Elastoplastic Damage Constitutive Model Research Articles

A thermodynamic consistent rate-dependent elastoplastic-damage model

In this article, a rate-dependent elastoplastic-damage constitutive model considering the effect of strain rate has been developed. The derivation of this model has been established based on the irreversible thermodynamics with internal variables within the fundamentals of Continuum damage mechanics (CDM). For investigating the rate effect, an additional power function dependent on the effective strain rate has been involved in the plastic dissipation function (dynamic plastic yield surface). The damage has been assumed as a tensor-type variable and based on the energy equivalence hypothesis, the damage evolution has been developed. The proposed constitutive model has been implemented into user-defined subroutines UMAT and VUMAT in the finite-element program ABAQUS/(Standard and Explicit). For this purpose, the implicit and explicit stress integration algorithms of the model have been explained. The model has been validated by comparing the predicted results with experimental data conducted on Al2024-T3. These experiments are including the tensile and double-notched tests. Furthermore, the numerical results have been compared with some data available in the literature. The numerical examples show the excellent correlation between experiments and simulations for stress (or force) and damage results.

An elasto-plastic damage constitutive model for jointed rock mass with an application

A forked tunnel, as a special complicated underground structure, is composed of big-arch tunnel, multi-arch tunnel, neighborhood tunnels and separate tunnels according to the different distances between two separate tunnels. Due to the complicated process of design and construction, surrounding jointed rock mass stability of the big-arch tunnel which belongs to the forked tunnel during excavation is a hot issue that needs special attentions. In this paper, an elasto-plastic damage constitutive model for jointed rock mass is proposed based on the coupling method considering elasto-plastic and damage theories, and the irreversible thermodynamics theory. Based on this elasto-plastic damage constitutive model, a three dimensional elasto-plastic damage finite element code (D-FEM) is implemented using Visual Fortran language, which can numerically simulate the whole excavation process of underground project and perform the structural stability of the surrounding rock mass. Comparing with a popular commercial computer code, three dimensional fast Lagrangian analysis of continua (FLAC3D), this D-FEM has advantages in terms of rapid computing process, element grouping function and providing more material models. After that, FLAC3D and D-FEM are simultaneously used to perform the structural stability analysis of the surrounding rock mass in the forked tunnel considering three different computing schemes. The final numerical results behave almost consistent using both FLAC3D and D-FEM. But from the point of numerically obtained damage softening areas, the numerical results obtained by D-FEM more closely approach the practical behaviors of in-situ surrounding rock mass.

Theoretical and Numerical Simulation of the Mining-Enhanced Permeability Model of Damaged Coal Seam

The pertinence and effectiveness of gas extraction for underground coal mining is an important issue for simultaneous exploitation of coal and gas. The key issue is the definition and analysis of mining-enhanced permeability of mining-induced fracture network. In order to describe the permeability evolution process during coal mining, the elasto-plastic damage constitutive model of coal was established. Based on the mining-enhanced permeability model, the effect of damage on permeability was considered, and the expression of mining-enhanced permeability considering damage was obtained. Using rock mechanics testing system and the permeability test system, the permeability test was conducted, and the permeability change law with damage was obtained. Based on the elasto-plastic damage constitutive model and the mining-enhanced permeability of damaged coal, the 3D-finite element program was developed according to the elasto-plastic damage theory, by which the analysis of mining process of one coal seam was made. Then we analyzed the distribution of permeability and mining-enhanced permeability. The result shows that: (1) considering the damage can reflect the influence of mining on fracture network and permeability of coal seam. (2) With the advance of the working face, coal units continue to break and the permeability of the coal seam increases continually. (3) The numerical simulation shows the dynamic evolution process of permeability and mining-enhanced permeability of the coal seam during the mining process. These results can provide quantitative and scientific methods for quantitative evaluation of permeability change of coal seam in mining engineering.

