavior of rubber and polymeric materials are influenced not only by the far-field stress conditions but also by the morphology, microstructures, and changes at the meso-level such as kinks, crosslinking, and micro tearing. Considering constants temperature applications, the occurrence of microtearing has a significant contribution on the performance of polymers, soft tissues and other rubber-like materials. In this paper, a unified damage mechanics and nonlinear elasticity approach is presented to model nonlinear behavior of rubber-like materials under constant temperatures. The theory is cast within the general framework of the internal variable theory of thermodynamics with large deformations where the Clausius-Duhem inequality is provoked to develop general damage potential. The strain energy density function is formulated in terms of an effective Lagrangian strain tensor that evolves with cumulative damage as cracking and micro-tearing take places. Piola-Kirchhoff (PK) stress tensor is presented and a new form of the damage response tensor is proposed. The model prediction is illustrated against experimental results with good agreement.

A Nonlinear Damage Model of Hardening-Softening Materials

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
M. Ganjiani
Keyword(s):  
Damage Mechanics ◽  
Damage Model ◽  
Continuum Damage Mechanics ◽  
Tensile Tests ◽  
Internal Variable ◽  
Integration Algorithm ◽  
Finite Element Program ◽  
Variable Theory ◽  
Numerical Predictions ◽  
Type Variable

In this paper, an elastoplastic-damage constitutive model is presented. The formulation is cast within the framework of continuum damage mechanics (CDM) by means of the internal variable theory of thermodynamics. The damage is assumed as a tensor type variable and its evolution is developed based on the energy equivalence hypothesis. In order to discriminate the plastic and damage deformation, two surfaces named as plastic and damage are introduced. The damage surface has been developed so that it can model the nonlinear variation of damage. The details of the model besides its implicit integration algorithm are presented. The model is implemented as a user-defined subroutine user-defined material (UMAT) in the abaqus/standard finite element program for numerical simulation purposes. In the regard of investigating the capability of model, the shear and tensile tests are experimentally conducted, and corresponding results are compared with those predicted numerically. These comparisons are also accomplished for several experiments available in the literature. Satisfactory agreement between experiments and numerical predictions provided by the model implies the capability of the model to predict the plastic deformation as well as damage evolution in the materials.

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.

Creep Behaviors Calculated by Varying Material Constants Obtained from Different Stress Regions for a Closed-End P91 Pipe

2016 ◽  
Vol 35 (5) ◽  
pp. 441-447
Author(s):  
Zhao Yanping ◽  
Gong Jianming ◽  
Wang Xiaowei ◽  
Li Qingnan
Keyword(s):  
Damage Mechanics ◽  
Creep Damage ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Creep Tests ◽  
Material Constants ◽  
Mechanics Model ◽  
Stress Region ◽  
Wide Range ◽  
Tertiary Stage

AbstractIn order to predict the creep life of a component at high temperature both accurately and economically, continuum damage mechanics approach is used based on experimental creep data. However, material constants used in the models have a great relationship with the performed stress range of creep tests. In this paper, several sets of material constants were obtained from a wide range of stresses on P91 steel. The creep damage tolerance parameter was used to classify these sets, and the modified continuum damage mechanics model was used to investigate a pipe under closed-end condition. Results have illustrated the main difference lies on the tertiary stage while slight difference on the primary and secondary stages, and the contribution of the tertiary stage to the total damage decreased when using material constants from higher stress region.

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.

Creep Life Prediction of Aircraft Turbine Disc Alloy Using Continuum Damage Mechanics

2017 ◽  
Vol 38 (1) ◽  
pp. 25-30
Author(s):  
Yan-Feng Li ◽  
Zhisheng Zhang ◽  
Chenglin Zhang ◽  
Jie Zhou ◽  
Hong-Zhong Huang
Keyword(s):  
Numerical Analysis ◽  
Test Data ◽  
Life Prediction ◽  
Damage Mechanics ◽  
Continuum Damage Mechanics ◽  
Creep Model ◽  
Continuum Damage ◽  
Creep Life ◽  
Creep Life Prediction ◽  
Turbine Disc

Abstract This paper deals with the creep characteristics of the aircraft turbine disc material of nickel-base superalloy GH4169 under high temperature. From the perspective of continuum damage mechanics, a new creep life prediction model is proposed to predict the creep life of metallic materials under both uniaxial and multiaxial stress states. The creep test data of GH4169 under different loading conditions are used to demonstrate the proposed model. Moreover, from the perspective of numerical simulation, the test data with analysis results obtained by using the finite element analysis based on Graham creep model is carried out for comparison. The results show that numerical analysis results are in good agreement with experimental data. By incorporating the numerical analysis and continuum damage mechanics, it provides an effective way to accurately describe the creep damage process of GH4169.

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