A coupled elastoplastic anisotropic damage model for rock materials

2020 ◽  
Vol 29 (8) ◽  
pp. 1222-1245
Author(s):  
Susheng Wang ◽  
Weiya Xu
Keyword(s):  
Coupling Effect ◽  
Damage Model ◽  
Coupled Model ◽  
Yield Function ◽  
Anisotropic Damage ◽  
Mapping Algorithm ◽  
Rock Materials ◽  
Return Mapping ◽  
Brittle Ductile Transition ◽  
Proposed Model

In this study, a rigorous constitutive model within the framework of thermodynamics is formulated to describe the coupling process between irreversible deformation and anisotropic damage of rock materials. The coupling effect is reflected based on the “two-surface” formulation. The plastic response is described by a yield function while the anisotropic damage is defined by a novel exponential damage criterion. In the proposed model, another feature lies in introducing parameters β and k in the proposed model to capture strain hardening/softening behaviors and brittle–ductile transition. The computational formulation scheme for the coupled model is deduced in detail by using return mapping algorithm. The validity of the coupled model is compared with the numerical simulation results and the experimental curves of the fine-grained sandstone, Beishan granite, and Jinping marble. The results indicate that the model can take into account the nonlinear mechanical behaviors of rock: coupling anisotropic damage and plasticity as well as brittle-ductile transition behaviors. Without loss of generality, the coupled model is versatile to describe the mechanical characteristics of rock materials.

Three-dimensional elastoplastic damage concrete model by dissipation-based arc-length method

2016 ◽  
Vol 19 (12) ◽  
pp. 1949-1962
Author(s):  
Cheng Ma ◽  
Wei-zhen Chen
Keyword(s):  
Damage Model ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Yield Function ◽  
Flow Rule ◽  
Arc Length ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Operator Split ◽  
Elastoplastic Damage

This article presents a three-dimensional isotropic elastoplastic damage model for concrete structures. The plasticity of concrete is described by a nonassociated flow rule, using a three-parameter yield function as well as a modified Drucker–Prager-type potential. The damage of concrete is seen as a contribution work of tensile and compressive damage, with the evolution histories driven by the internal tensile and compressive variables, respectively. The iterative solution of plasticity and damage is carried out according to the concept of operator split, where a return-mapping algorithm as well as a substepping strategy is used. The consistent tangent stiffness considering the recursive relationship among substeps is derived. For the solution of global iteration, a dissipation-based arc-length method is employed. Good agreements are found in comparisons between numerical results and experimental data on both elementary and structural levels. Furthermore, the sensitivities of parameters that control strain softening are investigated.

scholarly journals Rock Failure Analysis Based on a Coupled Elastoplastic-Logarithmic Damage Model

2017 ◽  
Vol 62 (4) ◽  
pp. 753-774
Author(s):  
M. Abdia ◽  
H. Molladavoodi ◽  
H. Salarirad
Keyword(s):  
Constitutive Model ◽  
Plastic Flow ◽  
Mechanical Response ◽  
Damage Model ◽  
Yield Function ◽  
Irreversible Thermodynamics ◽  
Stiffness Degradation ◽  
Shear Stresses ◽  
Rock Materials ◽  
Damage Process

Abstract The rock materials surrounding the underground excavations typically demonstrate nonlinear mechanical response and irreversible behavior in particular under high in-situ stress states. The dominant causes of irreversible behavior are plastic flow and damage process. The plastic flow is controlled by the presence of local shear stresses which cause the frictional sliding. During this process, the net number of bonds remains unchanged practically. The overall macroscopic consequence of plastic flow is that the elastic properties (e.g. the stiffness of the material) are insensitive to this type of irreversible change. The main cause of irreversible changes in quasi-brittle materials such as rock is the damage process occurring within the material. From a microscopic viewpoint, damage initiates with the nucleation and growth of microcracks. When the microcracks length reaches a critical value, the coalescence of them occurs and finally, the localized meso-cracks appear. The macroscopic and phenomenological consequence of damage process is stiffness degradation, dilatation and softening response. In this paper, a coupled elastoplastic-logarithmic damage model was used to simulate the irreversible deformations and stiffness degradation of rock materials under loading. In this model, damage evolution & plastic flow rules were formulated in the framework of irreversible thermodynamics principles. To take into account the stiffness degradation and softening on post-peak region, logarithmic damage variable was implemented. Also, a plastic model with Drucker-Prager yield function was used to model plastic strains. Then, an algorithm was proposed to calculate the numerical steps based on the proposed coupled plastic and damage constitutive model. The developed model has been programmed in VC++ environment. Then, it was used as a separate and new constitutive model in DEM code (UDEC). Finally, the experimental Oolitic limestone rock behavior was simulated based on the developed model. The irreversible strains, softening and stiffness degradation were reproduced in the numerical results. Furthermore, the confinement pressure dependency of rock behavior was simulated in according to experimental observations.