A damage model incorporating dynamic plastic yield surface

In this paper, a general elastoplastic-damage constitutive model considering the effect of strain rate has been developed. The derivation of this model has been cast into the irreversible thermodynamics with internal variables within the fundamentals of Continuum Damage Mechanics (CDM). The rate effect has been involved as an additional term into the plastic yield surface (dynamic plastic yield surface). Therefore, the plastic surface has been presented in the category of Consistency–type model in which the rate of state variables is considered as independent state variables. The damage has been assumed as a tensor type variable and based on the energy equivalence hypothesis the damage evolution has been developed. The proposed model has been validated for both rate-independent and rate-dependent deformation. For this manner, the generalized trapezoidal stress integration algorithm of the model has been explained and the model has been implemented into user-defined subroutines (UMAT and VUMAT) in the finite element program ABAQUS. The results of numerical simulation, statically and dynamically, have been compared to the experimental results of three aluminum and two steel alloys. Also, the results of simulation for shear and double-notched tests have been compared to their experiments. By comparing the predicted results with experimental data, the capability and validity of the model have been verified.

Predictive Elastoplastic Damage Constitutive Law: Establishment of Equivalence Relation between Intrinsic and Extrinsic Material Parameters

The purpose of the current work is the development and application of a new identification method of material parameters of elastoplastic damage constitutive model under large strains. A relationship relating the intrinsic and extrinsic parameters of a reference material is built and transformed in equivalence relation. Extrinsic parameters concern the shape of their experimental tensile force/elongation curve, however, intrinsic parameters deal with Swift hardening law coupled with an isotropic damage variable. The relationship is carried out from a statistical characterization of a material reference (standard-steel E24). It based on multiple linear regression of a data set obtained according to a full factor design of numerical simulations of mechanical tensile tests. All materials satisfying this equivalence relation belong to the same equivalence class. This is motivated by observing that gathered materials must behave somewhat like the reference material. The material parameters can be immediately identified by only one task by running the found relationship. The current method facilitates the identification procedure and offers a substantial savings in CPU time. However it just needs only one simulation for the identification of similar behavior instead of the few hundred required when using other methods.

Nonexistence and non-decoupling of the dissipative potential for geo-materials

Two fundamental issues exist in the damage theory of geo-material based on the concept of thermodynamics: existence or nonexistence of the dissipation potential, and whether the dissipation potential could be decoupled into a damage potential and a plastic one or not. Thermodynamics theory of elastoplastic damage assumes the existence of dissipation potential, but the presence of dissipation potential is conditional. Based on the dissipation inequality in accord with the second law of thermodynamics, the sufficient and necessary conditions are given for the existence of the dissipation potential separately in total and incremental forms firstly, and proved strictly in theory. With taking advantage of the basic mechanical properties of geo-materials, the nonexistence of the dissipative potential is verified. The sufficient and necessary conditions are also given and proved for the decoupling of the dissipation potential of geo-materials in total and incremental forms. Similarly, the non-decoupling of the dissipation potential has also been proved, which indicates the dissipation potential of geo-materials in total or incremental forms could not be decoupled into a dissipative potential for plasticity and that for damage respectively. The research results for the fundamental issues in the thermodynamics theory of damage will help establish and improve the theoretic basis of elastoplastic damage constitutive model for geo-materials.

Coupled fluid flow and elasto-plastic damage analysis for fractured porous chalk with induced wormhole

Acid injection in a carbonate oil reservoir can increase oil recovery by etching a part of the fractured porous reservoir and generating conductive channels (“wormholes”), which creates an easier path for oil production. However, it is crucial to predict the wormhole and reservoir strength and their failure for a successful acid treatment. For this purpose, a continuum-based computational method is developed. The model includes flow in the porous chalk reservoir, flow in the wormhole and reversible and irreversible deformation of chalk and fractures, which are modeled with an equivalent elasto-plastic damage constitutive model. The coupling between the reservoir flow and the fractured chalk deformation is done by explicit coupling method. The results found that the risk of the wormhole's walls failure is higher if the natural fractures are oriented along the wormhole; however, natural fractures with larger dip angles and higher inclinations in respect to the wormhole increase the risk of the rock failure. Results shows that increased fluid production from the wormhole, which can be the result of the further acid treatments, developing irreversible behaviors of the rock and reduces the natural fracture asperity at the wormhole's tip, in addition to increasing the wormhole's wall deformation, eventually leading to the wormhole's occlusion.

