Elastoplastic Damage Research Articles

Nonlinear Response of Tunnel Portal under Earthquake Waves with Different Vibration Directions

Tunnel portal sections often suffer serious damage in strong earthquake events. Earthquake waves may propagate in different directions, producing various dynamic responses in the tunnel portal. Based on the Galongla tunnel, which is located in a seismic region of China, three-dimensional seismic analysis is conducted to investigate the dynamic response of a tunnel portal subjected to earthquake waves with different vibration directions. In order to simulate the mechanic behavior of slope rock effectively, an elastoplastic damage model is adopted and applied to ABAQUS software by a self-compiled user material (UMAT) subroutine. Moreover, the seismic wave input method for tunnel portal is established to realize the seismic input under vertically incident earthquake waves with different vibration directions, e.g., S waves with a vibration direction perpendicular or parallel to the tunnel axis and P waves with a vibration direction perpendicular to the tunnel axis. The numerical results indicate that the seismic response and damage mechanisms of the tunnel portal section are related to the vibration direction of the earthquake waves. For vertically incident S waves running perpendicular to the tunnel axis, the hoop tensile strain at the spandrel and arch foot and the hoop shear strain at the vault and arch bottom are the main contributors to the plastic damage of the tunnel. The strain is initially concentrated around the tunnel foot and spandrel, before shifting to the tunnel vault and bottom farther away from the tunnel entrance. For vertically incident S waves running parallel to the tunnel axis, very large hoop shear strain and plastic damage appear at the tunnel haunches. This strain first increases and then decreases with distance from the tunnel entrance. For vertically incident P waves running perpendicular to the tunnel axis, the maximum damage factor of the slope rock and the maximum plastic strain of the tunnel are significantly lower than for S waves. Moreover, with increasing distance from the tunnel entrance, the plastic damage to the tunnel lining rapidly decreases.

Micromechanical study of multiple transverse cracking in cross-ply fiber-reinforced composite laminates

This paper integrates an efficient numerical framework with robust and accurate constitutive equations to study transverse behavior and multiple cracking of cross-ply fiber-reinforced composite laminates. A nonlinear cohesive interface-enriched generalized finite element method is used to simulate the realistic microstructural representation of the laminate. The considered constitutive equations include elastic, elasto-plastic damage model, and cohesive zone model to simulate fibers, matrix, and fiber/matrix interfaces, respectively. The 0° plies are modeled as a transversely isotropic elastic material. The 90° ply’s microstructural representation is generated based on an optical microscope image, containing more than five thousand fibers. The developed framework is validated versus the experimental results of several single-90° ply specimens. Then, the effects of fiber/matrix cohesive interface properties, matrix stiffness, and bounding plies stiffness on the transverse crack density, delamination, and intra-ply stress redistribution are investigated. The correlation between different stages of failure and the studied parameters are also presented and discussed.

Research on Dynamic Response Characteristics for Basement Structure of Heavy Haul Railway Tunnel with Defects

Based on the basic principle of thermodynamics, an elastoplastic damage constitutive model of concrete is constructed in this paper. The model is realized and verified in FLAC3D, which provides a solid foundation for the study of dynamic response and fatigue damage to the base structure of a heavy haul railway tunnel. The dynamic response and damage distribution of the base structure of a heavy-duty railway tunnel with defects were numerically simulated by the concrete elastic-plastic damage constitutive model. Then, by analyzing the response characteristics of the tunnel basement structure under different surrounding rock softening degrees, different foundation suspension range and different foundation structure damage degree are determined. The results show the following: (1) The elastoplastic damage constitutive model of concrete can well describe the stress–strain relationship of materials, especially with the simulation results of post peak softening being in good agreement with the test results, and the simulation effect of the unloading–reloading process of the cyclic loading and unloading test also meet the requirements. (2) The initial stress field and dynamic response of the tunnel basement structure under the action of train vibration load are very different from the ideal state of the structure design when the surrounding rock of the base is softened, the base is suspended, or the basement structure is damaged. With the surrounding rock softening, basement hanging, or basement structure damage developing to a certain extent, the basement structure will be damaged. (3) The horizontal dynamic stress amplitude increases with the increase in the softening degree of the basement surrounding rock. The horizontal dynamic stress of the measuring point increases with the increase in the width of the hanging out area when the hanging out area is located directly below the loading line. When the degree of damage to the basement structure is aggravated, the horizontal dynamic tensile stress of each measuring point gradually decreases. (4) The maximum principal stress increment increases with the increase in the fracture degree of the basement structure, while the minimum principal stress increment decreases with the increase in the fracture degree of the basement structure, but the variation range of the large and minimum principal stress increments is small. The research results have important theoretical and practical significance for further analysis of the damage mechanism and control technology of the foundation structure of a heavy haul railway tunnel with defects.