Cyclic Loading of Beams Based on Kinematics Hardening Behavior Coupled With Isotropic Damage

2006 ◽  
Author(s):  
Ali Nayebi ◽  
Kourosh H. Shirazi
Keyword(s):  
Cyclic Loading ◽  
Strain Hardening ◽  
Kinematic Hardening ◽  
Damage Model ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Tension And Compression ◽  
Computational Aspects ◽  
Isotropic Damage ◽  
Path Dependent

The kinematic hardening theory of plasticity based on the Prager model and incremental isotropic damage is used to evaluate the cyclic loading behavior of a beam under the axial, bending, and thermal loads. This allows damage to be path-dependent. The damage and inelastic deformation are incorporated and they are used for the analysis of the beam. The beam material is assumed to follow linear strain hardening property coupled with isotropic damage. The material strain hardening curves in tension and compression are assumed to be both identical for the isotropic material. Computational aspects of rate independent model is discussed and the constitutive equation of the rate independent plasticity coupled with the damage model are decomposed into the elastic, plastic and damage parts. Return Mapping Algorithm method is used for the correction of the elastoplastic state and for the damage model the algorithm is used according to the governed damage constitutive relation. The effect of the damage phenomenon coupled with the elastoplastic kinematic hardening is studied for deformation and load control loadings.

scholarly journals A Coupled Plastic Damage Model for Concrete considering the Effect of Damage on Plastic Flow

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Feng Zhou ◽  
Guangxu Cheng
Keyword(s):  
Damage Model ◽  
Compressive Loading ◽  
Plain Concrete ◽  
Yield Function ◽  
Reduction Factor ◽  
Loading History ◽  
Plastic Yield ◽  
Plastic Damage ◽  
Compliance Tensor ◽  
Proposed Model

A coupled plastic damage model with two damage scalars is proposed to describe the nonlinear features of concrete. The constitutive formulations are developed by assuming that damage can be represented effectively in the material compliance tensor. Damage evolution law and plastic damage coupling are described using the framework of irreversible thermodynamics. The plasticity part is developed without using the effective stress concept. A plastic yield function based on the true stress is adopted with two hardening functions, one for tensile loading history and the other for compressive loading history. To couple the damage to the plasticity, the damage parameters are introduced into the plastic yield function by considering a reduction of the plastic hardening rate. The specific reduction factor is then deduced from the compliance tensor of the damaged material. Finally, the proposed model is applied to plain concrete. Comparison between the experimental data and the numerical simulations shows that the proposed model is able to describe the main features of the mechanical performances observed in concrete material under uniaxial, biaxial, and cyclic loadings.

DUCTILE DAMAGE ANALYSIS BASED ON A J3-GTN-LIKE MODEL

2011 ◽  
Vol 03 (04) ◽  
pp. 189-215 ◽  
Author(s):  
LARBI SIAD
Keyword(s):  
Constitutive Model ◽  
Yield Function ◽  
Shear Loading ◽  
Isotropic Hardening ◽  
Single Element ◽  
Mapping Algorithm ◽  
Failure Initiation ◽  
Fully Implicit ◽  
Return Mapping ◽  
Return Mapping Algorithm

A GTN-like model which yield function explicitly depends upon the third stress invariant is first described in this paper. Subsequently, a fully implicit stress integration procedure of this constitutive model based on the return-mapping algorithm is developed. The validity and the performance of the implementation of the considered algorithm within a finite element code are checked through simulations of single element test and three-element test under hydrostatic tensile conditions and simple shear loading as well. Afterwards, as a numerical example, the presented constitutive model and, for the purpose of comparison, the GTN isotropic hardening model, are used to analyze the classical tensile test of axisymmetric notched specimens. The obtained results highlight similarities, good agreement between both models as long as failure initiation of specimen is not reached, and discrepancy as soon as failure of specimen starts.

ANISOTROPIC DAMAGE MODELS FOR GEOMATERIALS: THEORETICAL AND NUMERICAL CHALLENGES

2014 ◽  
Vol 11 (02) ◽  
pp. 1342007 ◽  
Author(s):  
HAO XU ◽  
CHLOÉ ARSON
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Damage Model ◽  
Damage Threshold ◽  
Yield Function ◽  
Flow Rule ◽  
Anisotropic Damage ◽  
Damage Models ◽  
Associate Flow Rule

A new anisotropic damage model for rock is formulated and discussed. Flow rules are derived with the energy release rate conjugate to damage, which is thermodynamically consistent. Drucker–Prager yield function is adapted to make the damage threshold depend on damage energy release rate and to distinguish between tension and compression strength. Positivity of dissipation is ensured by using a nonassociate flow rule for damage, while nonelastic deformation due to damage is computed by an associate flow rule. Simulations show that the model meets thermodynamic requirements, follows a rigorous formulation, and predicts expected trends for damage, deformation and stiffness.