Nonexistence and non-decoupling of the dissipative potential for geo-materials

Two fundamental issues exist in the damage theory of geo-material based on the concept of thermodynamics: existence or nonexistence of the dissipation potential, and whether the dissipation potential could be decoupled into a damage potential and a plastic one or not. Thermodynamics theory of elastoplastic damage assumes the existence of dissipation potential, but the presence of dissipation potential is conditional. Based on the dissipation inequality in accord with the second law of thermodynamics, the sufficient and necessary conditions are given for the existence of the dissipation potential separately in total and incremental forms firstly, and proved strictly in theory. With taking advantage of the basic mechanical properties of geo-materials, the nonexistence of the dissipative potential is verified. The sufficient and necessary conditions are also given and proved for the decoupling of the dissipation potential of geo-materials in total and incremental forms. Similarly, the non-decoupling of the dissipation potential has also been proved, which indicates the dissipation potential of geo-materials in total or incremental forms could not be decoupled into a dissipative potential for plasticity and that for damage respectively. The research results for the fundamental issues in the thermodynamics theory of damage will help establish and improve the theoretic basis of elastoplastic damage constitutive model for geo-materials.

Damage Mechanism Research of Yushu Airport Road Landslide No.3 Base on Elastoplastic Damage Constitutive Model

Due to the earthquake of Yushu in April 14, 2010, Airport Road landslide No.3 deformed cracking, resulting in lower stability of slope, triggering landslides and other diseases. Selecting the section 2-2 (mileage K823 + 809) of Airport Road landslide No.3 as the calculation section, we use the ABAQUS finite element program to establish landslide numerical mode. The slip mass of landslide was simulated by the elastic-plastic damage constitutive model, and the bedrock was analyzed as Mohr - Coulomb constitutive model. Landslide No3 is analyzed for example, and showed that earthquake triggering mechanism elastplastic damage constitutive model can describe the landslide very well.

A Multiparameter Damage Constitutive Model for Rock Based on Separation of Tension and Shear

By analysis of the microscopic damage mechanism of rock, a multiparameter elastoplastic damage constitutive model which considers damage mechanism of tension and shear is established. A revised general form of elastoplastic damage model containing damage internal variable of tensor form is derived by considering the hypothesis that damage strain is induced by the degeneration of elastic modulus. With decomposition of plastic strain introduced, the forms of tension damage variable and shear damage variable are derived, based on which effects of tension and shear damage on material’s stiffness and strength are considered simultaneously. Through the utilizing of Zienkiewicz-Pande criterion with tension limit, the specific form of the multiparameter damage model is derived. Numerical experiments show that the established model can simulate damage behavior of rock effectively.

Validation of Numerical Model by Means of Digital Image Correlation and Thermography

This paper presents experimental and numerical investigation of elasto-plastic-damage behaviour of aluminium alloys. The experimental procedure includes static and dynamic tensile tests at different strain rates as well as three point bending tests. Numerical modelling of deformation and failure process of the flat specimens is conducted by using non-isothermal elastoplastic damage constitutive model and two-dimensional plane stress finite elements. During the experiment the displacement and temperature distribution on the specimen's surface is measured by digital image correlation (DIC) method and infrared thermography (IR). This has enabled more precise calibration of material parameters in constitutive relations.