Prediction of low‐velocity impact dent for composite laminates based on an anisotropic elastoplastic damage model

AbstractIn this paper, a three‐dimensional finite element (FE) model based on an anisotropic elastoplastic damage model is established to simulate the impact dent of composite laminates subjected to low velocity impact (LVI) by implementing a user‐defined subroutine VUMAT in Abaqus/Explicit. To validate the FE model, numerical results are compared with the experimental data in terms of impact dent depth, contact force‐time response, and projected delamination shape. The simulation shows that considering tension‐compression asymmetry in the elastoplastic constitutive relation has a significant influence on the prediction of dent depth. Besides, it is found that before the knee point, the formation of the impact dent is mainly related to matrix plasticity and damage; while after the knee point, the significant increase of dent depth is caused by fiber breakage on the impact side. The increase of bending stiffness for thicker laminates can decrease the overall deflection, which leads to less fiber breakage and less visible dent.

Damage analysis of shear pre-deformed 3D angle-interlock woven composites using experiment and non-orthogonal finite element model

The shear pre-deformed 3D angle-interlock woven composites under tension load is studied using experimental and numerical methods. A novel non-orthogonal mesoscopic finite element (FE) model taking into consideration non-orthogonal periodic boundary conditions and elasto-plastic damage model is developed to predict the effective mechanical properties and reveal the damage and failure mechanisms. The predicted stress-strain curve is agreement with that of experiment, and the failure mechanisms are verified by Scanning Electron Microscopy (SEM). The effects of shear pre-deformed angle on the stiffness and strength of 3D angle-interlock woven composites are discussed based on simulation results. This study can be helpful of providing reliable guidance for analyzing and designing the woven composite complex structures with pre-deformation.

A Coupled Elastoplastic Damage Dynamic Model for Rock

Rock dynamic constitutive model plays an important role in understanding dynamic response and addressing rock dynamic problems. Based on elastoplastic mechanics and damage mechanics, a dynamic constitutive model of rock coupled with elastoplastic damage is established. In this model, unified strength theory is taken as the yield criterion; to reflect the different damage evolution law of rocks under tension and pressure conditions, the effective plastic strain and volumetric plastic strain are used to represent the compressive damage variable and the equivalent plastic strain is used to represent the tensile damage variable; the plastic hardening behavior and strain rate effect of rocks are characterized by piecewise function and dynamic increase factor function, respectively; Fortran language and LS-DYNA User-Defined Interface (Umat) are used to numerically implement the constitutive model; the constitutive model is verified by three classical examples of rock uniaxial and triaxial compression tests, rock uniaxial tensile test, and rock ballistic test. The results show that the constitutive model can describe the dynamic and static mechanical behavior of rock comprehensively.

Effect of Hole Arrangement on Failure Mechanism of Multiple-Hole Fiber Metal Laminate under On-Axis and Off-Axis Loading.

