An anisotropic damage–plasticity model for saturated quasi‐brittle materials

This article is devoted to numerical modeling of anisotropic damage and plasticity in saturated quasi‐brittle materials such as rocks and concrete. The damaged materials are represented by an isotropic poroelastic matrix containing a number of families of microcracks. Based on previous works, a discrete thermodynamic approach is proposed. Each family of microcracks exhibits frictional sliding along crack surfaces as well as crack propagation. The frictional sliding is described by a Coulomb–Mohr‐type plastic criterion by taking into account the effect of fluid pressure through a generalized effective stress concept. The damage evolution is entirely controlled by and coupled with the frictional sliding. The effective elastic properties as well as Biot's coefficients of cracked porous materials are determined as functions of induced damage. The inelastic deformation due to frictional sliding is also taken into account. The procedure for the identification of the model's parameters is presented. The proposed model is finally applied to study both mechanical and poromechanical responses of a typical porous brittle rock in drained and undrained compression tests as well as in interstitial pressure controlled tests. The main features of material behaviors are well reproduced by the model. Copyright © 2012 John Wiley & Sons, Ltd.     

A mesoscopic model for the behaviour of concrete under high confinement

When impact loaded, concrete is submitted to high triaxial stresses. The experimental response of concrete under quasi‐static triaxial compression is studied using a triaxial press capable of applying a mean pressure greater than 1 GPa on cylindrical samples measuring 7 cm in diameter and 14 cm high. A numerical analysis of these previous experiments is performed herein at a mesoscopic scale. Concrete is modelled as a biphasic material consisting of a mortar (cement paste and fine aggregates) and roughly spherical aggregates (with a diameter exceeding 2 mm) whose characteristics are applied on a regular cubic finite element mesh. A damage‐plasticity model is then used to model the behaviour of mortar. An identification of model parameters on mortar samples and the subsequent comparison between numerical and experimental tests will be presented for hydrostatic and triaxial compression. Copyright © 2009 John Wiley & Sons, Ltd.     

Thermodynamic‐based model for coupling temperature‐dependent viscoelastic,viscoplastic, and viscodamage constitutive behavior of asphalt mixtures

Based on the continuum damage mechanics, a general and comprehensive thermodynamic‐based framework for coupling the temperature‐dependent viscoelastic, viscoplastic, and viscodamage behaviors of bituminous materials is presented. This general framework derives systematically Schapery‐type nonlinear viscoelasticity, Perzyna‐type viscoplasticity, and a viscodamage model analogous to the Perzyna‐type viscoplasticity. The resulting constitutive equations are implemented in the well‐known finite element code Abaqus via the user material subroutine UMAT. A systematic procedure for identifying the model parameters is discussed. Finally, the model is validated by comparing the model predictions with a comprehensive set of experimental data on hot mix asphalt that include creep‐recovery, creep, uniaxial constant strain rate, and repeated creep‐recovery tests in both tension and compression over a range of temperatures, stress levels, and strain rates. Comparisons between model predictions and experimental measurements show that the presented constitutive model is capable of predicting the nonlinear behavior of asphaltic mixes under different loading conditions. Copyright © 2011 John Wiley & Sons, Ltd.     

Implementation of a coupled plastic damage distinct lattice spring model for dynamic crack propagation in geomaterials

This paper studies dynamic crack propagation by employing the distinct lattice spring model (DLSM) and 3‐dimensional (3D) printing technique. A damage‐plasticity model was developed and implemented in a 2D DLSM. Applicability of the damage‐plasticity DLSM was verified against analytical elastic solutions and experimental results for crack propagation. As a physical analogy, dynamic fracturing tests were conducted on 3D printed specimens using the split Hopkinson pressure bar. The dynamic stress intensity factors were recorded, and crack paths were captured by a high‐speed camera. A parametric study was conducted to find the influences of the parameters on cracking behaviors, including initial and peak fracture toughness, crack speed, and crack patterns. Finally, selection of parameters for the damage‐plasticity model was determined through the comparison of numerical predictions and the experimentally observed cracking features.     

Parameter identification in a damage model for rock mechanics

Attention is focused on the mechanical behaviour of rock-like materials. Developments and applications of a constitutive model based on damage theory are presented. The internal damage model is calibrated for a hard brittle rock, Bushveld Norite, and through this process the identification of the material parameters is carried out. Emphasis is placed on the identification of the material parameters in the damage evolution law. The uniqueness of solutions in the softening regime is investigated through finite element mesh sensitivity studies of non-uniform deformation triaxial compression tests.     

