Modelling of concrete behaviour in uniaxial compression and tension with DEM

The paper focuses on the DEM modelling of the behaviour of plain concrete during uniaxial compression and uniaxial tension using the discrete element method. The model takes into account the concrete heterogeneity at the meso-scale level. The effects of concrete density, size of aggregate grains and specimen size on the stress–strain curve, volume changes and fracture process are studied. In addition, the evolution of contact forces, grain rotations, displacement fluctuations and strain localization during deformation is investigated. The elastic, kinetic, plastic and numerical dissipated energy is calculated and analysed at a different stress–strain stage. Concrete is described as a 1-phase or 3-phase material. The macroscopic 2D and 3D results are compared with the corresponding experiments. A satisfactory agreement between experiments and calculations is achieved.

     

Computational applications of a coupled plasticity-damage constitutive model for simulating plain concrete fracture

A coupled plasticity-damage model for plain concrete is presented in this paper. Based on continuum damage mechanics (CDM), an isotropic and anisotropic damage model coupled with a plasticity model is proposed in order to effectively predict and simulate plain concrete fracture. Two different damage evolution laws for both tension and compression are formulated for a more accurate prediction of the plain concrete behavior. In order to derive the constitutive equations and for the easiness in the numerical implementation, in the CDM framework the strain equivalence hypothesis is adopted such that the strain in the effective (undamaged) configuration is equivalent to the strain in the nominal (damaged) configuration. The proposed constitutive model has been shown to satisfy the thermodynamics requirements. Detailed numerical algorithms are developed for the finite element implementation of the proposed coupled plasticity-damage model. The numerical algorithm is coded using the user subroutine UMAT and then implemented in the commercial finite element analysis program Abaqus. Special emphasis is placed on identifying the plasticity and damage model material parameters from loading-unloading uniaxial test results. The overall performance of the proposed model is verified by comparing the model predictions to various experimental data, such as monotonic uniaxial tension and compression tests, monotonic biaxial compression test, loading-unloading uniaxial tensile and compressive tests, and mixed-mode fracture tests.     

Mechanical and damage analysis along a flat-rolled wire cold forming schedule

Numerical simulation is used to study patented high-C steel flat-rolled wire cold forming processes. An elasto-plastic power law, identified from mechanical tests, is used into Forge2005? finite element (FEM) package in order to describe the material behaviour during wire drawing followed by cold rolling. A through-process approach has been favoured, transferring residual wire-drawing stresses and strain into the flat-rolling preform. This mechanical analysis, associated with a triaxiality study, points to dangerous areas where fracture may initiate due to high tensile stresses. Lema?tre’s isotropic damage criterion, including crack closure effect, a -1/3 cut-off value of stress triaxiality, and tension/compression damage asymmetry, has been used and has confirmed the previous analysis. A number of non-coalesced voids nucleated on inclusions have been observed in the Scanning Electron Microscopy (SEM), especially in high-deformation zones (“blacksmith’s cross”). Their evolution has been simulated in the FEM model using spherical numerical markers, which deform into oblate or prolate ellipsoids. The deformation-induced morphological evolution of voids observed in the SEM compares well with the geometrical evolution of the markers, which suggests that the morphologies observed do not result from micro-crack propagation, but from material transport of the nucleated voids.     

Energy dissipation capacity of fibre reinforced concrete under biaxial tension–compression load. Part I: Test equipment and work of fracture

The objective of this research was to analyse the differences in the dissipated energy under uniaxial tension and biaxial tension–compression load of fibre reinforced concretes using the Wedge Splitting Test. Under biaxial load the specimens were subjected to compressive stress ratios from 10% to 50% of the concrete compressive strength perpendicular to the direction of the tensile load.Under biaxial tension–compression load the energy dissipation capacity of the specimens decreases compared to the uniaxial tension load case on average 20–30%. It is believed that the decrease is a result of the damage mechanism of the concrete matrix and deterioration of the fibre–matrix and/or aggregate–cement paste interfaces in case the section is additionally loaded with compression stresses. This indicates that dimensioning of concrete elements under biaxial stress states using material parameters obtained from tests conducted on specimens under uniaxial tensile load is unsafe and could potentially lead to a non-conservative design.In the second part of this paper the extent of the fracture process zone under uniaxial tension and biaxial tension–compression load will be examined with the Acoustic Emission technique and the reasons for decrease of the energy dissipation capacity under biaxial load will be further discussed.     