Dynamic response of underground gas storage salt cavern under seismic loads

A dynamic elastoplastic damage constitutive model is proposed based on the failure characteristic of rock salt under seismic loads. The coding of the proposed model is achieved by the embedded FISH (short for FLACish) language of FLAC3D (Fast Lagrangian Analysis of Continua). Numerical models of bedded salt cavern gas storage facilities in China are developed by using FLAC3D, and the proposed constitutive model is used in the simulations. The effects of seismic input angle, seismic acceleration, seismic moment, types of seismic waves, and gas pressure on the dynamic response, stress, displacement, plastic zone, and safety factor (SF) of rock masses that surround salt cavern gas storage facilities are studied. Results show that the seismic wave perpendicular to the surface poses the greatest risk to the safety of the cavern. With an increase in seismic acceleration, the cavern’s SF decreases and that of the lower structure of the cavern decreases more than that of the upper section. Plastic zones propagate from the cavern’s internal surface to the pillar, and then to the pillar and floor along the right and left corners of the cavern bottom. Higher internal gas pressure improves cavern safety. The acceleration and duration of seismic waves are critical factors in ensuring the safety of the cavern. The SF of the cavern’s lower structure is more sensitive to changes in seismic parameters than that of the other locations, which makes the cavern bottom more likely to be destroyed during an earthquake. Therefore, the lower structure should be the study target in the seismic design for a salt cavern gas storage facility. Results have been used in the seismic design of salt cavern gas storage facilities in China.

An experimental and numerical study of ductile failure under quasi-static and impact loadings of Inconel 718 nickel-base superalloy

A numerical and experimental study of ballistic impacts at various temperatures on precipitation hardened Inconel 718 nickel-base superalloy plates has been performed. A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion has been implemented in LS-DYNA non-linear finite element code to model the mechanical behaviour of such an alloy. The ballistic impact tests have been carried out at three temperatures: room temperature (25 °C), 400 °C and 700 °C. The numerical study showed that the mesh size is crucial to predict correctly the shear bands detected in the tested plates. Moreover, the mesh size convergence has been achieved for element sizes on the same order that the shear bands. The residual velocity as well as the ballistic limit prediction has been considered excellent for high temperature ballistic tests. Nevertheless, the model has been less accurate for the numerical simulations performed at room temperature, being though in reasonable agreement with the experimental data. Additionally, the influence that the Lode angle had on quasi-static failure patterns such as cup-cone and slanted failure has been studied numerically. The study has revealed that the combined action of weakened constitutive equations and Lode angle dependent failure criterion has been necessary to predict the previously-mentioned failure patterns.

A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion

A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion for high strain and ballistic applications is presented. A Lode angle dependent function is added to the equivalent plastic strain to failure definition of the Johnson–Cook failure criterion. The weakening in the elastic law and in the Johnson–Cook-like constitutive relation implicitly introduces the Lode angle dependency in the elastoplastic behaviour. The material model is calibrated for precipitation hardened Inconel 718 nickel-base superalloy. The combination of a Lode angle dependent failure criterion with weakened constitutive equations is proven to predict fracture patterns of the mechanical tests performed and provide reliable results. Additionally, the mesh size dependency on the prediction of the fracture patterns was studied, showing that was crucial to predict such patterns.

Numerical simulation on pressure-relief deformation characteristics of underlying coal-rock mass after upper protective layer excavation

Based on the occurrence features of Group B coal-seams at a coal mine in the Huainan coal mining area, the elasto-plastic mechanical damage constitutive functions and numerical model for the protective layer excavation were established. With the UDEC2D computer program, after the upper protective layer was mined, the stress field change trends, crack development, and expansion deformation trends of underlying coal rock seams in the floor of the working face were simulated and analyzed. The simulation results show the stress changes in coal rock seams, the evolution process of pre-cracks during the process of upper protective layer mining, the caved zone and fractured zone of the underlying coal rock seams. At the same time, the results from the actual investigation and analysis of protected layer deformation match the simulation values, which verifies the validity and accuracy of numerical simulation results. The study results have an important guiding significance for gas management in low permeability and high gas coal seams with similar mining conditions.