Generalized plasticity state parameter‐based model for saturated and unsaturated soils. Part II: Unsaturated soil modeling

The aim of this paper is to extend the generalized plasticity state parameter‐based model presented in part 1 to reproduce the hydro‐mechanical behavior of unsaturated soils. The proposed model is based on two pairs of stress–strain variables and a suitable hardening law taking into account the bonding—debonding effect of suction and degree of saturation. A generalized state parameter for unsaturated state is proposed to reproduce soil behavior using a single set of material parameters. Generalized plasticity gives a suitable framework to reproduce not only monotonic stress path but also cyclic behavior. The hydraulic hysteresis during a drying—wetting cycle and the void ratio effect on the hydraulic behavior is introduced. Comparison between model simulations and a series of experimental data available, both cohesive and granular, are given to illustrate the accuracy of the enhanced generalized plasticity equation. Copyright © 2010 John Wiley & Sons, Ltd.     

Predictions of a continuous hyperplasticity model for Bangkok clay

The performance of a new constitutive model called ‘kinematic hardening modified Cam clay’ (KHMCC) is presented. The model is described using the ‘continuous hyperplasticity’ framework. Essentially this involves an infinite number of yield surfaces, thus allowing a smooth transition between elasticity and plasticity. The framework allows soil models to be developed in a relatively succinct mathematical form, since the entire constitutive behaviour can be determined through the specification of two scalar potentials. An implementation of the continuous hyperplasticity model is also described. The model requires eight parameters plus a viscosity coefficient for rate-dependent analysis. The model is defined in terms of triaxial stress–strain variables for this study, and is used to model monotonic triaxial tests on Bangkok clay. Comparisons of the theoretical predictions with the results of cyclic undrained triaxial compression tests on Bangkok clay are also presented.     

A viscoplastic model including anisotropic damage for the time dependent behaviour of rock

This paper presents a new constitutive model for the time dependent mechanical behaviour of rock which takes into account both viscoplastic behaviour and evolution of damage with respect to time. This model is built by associating a viscoplastic constitutive law to the damage theory. The main characteristics of this model are the account of a viscoplastic volumetric strain (i.e. contractancy and dilatancy) as well as the anisotropy of damage. The latter is described by a second rank tensor. Using this model, it is possible to predict delayed rupture by determining time to failure, in creep tests for example. The identification of the model parameters is based on experiments such as creep tests, relaxation tests and quasi‐static tests. The physical meaning of these parameters is discussed and comparisons with lab tests are presented. The ability of the model to reproduce the delayed failure observed in tertiary creep is demonstrated as well as the sensitivity of the mechanical response to the rate of loading. The model could be used to simulate the evolution of the excavated damage zone around underground openings. Copyright © 2005 John Wiley & Sons, Ltd.     

Optimization routine for identification of model parameters in soil plasticity

The paper presents an optimization routine especially developed for the identification of model parameters in soil plasticity on the basis of different soil tests. Main focus is put on the mathematical aspects and the experience from application of this optimization routine. Mathematically, for the optimization, an objective function and a search strategy are needed. Some alternative expressions for the objective function are formulated. They capture the overall soil behaviour and can be used in a simultaneous optimization against several laboratory tests. Two different search strategies, Rosenbrock's method and the Simplex method, both belonging to the category of direct search methods, are utilized in the routine. Direct search methods have generally proved to be reliable and their relative simplicity make them quite easy to program into workable codes. The Rosenbrock and simplex methods are modified to make the search strategies as efficient and user‐friendly as possible for the type of optimization problem addressed here. Since these search strategies are of a heuristic nature, which makes it difficult (or even impossible) to analyse their performance in a theoretical way, representative optimization examples against both simulated experimental results as well as performed triaxial tests are presented to show the efficiency of the optimization routine. From these examples, it has been concluded that the optimization routine is able to locate a minimum with a good accuracy, fast enough to be a very useful tool for identification of model parameters in soil plasticity. Copyright © 2001 John Wiley & Sons, Ltd.     