Mechanical joints are commonly required in structures made of fiber metal laminate (FML), which pose a threat due to multi-site stress concentrations at rivet or bolt holes. Thus, for a reasonably designed FML joint, it is essential to characterize the failure mechanism of multiple-hole FML; however, little information about this has been found in open literature. In the present work, influences of hole arrangement and loading strategy (on-axis or off-axis) on the failure mechanism of multiple-hole FML were investigated, by performing finite element analyses and energy dissipation analyses with elastoplastic progressive damage models that took curing stress into account. Six types of specimens with holes arranged in parallel and staggered forms were designed, whose geometrical parameters were in strict accordance with those specified for composites joints. It indicated that the stress distribution, gross/net notched strength, critical fracture path, and damage evaluation process were only slightly influenced by the hole number and hole arrangement. On the other hand, they were strongly influenced by the loading strategy, due to the transition of failure domination. Results presented here can provide evidence for introducing design regulations of composite joints into the more hybrid FML, and for reasonably determining its multiple-hole strength merely based on the sing-hole specimen.

Stability analysis of surrounding rock of high-pressure cavern tunnel under coupled stress-damage-seepage

The high-pressure cavern is located below the diversion tunnel, which will produce a large seepage force during the excavation process. Consider the effect of seepage field on the stress field with the seepage force, consider the effect of stress and damage on the seepage field through the improved Louis formula, and establish the stress-damage-permeability coefficient equation to consider the effect of stress and damage on the seepage field. The three-dimensional elastoplastic damage finite element analysis of rock mass structure has established a stress-damage-seepage calculation model for surrounding rock excavation of a diversion tunnel with high-pressure cavities. A sequential iteration method is proposed to summarize the above factors and then iteratively solve them in a certain order. Based on a water diversion project, the relevant calculation examples are appropriately simplified. The results show that the seepage effect has a greater impact on the stability of the surrounding rock of the diversion tunnel, and it can be seen that the coupling effect cannot be ignored in the analysis of the stability of the surrounding rock of the excavation of the diversion tunnel.

Multiscale damage constitutive model of jointed rock masses based on the influence of crack initiation

A rock mass has a large number of macroscopic and microscopic defects, such as joint cracks and microcracks, which greatly affect its physical and mechanical properties. In this study, a multiscale elastoplastic damage model was proposed to describe the influence of the existence and evolution of two types of cracks on rocks. The macroscopic damage variable expressed by the stress intensity factor was derived on the basis of damage mechanics and fracture mechanics and regarded as a piecewise function with initiation stress as the dividing point. The rock was divided into two parts based on micromechanics: matrix and microcracks. The macroscopic damage was considered the deterioration of the mechanical properties of the rock matrix. Under the framework of thermodynamics, a constitutive model that could reflect the growth of macrocracks and the friction–damage coupling of microcracks was constructed. This model could reflect the physical mechanism of macroscopic and microscopic damage of jointed rock masses, so the physical parameters of the model had clear meanings. Lastly, the rationality of the model was verified via uniaxial compression tests of rock-like materials with a single flaw of different inclination angles.

Numerical implementation, comparison and validation of a pressure dependent model for polymer composites

A pressure-dependent elastoplastic damage constitutive model for polymer composites is established, in which the Implicit and Explicit numerical algorithm has been implemented in ABAQUS/Standard in terms of elasto-plastic phase with the aid of UMAT. The off-axis tension/compression tests for T800H/3633,T800S/3900-2B carbon/epoxy laminated composites, and quasi-isotropic compression tests for T800H/3633 laminated composites, have been simulated, in order to validate the efficiencies and accuracies of two algorithms. Additionally, the open-hole compression simulation is employed to analyze the progressive failure of T800H/3633 laminated composites. Compared with the Implicit and Explicit algorithm based the elasto-plastic model, the Explicit algorithm is recommended based on the computational efficiency on the premise of ensuring the numerical convergence, which may be extended to the large-scale engineering applications either statics or dynamics. Furthermore, the open-hole compression simulation of T800H/3633 composites shows the developed elasto-plastic damage model can predict well the stiffness and strength properties of the specimen. The failure mode and deformation of the open-hole specimen of T800H/3633 composites are also briefly discussed.