An elastoplastic damage constitutive model for concrete

An elastoplastic damage constitutive model to simulate nonlinear behavior of concrete is presented. Similar to traditional plastic theory, the irreversible deformation is modeled in effective stress space. In order to better describe different stiffness degradation mechanisms of concrete under tensile and compressive loading conditions, two damage variables, i.e., tension and compression are introduced, to quantitatively evaluate the degree of deterioration of concrete structure. The rate dependent behavior is taken into account, and this model is derived firmly in the framework of irreversible thermodynamics. Fully implicit backward-Euler algorithm is suggested to perform constitutive integration. Numerical results of the model accord well with the test results for specimens under uniaxial tension and compression, biaxial loading and triaxial loading. Failure processes of double-edge-notched (DEN) specimen are also simulated to further validate the proposed model.

Coupled Damage and Plasticity Modeling in Failure Analysis of Heated Concrete

A coupled elastoplastic-damage constitutive model with consideration of chemo-induced material elastoplastic-damage effects due to heating concrete is proposed. A consistent return mapping algorithm for the integration of the rate coupled constitutive equations is developed. Consistent tangent modulus matrices for coupled chemo-thermo-hygro-mechanical analysis are derived to preserve the quadratic rate of convergence of the global Newton iterative procedure. Numerical results demonstrate the validity of the presented algorithm and illustrate the performance of the proposed constitutive model in reproducing coupled chemo-thermo-hygro-mechanical behavior in concretes subjected to fire.

An Elastoplastic Damage Constitutive Model for Cementitious Materials under Wet-Dry Cyclic Sulfate Attack

The mechanical properties of cement mortars subjected to wet-dry cyclic sulfate attack were studied by the compression strength test. The results showed that the ultimate compressive strength increased with number of cycles at the initial stage. However, after a certain time, it started to decrease with further increases in the number of cycles. Moreover, the concentration of the sodium sulfate solution proved to be an important factor affecting the ultimate compressive strength. Based on continuum damage mechanics theory, an elastoplastic damage constitutive model is presented to describe the mechanical behavior of cementitious materials under compressive stress. The results obtained agree well with the experimentally observed elastic, plastic, and damage characteristics of cement mortars under compressive stress.

Research on elastoplastic damage constitutive model of intact Q2l loess in northwestern of China

Based on the unsaturated triaxial experiments for the intact fourth period Middle Pleistocene Epoch loess (Q2l loess), the mechanical characteristic of Q2l loess is studied. According to the continuum damage mechanics and elastic–plastic theory, the damage potential function and loading function were deduced. Besides, plastic deformation and irreversible damage deformation are supposed to obey Hyushin’s postulate. The elastoplastic damage constitutive model and damage evolution law of the unsaturated intact Q2 loess are set up. Comparing the experiment curves with the computation result of this model, it is shown that the model can stimulate the mechanics characteristics of Q2 loess well.

Modeling fracture in large scale shell structures

We consider a problem of modeling fracture and failure preceded by large scale yielding of ductile shells from the point of view of large-scale structural analysis. We place a special emphasis on the computational efficiency of the constitutive formulation. In this context, we seek the formulation embedded in the shell mechanics framework, which is both theoretically sound and easily implementable into a large-scale explicit dynamic finite element code without precluding vectorization or parallelization. This is achieved through the elasto-plastic damage constitutive model for finite-element analysis of plates and shells. The proposed damage model is purely phenomenological with a scalar damage parameter, which has no physical interpretation, except that it represents on a global scale the micromechanical changes the material undergoes during the process of necking and fracture. The localization leading to softening and fracture is represented by the damage calibration function with exponential damage growth after the onset of necking. The proposed phenomenological damage model uses a general plasticity and shell mechanics frameworks which makes it general and easily implementable into existing finite element codes. The proposed formulation has been implemented into the explicit dynamic finite element software code EPSA (Atkatsh et al., 1980, 1983).