A thermo-mechanical damage model for rock stiffness during anisotropic crack opening and closure

A thermodynamic framework is proposed to couple the effect of mechanical stress and temperature on crack opening and closure in rocks. The model is based on continuum damage mechanics, with damage defined as the second-order crack density tensor. The free energy of the damaged rock is expressed as a function of deformation, temperature, and damage. The damage criterion captures mode I crack propagation, the reduction in toughness due to heating, and the increase in energy release rate with cumulated damage. Crack closure is modeled through unilateral effects produced on rock stiffness. The model was calibrated and verified against published experimental data. Thermo-mechanical crack opening (resp. closure) was studied by simulating a triaxial compression test (resp. uniaxial extension test), including a thermal loading phase. The degradation of stiffness due to tensile stress and recovery of stiffness induced by both mechanical and thermo-mechanical unilateral effects are well captured. The thermo-mechanical energy release rate increases with thermal dilation and also decreases with ambient temperature. It was observed that there is a temperature threshold, below which the rock behaves elastically. A parametric study also showed that the model can capture hardening and softening during thermo-mechanical closure (for specific sets of parameters). These numerical observations may guide the choice of rock material used in geotechnical design, especially for nuclear waste disposals or compressed-air storage facilities.     

基于损伤塑性模型的地下洞室结构地震作用分析

基于损伤力学原理,通过引入损伤变量的方法,详细推导了ABAQUS中的损伤塑性本构模型,描述混凝土后继屈服阶段及其卸荷后的损伤机制和力学行为。此本构模型可考虑循环荷载条件下材料刚度退化和应变率的影响,适用于类似混凝土材料的脆性材料,如岩石等。以某水电站地下厂房洞室结构为例,进行二维动力时程非线性分析,考虑不同的刚度恢复权重因子和应变率相关性对结构损伤的影响。多个数值算例表明：洞室混凝土结构和其周围一定深度的围岩的损伤是一个渐进积累的过程;材料的率相关性效应并不是在地震动作用开始时就立即产生,而是在一段时间后,结构经历一定程度的损伤后才慢慢体现出来;此损伤塑性模型适合地震荷载等循环荷载作用下地下洞室结构的动力时程非线性分析,尤其是强震下采用此损伤塑性模型是合理和必要的。     

A kinematic hardening constitutive model for sands: the multiaxial formulation

This paper explores the possibility of using well-accepted concepts—Mohr-Coulomb-like strength criterion, critical state, existence of a small strain elastic region, hyperbolic relationship for representing global plastic stress–strain behaviour, dependence of strength on state parameter and flow rules derived from the Cam-Clay Model—to represent the general multiaxial stress–strain behaviour of granular materials over the full range of void ratios and stress level (neglecting grain crushing). The result is a simple model based on bounding surface and kinematic hardening plasticity, which is based on a single set of constitutive parameters, namely two for the elastic behaviour plus eight for the plastic behaviour, which all have a clear and easily understandable physical meaning. In order to assist the convenience of the numerical implementation, the model is defined in a ‘normalized’ stress space in which the stress–strain behaviour does not undergo any strain softening and so certain potential numerical difficulties are avoided. In the first part the multiaxial formulation of the model is described in detail, using appropriate mixed invariants, which rationally combine stress history and stress. The model simulations are compared with some experimental results for tests on granular soils along stress paths lying outside the triaxial plane over a wide range of densities and mean stresses, using constitutive parameters calibrated using triaxial tests. Furthermore, the study is extended to the analysis of the effects induced by the different shapes of the yield and bounding surfaces, revealing the different role played by the size and the curvature of the bounding surface on the simulated behaviour of completely stress- and partly strain-driven tests. Copyright © 1999 John Wiley & Sons, Ltd.     

A micromechanics-based elastoplastic damage model for quasi-brittle rocks

This paper presents a micromechanics-based elastoplastic damage model for quasi-brittle rocks under a compressive stress state. The plastic strain is considered to be related to frictional sliding along micro-cracks, and it is coupled inherently with damage evolution. By following a homogenization procedure, we determine the free energy of the matrix-cracks system. The thermodynamic force associated with the inelastic strain contains a back stress, which controls material hardening. Next, in order to determine plastic flow and crack propagation, we propose a Coulomb-type friction criterion, which is used as the plastic yielding function, and a damage criterion based on strain energy release rate. These thermodynamic formulations with a micro–macro scale change allow reducing significantly the number of model parameters, as compared to phenomenological models. Our model is applied to simulate triaxial compression tests on two sets of diabase samples. The first sample set is cored from a fresh diabase rock mass, and the second from a slightly weathered one. Comparisons between numerical predictions and test data are presented.     