An iterative residual-based procedure for solving coupled elastoplastic damage problems

In the computational damage mechanics, the coupled elastoplastic damage model involves a nonsymmetric tangent operator. This implies that a sparse matrix solver is needed, which means more computational cost to solve the problem. In the context of Lemaitre’s coupled damage model, a new iterative residual-based procedure is proposed to solve the Lemaitre’s coupled elastoplastic damage problems. The elastoplastic damaged tangent operator is decomposed into symmetric and nonsymmetric parts. The symmetric part of the tangent operator is contributed to the overall stiffness matrix, while the nonsymmetric part is considered as an additional residual force contributed to the overall force vector. The symmetry and banded format of the stiffness matrix is maintained, consequently the computational costs are largely reduced. The Lemaitre coupled damage model is implemented in ABAQUS commercial Software using a developed user material user subroutine, while the proposed procedure is implemented into a nonlinear 2 D FE model. Two different problems are analyzed to illustrate the applicability and effectiveness of the proposed iterative residual-based procedure. The analysis show that results of the Lemaitre’s coupled damage model and the proposed procedure are very close.

Mechanism of Splitting Failure for High Sidewall Cavern of Hydropower Station Based on Complex Function and Strain Gradient

With the rapid development of society, the number of hydropower projects has increased. During the construction of these projects, due to excavation-induced unloading, the high sidewalls of the hydropower station are often subject to splitting failure, which produces many adverse effects on the construction of the cavern. In order to reveal the formation mechanism of splitting failure of hydropower stations, based on the strain gradient theory and elasto-plastic damage theory, we proposed an elasto-plastic damage softening model. Using the ODE45 program in MATLAB, we solved the numerical solution of displacement and stress of circular cavern based on our proposed elastoplastic damage model. Then, we apply the complex function method and use the Schwarz–Christoffel integral formula to obtain the mapping function from the outer domain of the high sidewall cavern to the outer domain of the unit circle. Finally, the elastic-plastic region and displacement distribution of the high sidewall cavern are obtained by mapping the obtained elastic-plastic solution of the circular cavern under the axisymmetric condition. In future research, it is necessary to further study the corresponding relationship between the internal length parameter of the material and its internal microstructure in order to accurately determine the internal length parameter.

An elasto-plastic damage accumulation model for fatigue life predication of ductile metals at the yield stress

From the analysis of massive fatigue test data, we find a mismatch between the fatigue life predictions done by stress-life method (SN) and those by strain-life method (εN) around the yield stress of ductile metals. Since the SN and εN methods are widely used in engineering applications, this work aims to explain such mismatch and thereby to address the fatigue life prediction at material’s yield stress, at which the material’s elastic damage and plastic damage are comparable. Based on a normalized damage concept, we propose an elasto-plastic damage accumulation model, a data-driven approach, to evaluate the fatigue damage at the yield stress. By differentiating the damage caused by the elastic from the plastic, the damage of each loading cycle is formulated as a function of both stress and strain amplitudes to accurately capture the material’s response state. With introducing the strain-energy-density based weighting factor, the proposed model can accord well with the classical methods from low-cycle fatigue to high-cycle fatigue. When it comes to the yield stress, the fatigue life estimated by the proposed model compares favorably with the fatigue test data. Therefore, beyond clarifying the mismatch between the classical approaches, the proposed model is expected to improve the accuracy in fatigue damage evaluation of ductile metals at the yield stress.

A Numerical Meso-Scale Elasto-Plastic Damage Model for Modeling the Deformation and Fracturing of Sandstone Under Cyclic Loading