Fast Plastic Integration Algorithm for Damage Prediction in Forming Process Simulations

2015 ◽  
Vol 784 ◽  
pp. 342-349
Author(s):  
Ali Halouani ◽  
Yu Ming Li ◽  
Boussad Abbès ◽  
Ying Qiao Guo
Keyword(s):  
Large Strain ◽  
Damage Model ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Forming Process ◽  
Integration Algorithm ◽  
Damage Prediction ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Process Simulations

The iterative Return Mapping Algorithm (RMA) is widely used for the plastic integration owing to its accuracy and efficiency, but it is CPU time consuming and may cause divergence problems in case of large strain increments. This paper presents a fast plastic integration method called Direct Scalar Algorithm (DSA) for the damage prediction in forming process simulations. A simplified three-dimensional (3D) strain-based damage model is coupled with the plasticity and implemented into the DSA which does not need iterative solution to make the plastic integration very fast and robust even for very large strain increments. The basic idea is to transform the constitutive equations in terms of the unknown stress vectors into a scalar equation in terms of the equivalent stresses which can be determined by using the experimental tensile curve; thus, the plastic multiplier ∆λ can be directly calculated. The DSA is as accurate as RMA but much faster for the plastic integration.

Use of a Continuum Damage Model Based on Energy Equivalence to Predict the Response of a Single-Crystal Superalloy

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
P. Grammenoudis ◽  
D. Reckwerth ◽  
Ch. Tsakmakis
Keyword(s):  
Equivalence Principle ◽  
Evolution Equations ◽  
Dynamic Recovery ◽  
Damage Model ◽  
Yield Function ◽  
Anisotropic Damage ◽  
Continuum Damage ◽  
Energy Equivalence ◽  
Deformation Processes ◽  
Multiple Holes

Anisotropic viscoplasticity coupled with anisotropic damage has been modeled in previous works by using the energy equivalence principle appropriately adjusted. Isotropic and kinematic hardenings are present in the viscoplastic part of the model and the evolution equations for the hardening variables incorporate both static and dynamic recovery terms. The main difference to other approaches consists in the formulation of the energy equivalence principle for the plastic stress power and the rate of hardening energy stored in the material. As a practical consequence, a yield function has been established, which depends, besides effective stress variables, on specific functions of damage. The present paper addresses the capabilities of the model in predicting responses of deformation processes with complex specimen geometry. In particular, multiple notched circular specimens and plates with multiple holes under cyclic loading conditions are considered. Comparison of predicted responses with experimental results confirms the convenience of the proposed theory for describing anisotropic damage effects.

Application of an efficient anisotropic damage model to the prediction of the failure of metal forming processes

2019 ◽  
Vol 28 (10) ◽  
pp. 1556-1579 ◽  
Author(s):  
Ali Salehi Nasab ◽  
Mohammad Mashayekhi
Keyword(s):  
Constitutive Equations ◽  
Metal Forming ◽  
Kinematic Hardening ◽  
Ductile Damage ◽  
Irreversible Processes ◽  
Anisotropic Damage ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Integration Schemes ◽  
Return Mapping Algorithm

The main objective of this study is the numerical implementation of an advanced elastic–plastic model fully coupled with anisotropic ductile damage. The implemented formulation has been defined in the framework of thermodynamics of irreversible processes and a symmetric second-order tensor is adopted to describe the anisotropic damage state variable. After a summary of the main constitutive equations is given, the numerical integration of constitutive equations is performed using implicit and asymptotic integration schemes. Finite element simulation is performed using ABAQUS/Explicit software and the developed VUMAT subroutine. Next, the application of the developed model to T-shaped hydroforming of tubes and square-cup deep drawing metal forming processes is thoroughly discussed and failure onset zones due to anisotropic ductile damage growth are predicted and the results were consistent with the literature. Finally, by making an assumption that kinematic hardening can be ignored, an elastic predictor/plastic corrector algorithm requiring the solution of one equation is introduced. The assessment of the developed one-equation return-mapping algorithm is carried out by applying it to the simulation of the tensile test of a pre-notched bar. The Central Prossessing Unit time decreases noticeably using one-equation return mapping algorithm compared to the conventional return mapping algorithm and the numerical results are in good agreement with previous numerical simulations and experiments.

Flow Stress and Damage Behavior of C45 Steel Over a Range of Temperatures and Loading Rates

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Farid H. Abed ◽  
Mohammad H. Saffarini ◽  
Akrum Abdul-Latif ◽  
George Z. Voyiadjis
Keyword(s):  
Coupling Effect ◽  
Damage Model ◽  
Ductile Failure ◽  
Tensile Tests ◽  
Dynamic Strain ◽  
Strain Rates ◽  
Sem Images ◽  
Proposed Model ◽  
Static Tensile ◽  
Structural Responses

This research aims to describe the behavior of C45 steel and provide better understanding of the thermomechanical ductile failure that occurs due to accumulation of microcracks and voids along with plastic deformation to enable proper structural design, and hence provide better serviceability. A series of quasi-static tensile tests are conducted on C45 steel at a range of temperatures between 298 K and 923 K for strain rates up to 0.15 s−1. Drop hammer dynamic tests are also performed considering different masses and heights to study the material response at higher strain rates. Scanning electron microscopy (SEM) images are taken to quantify the density of microcracks and voids of each fractured specimens, which are needed to define the evolution of internal defects using an energy-based damage model. The coupling effect of damage and plasticity is incorporated to accurately define the constitutive relation that can simulate the different structural responses of this material. Good correlation was observed between the proposed model predictions and experiments particularly at regions where dynamic strain aging (DSA) is not present.

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