Viscoelastic damage model for asphalt concrete

The strain rate-dependent mechanical behavior of asphalt concrete was characterized using unconfined compression tests carried out at different loading rates. It was shown that at high strain rates, the elastic deformation and peak axial stress are highly sensitive to strain rate. Both increase as the strain rate increases. At very low strain rates, elastic response and unconfined compressive strength are relatively independent of the loading rate. Based on the experimental observations, a simple viscoelastic damage model is proposed for the strain rate-dependent unconfined compression behavior of asphalt concrete. In the model, strain rate response is modeled by a two-component viscoelastic model consisting of a constant elastic modulus and a viscous modulus that is related by a power-law function to the axial strain rate. Failure and strain softening are modeled via a damage formulation where damage evolution in the asphalt concrete is given by a simple form of the Weibull distribution function. The model was shown to be capable of describing the strain rate-dependent deformation, compressive strength, strain-softening and creep behavior of asphalt concrete. The model is relatively simple and requires only five material parameters.     

Finite element modelling of laterally loaded lime–cement columns using a damage plasticity model

The behaviour of laterally loaded lime–cement columns in a shear box was studied. Laboratory tests are presented together with numerical analyses where the columns are simulated by a concrete damage plasticity model that considers stiffness degradation. Seven model tests were investigated where the columns were installed in a single column pattern and in rows with different column overlap in order to investigate the influence of the degree of overlapping of the columns in the rows. The results of the numerical evaluations showed good agreement with the experimental shear stress–displacement relation and a good accuracy with respect to the fractures developed.     

Thermo-elastoplastic constitutive model for unsaturated soils

This study presents a simple approach to modelling the effect of temperature on the deformation and strength of unsaturated/saturated soils by using the average skeleton stress and degree of saturation. The concept of thermo-induced equivalent stress is introduced to consider the influence of temperature on the pre-consolidated stress. A skeleton stress–saturation framework is applied to enable the model to describe the thermo-elastoplastic behaviour of both unsaturated and saturated soils, as the skeleton stress can smoothly shift to Terzaghi’s effective stress if saturation changes from the unsaturated to the saturated condition. The new model only employs seven parameters, of which five parameters are the same as those used in the Cam-Clay model. The other two parameters can be easily determined by oedometer tests and simple thermo-mechanical tests. Numerical simulations of isotropic loading tests and triaxial shear tests under different conditions are conducted to illustrate the performance of the proposed model. By comparing with experimental temperature controlled oedometer tests and triaxial tests, it is confirmed that the proposed model is able to capture the thermo-mechanical behaviour of unsaturated/saturated normally and over-consolidated soils with a set of unified parameters.     

Non‐isothermal plasticity model for cyclic behaviour of soils

On the one hand, it has been observed that liquefaction‐induced shear deformation of soils accumulates in a cycle‐by‐cycle pattern. On the other hand, it is known that heating could induce plastic hardening. This study deals with the constitutive modelling of the effect that heat may have on the cyclic mechanical properties of cohesive soils, a relatively new area of interest in soil mechanics. In this paper, after a presentation of the thermo‐mechanical framework, a non‐isothermal plasticity cyclic model formulation is presented and discussed. The model calibration is described based on data from laboratory sample tests. It includes numerical simulations of triaxial shear tests at various constant temperatures. Then, the model predictions are compared with experimental results and discussed in the final section. Both drained and undrained loading conditions are considered. The proposed constitutive model shows good ability to capture the characteristic features of behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

Single hardening constitutive model for frictional materials III. Comparisons with experimental data

A unified constitutive model for the behavior of frictional materials is described. The model is based on concepts from elasticity and plasticity theories. In addition to Hooke's law for the elastic behavior, the framework for the plastic behavior consists of a failure criterion, a nonassociated flow rule, a yield criterion that describes contours of equal plastic work, and a work-hardening/softening law. The functions that describe these components are all expressed in terms of stress invariants. The model incorporates twelve parameters which can all be determined from simple experiments such as isotropic compression and conventional triaxial compression tests. Validation of the model is achieved by comparison of predicted and measured stress-strain curves for various two- and three-dimensional stress-paths obtained for different types of frictional materials.