Cohesive zone with continuum damage properties for simulation of delamination development in fibre composites and failure of adhesive joints

A new approach is developed to implement the cohesive zone concept for the simulation of delamination in fibre composites or crack growth in adhesive joints in tension or shear mode of fracture. The model adopts a bilinear damage evolution law, and uses critical energy release rate as the energy required for generating fully damaged unit area. Multi-axial-stress criterion is used to govern the damage initiation so that the model is able to show the hydrostatic stress effect on the damage development. The damage material model is implemented in a finite element model consisting of continuum solid elements to mimic the damage development. The validity of the model was firstly examined by simulating delamination growth in pre-cracked coupon specimens of fibre composites: the double-cantilever beam test, the end-notched flexure test and the end-loaded split test, with either stable or unstable crack growth. The model was then used to simulate damage initiation in a composite specimen for delamination without a starting defect (or a pre-crack). The results were compared with those from the same finite element model (FEM) but based on a traditional damage initiation criterion and those from the experimental studies, for the physical locations of the delamination initiation and the final crack size developed. The paper also presents a parametric study that investigates the influence of material strength on the damage initiation for delamination.     

基于能量的弹塑性损伤实用本构模型

建立一个实用的弹塑性损伤本构模型。在有效应力空间采用经验公式计算塑性变形,能将模型塑性部分与损伤部分解耦,降低模型的数值处理复杂性,同时大大简化模型塑性应变的计算。结合不可逆热力学理论,基于损伤能量释放率建立损伤准则,损伤能量释放率由修正后的弹性Helmholtz自由能导出,模型中将弹性Helmholtz自由能分解为应力球量部分和应力偏量部分,将其应力球量部分产生的损伤取为零,同时根据应力状态引入折减系数对其应力偏量部分进行修正,使得模型能较为准确的模拟混凝土材料在双轴加载下的本构行为。将应力张量谱分解为正、负两部分以分别定义材料受拉、受压损伤演化,并采用受拉损伤变量、受压损伤变量分别模拟混凝土材料在拉、压加载下的本构特性。引入一个加权损伤变量使得模型能较准确的反映混凝土材料的“拉-压软化效应”。最后该文给出初步试验验证,证明了该文模型的有效性。     

A new expression for crack opening stress determined based on maximum crack opening displacement under tension–compression cyclic loading

The maximum crack opening displacement is introduced to investigate the effect of compressive loads on crack opening stress in tension–compression loading cycles. Based on elastic–plastic finite element analysis of centre cracked finite plate and accounting for the effects of crack geometry size, Young's modulus, yield stress and strain hardening, the explicit expression of crack opening stress versus maximum crack opening displacement is presented. This model considers the effect of compressive loads on crack opening stress and avoids adopting fracture parameters around crack tip. Besides, it could be applied in a wide range of materials and load conditions. Further studies show that experimental results of da/dN ? ΔK curves with negative stress ratios could be condensed to a single curve using this crack opening stress model.     

Experimental and numerical investigations on fracture process zone of rock–concrete interface

A crack propagation criterion for a rock–concrete interface is employed to investigate the evolution of the fracture process zone (FPZ) in rock–concrete composite beams under three‐point bending (TPB). According to the criterion, cracking initiates along the interface when the difference between the mode I stress intensity factor at the crack tip caused by external loading and the one caused by the cohesive stress acting on the fictitious crack surfaces reaches the initial fracture toughness of a rock–concrete interface. From the experimental results of the composite beams with various initial crack lengths but equal depths under TPB, the interface fracture parameters are determined. In addition, the FPZ evolution in a TPB specimen is investigated by using a digital image correlation technique. Thus, the fracture processes of the rock–concrete composite beams can be simulated by introducing the initial fracture criterion to determine the crack propagation. By comparing the load versus crack mouth opening displacement curves and FPZ evolution, the numerical and experimental results show a reasonable agreement, which verifies the numerical method developed in this study for analysing the crack propagation along the rock–concrete interface. Finally, based on the numerical results, the effect of ligament length on the FPZ evolution and the variations of the fracture model during crack propagation are discussed for the rock–concrete interface fracture under TPB. The results indicate that ligament length significantly affects the FPZ evolution at the rock–concrete interface under TPB and the stress intensity factor ratio of modes II to I is influenced by the specimen size during the propagation of the interfacial crack.     