A sound understanding of the influence of cyclic loading on mechanical properties of rock is of great importance for the management and optimization of engineering rock mass structures such as nuclear waste repositories and geothermal resources. In the present manuscript, we first performed a series of conventional uniaxial compressive tests and fatigue failure tests (i.e. cyclic loading tests) on sandstone samples from Sichuan Province, China. The experimental results show that the fatigue failure of sandstone is achieved once the cumulative axial deformation under cyclic loading reaches the axial strain that corresponds to the post-peak phase of the stress–strain curve from a conventional uniaxial test. Based on our laboratory data, and considering that the fatigue process is characterized by local material degradation as well as irreversible deformation that accumulates during each loading cycle, we propose here a two-dimensional meso-scale elasto-plastic damage model to simulate the fatigue behavior of rock during cyclic loading. We then performed a suite of numerical simulations using this model to better understand the fatigue process in sandstone. The results of our numerical modeling show that the ratios of maximum stress and stress amplitude to the uniaxial compressive strength are the most important factors affecting the fatigue life of sandstone. A larger maximum stress and/or stress amplitude results in a shorter fatigue life for the numerical sandstone specimen. However, we find no significant correlation between sample homogeneity and fatigue life. Importantly, our modeled results show that specimen failure occurs once the cumulative axial deformation under cyclic loading reaches the axial strain that corresponds to the post-peak phase of the stress–strain curve from a conventional uniaxial test simulation, in accordance with our laboratory testing. Therefore, the model presented herein provides a new platform to investigate the fatigue failure of rocks.

On the use of constrained reactive mixtures of solids to model finite deformation isothermal elastoplasticity and elastoplastic damage mechanics

This study presents a framework for plasticity and elastoplastic damage mechanics by treating materials as reactive solids whose internal composition evolves in response to applied loading. Using the framework of constrained reactive mixtures, plastic deformation is accounted for by allowing loaded bonds within the material to break and reform in a stressed state. Bonds which break and reform represent a new generation with a new reference configuration, which is time-invariant and provided by constitutive assumption. The constitutive relation for the reference configuration of each generation may depend on the selection of a suitable yield measure. The choice of this measure and the resulting plastic flow conditions are constrained by the Clausius–Duhem inequality. We show that this framework remains consistent with classical plasticity approaches and principles. Verification of this reactive plasticity framework, which is implemented in the open source FEBio finite element software (febio.org), is performed against standard 2D and 3D benchmark problems. Damage is incorporated into this reactive framework by allowing loaded bonds to break permanently according to a suitable damage measure, where broken bonds can no longer store free energy. Validation is also demonstrated against experimental data for problems involving plasticity and plastic damage. This study demonstrates that it is possible to formulate simple elastoplasticity and elastoplastic damage models within a consistent framework which uses measures of material mass composition as theoretically observable state variables. This theoretical frame can be expanded in scope to account for more complex behaviors.

Study on the pressure relief effect in gob‐side coal body during mining an inclined longwall panel

AbstractThis study combined multi‐field coupled numerical calculations and field measurements to analyze the gas pressure relief and the outburst elimination range of the coal body in the lower side of a gob induced by excavating an inclined seam. A coal seam gas flow solid‐gas coupled model allowing for elastoplastic damage was established based on an inclined longwall panel of the Hongyan Coal Mine in Chongqing, China. To inspect the gas depressurization effect, this study simulated the collapse and damage of strata surrounding the longwall panel after mining by using a constitutive model of the interlayer weak plane, the changes in the damage, gas pressure, and stress concentration in the gob‐side coal seam were analyzed numerically. Besides, variation in gas pressure within 10‐23 m away from the panel margin was measured on‐site during the advancement of the longwall face to validate and modify the results of modeling. The simulation results showed that the advancing of the panel is highly effective in releasing gas from the gob‐side coal body. The rupture penetration, stress concentration, and original elastic zone will be formed in the gob‐side coal body with increasing distance away from the gob after mining the 3603‐2 panel. The permeability increased dramatically and the gas was almost exhausted in the rupture penetration zone. The field measurement results indicated that gas pressure decreased in three stages with advancement. After completion of excavation activities, the drop rates of gas pressure and gas content within 10‐23 m from the gob were 26.55%‐73.58% and 34%‐71%, respectively. Additionally, it was proved that the numerical simulation results were instructive for predicting the range of gas outburst‐proneness elimination belt by comparing simulation and field results, and the outburst elimination range of the inclined longwall panel of the Hongyan Coal Mine was determined to be 10 m.

