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.

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.

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.

Stochastic Continuum Damage Mechanics Using Spring Lattice Models

2015 ◽  
Vol 784 ◽  
pp. 350-357 ◽  
Author(s):  
Sohan Kale ◽  
Seid Koric ◽  
Martin Ostoja-Starzewski
Keyword(s):  
Damage Mechanics ◽  
Lattice Models ◽  
Continuum Damage Mechanics ◽  
Constitutive Law ◽  
Disordered Media ◽  
Length Scale ◽  
Continuum Damage ◽  
Perfectly Plastic ◽  
Discrete Nature ◽  
Plastic Responses

In this study, a planar spring lattice model is used to study the evolution of damage variabledLin disordered media. An elastoplastic softening damage constitutive law is implemented which introduces a cohesive length scale in addition to the disorder-induced one. The cohesive length scale affects the macroscopic response of the lattice with the limiting cases of perfectly brittle and perfectly plastic responses. The cohesive length scale is shown to affect the strength-size scaling such that the strength increases with increasing cohesive length scale for a given size. The formation and interaction of the microcracks is easily captured by the inherent discrete nature of the model and governs the evolution ofdL. The proposed method provides a way to extract a mesoscale dependent damage evolution rule that is linked directly to the microstructural disorder.

Coupling of Continuum Damage Mechanics with De-Cohesive Element for Delamination Analysis in Laminated Composites

2010 ◽  
Vol 123-125 ◽  
pp. 527-530
Author(s):  
Hossein Hosseini-Toudeshky ◽  
Bijan Mohammadi
Keyword(s):  
Mesh Generation ◽  
Composite Laminates ◽  
Damage Mechanics ◽  
Plate Theory ◽  
Continuum Damage Mechanics ◽  
Constitutive Law ◽  
Interface Element ◽  
Continuum Damage ◽  
Interface Modeling ◽  
Edge Delamination

To predict the progressive damages including the large delamination growth in composite laminates, a new interface de-cohesive constitutive law is developed which is compatible with 3D continuum damage mechanics (CDM). To avoid the difficulties of 3D mesh generation and 3D interface modeling between the layers, the interface element is implemented in the Reddy’s full layer-wise plate theory. An angle-ply laminate is analyzed to evaluate the developed CDM+Interface procedure in edge delamination initiation and evolution at final stage of CDM damage progress.

Study on Continuum Damage Mechanics Model for High Cycle Fatigue

2016 ◽  
Vol 835 ◽  
pp. 564-567
Author(s):  
Xin Tong Shi ◽  
Ying Chun Xiao ◽  
Hong Chen ◽  
Bo Huang
Keyword(s):  
Experimental Data ◽  
Damage Mechanics ◽  
High Cycle Fatigue ◽  
Continuum Damage Mechanics ◽  
Fatigue Loading ◽  
Continuum Damage ◽  
Cycle Fatigue ◽  
Stress Effects ◽  
Mechanics Model ◽  
Proposed Model

A continuum damage mechanics model was proposed to predict the high cycle fatigue life. In order to consider mean stress effects, the Walker correction was introduced in proposed model. The model was verified by experimental data on LC4 and LY12CZ aluminum alloy under high cycle fatigue loading. The results showed that the predicted life of proposed model well correlated with experimental data.

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.

Evolution of Damage in Near α IMI-834 Titanium Alloy Under Monotonic Loading Condition: A Continuum Damage Mechanics Approach

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Jalaj Kumar ◽  
S. Padma ◽  
B. Srivathsa ◽  
N. Vyaghreswara Rao ◽  
Vikas Kumar
Keyword(s):  
Titanium Alloy ◽  
Loading Condition ◽  
Damage Mechanics ◽  
Equivalent Stress ◽  
Damage Model ◽  
Continuum Damage Mechanics ◽  
Monotonic Loading ◽  
Model Parameters ◽  
Continuum Damage ◽  
Imi 834

In the present work, a continuum damage mechanics model, based on Lemaitre’s concept of equivalent stress hypothesis (1986, “Local Approach to Fracture,” Eng. Fract. Mech., 25, pp. 523–537), has been applied to study the evolution of damage under monotonic loading condition in a near α IMI-834 titanium alloy, used for aeroengine components in compressor module. The damage model parameters have been experimentally identified by in situ measurement of damage during monotonic deformation using alternating current potential drop technique. The damage model has been applied to predict damage evolution in an axisymmetrically notched specimen using finite element analysis. A reasonably good agreement has been observed between numerically simulated and experimentally measured damage behaviors. Damage micromechanisms operative in this alloy have also been identified which show multiple damage events.

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.

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