A viscoelastic Unitary Crack-Opening strain tensor for crack width assessment in fractured concrete structures

A post-processing technique which allows computing crack width in concrete is proposed for a viscoelastic damage model. Concrete creep is modeled by means of a Kelvin–Voight cell while the damage model is that of Mazars in its local form. Due to the local damage approach, the constitutive model is regularized with respect to finite element mesh to avoid mesh dependency in the computed solution (regularization is based on fracture energy).The presented method is an extension to viscoelasticity of the approach proposed by Matallah et al. (Int. J. Numer. Anal. Methods Geomech. 34(15):1615–1633, 2010) for a purely elastic damage model. The viscoelastic Unitary Crack-Opening (UCO) strain tensor is computed accounting for evolution with time of surplus of stress related to damage; this stress is obtained from decomposition of the effective stress tensor. From UCO the normal crack width is then derived accounting for finite element characteristic length in the direction orthogonal to crack. This extension is quite natural and allows for accounting of creep impact on opening/closing of cracks in time dependent problems. A graphical interpretation of the viscoelastic UCO using Mohr’s circles is proposed and application cases together with a theoretical validation are presented to show physical consistency of computed viscoelastic UCO.     

Modelling multiple cohesive crack propagation using a finite element–scaled boundary finite element coupled method

This paper presents an extension of the recently-developed finite element–scaled boundary finite element (FEM–SBFEM) coupled method to model multiple crack propagation in concrete. The concrete bulk and fracture process zones are modelled using SBFEM and nonlinear cohesive interface finite elements (CIEs), respectively. The CIEs are automatically inserted into the SBFEM mesh as the cracks propagate. The algorithm previously devised for single crack propagation is augmented to model problems with multiple cracks and to allow cracks to initiate in an un-cracked SBFEM mesh. It also addresses crack propagation from one subdomain into another, as a result of partitioning a coarse SBFEM mesh, required for some mixed–mode problems. Each crack in the SBFEM mesh propagates when the sign of the Mode-I stress intensity factor at the crack tip turns positive from negative. Its propagation angle is determined using linear elastic fracture mechanics criteria. Three concrete beams involving multiple crack propagation are modelled. The predicted crack propagation patterns and load–displacement curves are in good agreement with data reported in literature.     

Study on coexistence of brittle and ductile fractures in nano reinforcement composites under different loading conditions

Experimental study on high volume fraction of metallic matrix nano composites (MMNCs) was conducted, including uniaxial tension, uniaxial compression, and three-point bending. The example materials were two magnesium matrix composites reinforced with 10 and 15% vol. SiC particles (50 nm size). Brittle fracture mode was exhibited under uniaxial tension and three-point bending, while shear dominated ductile fracture mode (up to 12% fracture strain) was observed under uniaxial compression. The original Modified Mohr–Coulomb (MMC) fracture model (Bai and Wierzbicki in Int J Fract 161:1–20, 2010; in a mixed space of stress invariants and equivalent strain) was transferred into a stress based MMC (sMMC) model. This model was demonstrated to be capable of predicting the coexistence of brittle and ductile fracture modes under different loading conditions for MMNCs. A material post-failure softening model was postulated along the damage accumulation to capture the above two different failure modes. This model was implemented to the Abaqus/Explicit as a material subroutine. Numerical simulations using finite element method well duplicated the material strength, fracture initiation sites and crack propagation modes of the Mg/SiC nano composites with a good accuracy. The proposed model has a good potential to predict fracture for a wide range of material with strength asymmetry and coexistence of brittle and ductile fractures modes.     

Analysis of the energy and damage evolution rule for sandstone based on the particle flow method

We use the particle flow code PFC3D to simulate the triaxial compression of sandstone under various radial stresses and loading strain rates to determine the triaxial stress-strain curves, crack propagation path, and contact forces to investigate the failure process of sandstone. We analyze the energy and damage evolution during triaxial compression. The results indicate that the tension and shear-induced cracks increase with the increase of radial stress under the same loading strain rate. Both normal and tangential contact forces exhibit strong anisotropy and increase with radial stress and strain rate. The normal contact force has an approximately symmetrical distribution with respect to the horizontal plane, whereas the tangential contact force has an approximately symmetrical distribution with respect to the axis. For the characteristics of the energy evolution, the boundary energy density, strain energy density, and dissipated energy density all increase linearly with the radial stress, and the boundary energy density increases at the fastest rate, followed by the strain energy density and dissipated energy density. In the post-peak stage the primary energy consumption is the dissipated energy. After that, in the remaining stage the strain energy decreases gradually. By analyzing the evolution of the damage variables in the prepeak area we observed that the damage variable followed an exponential relationship with the axial strain. When the loading strain rate is constant, the damage variable corresponding to the same strain value decreases with increase of radial stress. The results indicate that the increase in radial stress delays the damage acceleration. In contrast, the effect of the loading strain rate on the damage variable is small. The findings reveal the internal structural evolution of rocks during deformation and failure.