Numerical simulation and experimental verification studies on a unified strength theory-based elastoplastic damage constitutive model of shale

The purpose of this study is to establish an elastic–plastic damage constitutive model of shale and simulate the elastic–plastic damage characteristics of shale under stress. Based on the unified strength theory and the mechanics of shale rock samples characterized in laboratory tests, a new elastic–plastic damage constitutive model for shale is established by introducing compression factors and damage variables. The main considerations include the compressibility of primary fractures and pores in the shale core, and the formation of secondary cracks in the rock matrix under stress. A fully implicit backward Euler regression mapping algorithm has been used to solve the model, and the numerical simulation results are in good agreement with the experimental results. The results show that the model established in this paper can accurately simulate the elastic–plastic damage characteristics of shale under stress, and that it provides a new numerical simulation method for describing the elastic–plastic damage in shale.

Micromechanics-based elasto-plastic–damage energy formulation for strain gradient solids with granular microstructure

Micromechanics-based elasto-plastic–damage energy formulation for strain gradient solids with granular microstructure

Simulating the Formation of Blasting-Excavation-Induced Zonal Integration in Deep Tunnels with an Elastoplastic Damage Model

More deep tunneling projects will be constructed due to the increasing demand of underground energy and resource. The zonal disintegration phenomena are frequently encountered with the surrounding rock of deep tunnels. To explain the mechanisms underlying the formation of zonal disintegration, an elastoplastic damage model and failure criterion are proposed in this study based on the strain gradient theory and the damage property of rock mass. A coupling calculation subroutine is thereafter developed by the ABAQUS code. The dynamic formation and development regularity of zonal disintegration in the deep tunnel are simulated by this subroutine. The radial displacement, radial stress, and tangential stress show the oscillated variation of peaks and troughs alternately. The coupling effect of the blasting load and the initial geostress transient unloading leads to the variation of alternation oscillation in the surrounding rock stress field, which is an important reason for the zonal disintegration of the surrounding rock. The morphological characteristics of fractured zones and nonfractured zones obtained from numerical simulations are in good agreement with the results from the in situ observations, which confirm the correctness and feasibility of the damage and numerical approach. The method proposed in the current study can be utilized to provide a basis for the prediction and supporting design of fractured modes.

Damage mechanism modelling of shield tunnel with longitudinal differential deformation based on elastoplastic damage model

Shield tunnels with great longitudinal differential deformations will adversely affect the service performance and optional safety of the metro system. Previous studies on the longitudinal mechanical behavior of shield tunnel are mostly carried out within the framework of elastic or elastic–plastic theory. However, assuming the concrete as elastoplastic body cannot properly reflect its nonlinear mechanical characteristics such as strain softening, stiffness degradation, etc., while damage or crack inevitably occurs when shield tunnel suffers large deformations. Therefore, the nonlinear damage characteristics of concrete material are considered in this paper, a novel positive/negative decomposition of stress tensor in energy norm is introduced herein to consider the asymmetric tensile/compressive material behavior of concrete, and a bi–scalar damage constitutive model of concrete is developed in turn. Then, to investigate the damage and degradation mechanisms of shield tunnel with differential deformation, the 3D discontinuous contact model is employed to develop the elaborate tunnel–soil numerical model. Results show that when shield tunnel suffers differential deformation, tensile damage dominates while compressive damage is minor, additional shear force and bending moment are induced, the ovality of tunnel cross section and serviceability also vary along the longitudinal direction. The damage and degradation of concrete material will reduce the tunnel integral stiffness and attenuate its ability to resist longitudinal and circumferential deformation. Besides, the segmental rebar is hard to yield, while the longitudinal coupling bolts on the lower half of tunnel segments with large deformation are inclined to yield. It should be noted that, the segmental rings near the inflection point of longitudinal deformation profile are most severely damaged, and exhibit the largest convergence deformation and lowest serviceability, where special attentions should be paid.