     

Multi-crack analysis of hydraulically pumped cone fracture in brittle solids under cyclic spherical contact

The evolution of surface damage in bilayers due to cyclic spherical indentation in the presence of incompressible lubricant is studied using an all-transparent glass/polycarbonate system as a model for more practical applications such as dental crowns and rolling contact fatigue. In situ observations and post-mortem material sectioning reveal that inner cone cracks evolve sequentially from the contact edge inward by slow growth in a process controlled by stress shielding from preceding cracks. The embryonic cracks are then accelerated by the action of fluid pressure into the flexural tensile stress at the lower part of the coating, where crossover fracture leading to delamination between the coating and substrate may ensue. A consistent FEM brittle fracture analysis incorporating multiple cracks, rate-dependent toughness and liquid pressure is used to follow the damage evolution in the coating. Crack trajectories are determined incrementally under the dual constraint K _I = K _II = 0, which maximize the tension at the crack tip upon the application of fluid pressure. The latter, evaluated at each increment with the aid of a fluid entrapment model, helps drive the leading crack past the compression zone beneath the contact via a hydraulic pump like action. In the early stages of fracture, the liquid pressure is reasonably well approximated by the Hertzian radial surface stress at the crack mouth. Fluid trapped in secondary cracks accentuate the compression beneath the contact. This helps squeeze more liquid into the tip of the leading crack in a zipping like action, which further enhance the crack driving force in the far field. The analytic predictions generally collaborate well with the tests.     

The Effect of Initial Defects on Overall Mechanical Properties of Concrete Material

Considering the fact that the initial defects, like the imperfect interfacial transition zones (ITZ) and the micro voids in mortar matrix, weaken the mechanical properties of concrete, this study develops corresponding constitutive models for ITZ and matrix, and simulates the concrete failure with finite element methods. Specifically, an elastic-damage traction-separation model for ITZ is constructed, and an anisotropic plastic-damage model distinguishing the strength-difference under tension and compression for mortar matrix is proposed as well. In this anisotropic plastic-damage model, the weakening effect of micro voids is reflected by introducing initial isotropic damage, the distinct characteristic of tension and compression which described by decomposing damage tensor into tensile and compressive components, and the plastic yield surface which established on the effective stress space. Furthermore, by tracking the damage evolution of concrete specimens suffering uniaxial tension and compression, the effects of imperfect status of ITZ and volume fraction of initial voids on the concrete mechanical properties are investigated.     

Koyna混凝土重力坝的塑性地震损伤响应分析

考虑了混凝土拉压异性损伤变量，根据相关流动法则推导了混凝土的损伤本构方程。通过有限元方法模拟坝体在地震激励下的非线性损伤演化过程，数值计算过程中考虑了库坝动力耦合及混凝土后继屈服的强化效应，采用四参数Ottosen屈服准则及相应的损伤型本构，算例验证了Koyna混凝土重力坝在竖向和横向实测地震激励下的非线性损伤响应特性。     

Progressive damage modeling in fiber-reinforced materials

This paper presents an anisotropic damage model suitable for predicting failure and post-failure behavior in fiber-reinforced materials. In the model the plane stress formulation is used and the response of the undamaged material is assumed to be linearly elastic. The model is intended to predict behavior of elastic-brittle materials that show no significant plastic deformation before failure. Four different failure modes – fiber tension, fiber compression, matrix tension, and matrix compression – are considered and modeled separately. The onset of damage is predicted using Hashin’s initiation criteria [Hashin Z, Rotem A. A fatigue failure criterion for fiber-reinforced materials. J Compos Mater 1973;7:448; Hashin Z. Failure criteria for unidirectional fiber composites. J Appl Mech 1980;47:329–34] and the progression of damage is controlled by a new damage evolution law, which is easy to implement in a finite element code. The evolution law is based on fracture energy dissipation during the damage process and the increase in damage is controlled by equivalent displacements. The issues related to numerical implementation, such as mesh sensitivity and convergence in the softening regime, are also addressed.     

A nonlocal continuum damage mechanics approach to simulation of creep fracture in ice sheets

We present a Lagrangian finite element formulation aimed at modeling creep fracture in ice-sheets using nonlocal continuum damage mechanics. The proposed formulation is based on a thermo-viscoelastic constitutive model and a creep damage model for polycrystalline ice with different behavior in tension and compression. In this paper, mainly, we detail the nonlocal numerical implementation of the constitutive damage model into commercial finite element codes (e.g. Abaqus), wherein a procedure to handle the abrupt failure (rupture) of ice under tension is proposed. Then, we present numerical examples of creep fracture under four-point bending, uniaxial tension, and biaxial tension in order to illustrate the viability of the current approach. Finally, we present simulations of creep crack propagation in idealized rectangular ice slabs so as to estimate calving rates at low deformation rates. The examples presented demonstrate the mesh size and mesh directionality independence of the proposed nonlocal implementation.     

Analysis on the fatigue damage evolution of notched specimens with consideration of cyclic plasticity

This paper presents a damage mechanics method applied successfully to assess fatigue life of notched specimens with plastic deformation at the notch tip. A damage‐coupled elasto‐plastic constitutive model is employed in which nonlinear kinematic hardening is considered. The accumulated damage is described by a stress‐based damage model and a plastic strain‐based damage model, which depend on the cyclic stress and accumulated plastic strain, respectively. A three‐dimensional finite element implementation of these models is developed to predict the crack initiation life of notched specimens. Two cases, a notched plate under tension‐compression loadings and an SAE notched shaft under bending‐torsion loadings including non‐proportional loadings, are studied and the predicted results are compared with experimental data.     

Multi-scale finite element analysis for tension and ballistic penetration damage characterizations of 2D triaxially braided composite

The multi-scale finite element model is presented to analyze tension and ballistic penetration damage characterizations of 2D triaxially braided composite (2DTBC). At the mesoscopic level, the damage of fiber tows is initiated with 3D Hashin criteria, and the damage initiation of pure matrix is predicted by the modified von Mises. The progressive degradation scheme and energy dissipation method are adopted to capture softening behaviors of tow and matrix. The macro-scale damage model is established by maximum-stress criteria and exponential damage evolution. To simulate interface debonding and inter-ply delamination, a triangle traction–separation law is adopted in each scale. Both scale damage models are verified with available experimental results. Based on numerical predictions, the stress–strain responses and damage developments of 2DTBC under axial and transverse tension loading are studied. For ballistic penetration loading, the meso-scale damage mechanisms of 2DTBC are predicted using 1/4 model, 1/2 model, 1-layer model, 2-layer model and 3-layer model. Then, effects of different model and impactor radius on damage modes are analyzed. Additionally, the macro-scale ballistic penetration behaviors of 2DTBC are simulated and compared with experiment. The prediction results for tension and penetration correlate well with experiment results. Both tension and penetration damage characterizations for tow, matrix within tow, pure matrix, interface and inter-ply delamination are revealed. A comparison of penetration damage between meso- and macro-scale presents a similar crack mechanism between two scales.     

Microplane damage model for fatigue of quasibrittle materials: Sub-critical crack growth,lifetime and residual strength

In contrast to metals and fine grained ceramics, fatigue in concrete and other quasibrittle materials occurs in a large fracture process zone that is not negligible compared to the structure size. This causes the fatigue to be combined with triaxial softening damage whose localization is governed by a finite material characteristic length. A realistic model applicable to both has apparently not yet been developed and is the goal of this paper. Microplane model M7, shown previously to capture well the nonlinear triaxial behavior of concrete under a great variety of loadings paths, is extended by incorporating a new law for hysteresis and fatigue degradation, which is formulated as a function of the length of the path of the inelastic volumetric strain in the strain space. The crack band model, whose band width represents a material characteristic length preventing spurious localization, is used to simulate propagation of the fatigue fracture process zone. Thus the fatigue crack with its wide and long process zone is simulated as a damage band of a finite width. For constant amplitude cycles, the model is shown to reproduce well, up to several thousands of cycles, the Paris law behavior with a high exponent previously identified for concrete and ceramics, but with a crack growth rate depending on the structure size. Good agreement with the crack growth histories and lifetimes previously measured on three-point bend beams of normal and high strength concretes is demonstrated. The calculated compliance evolution of the specimens also matches the previous experiments. The model can be applied to load cycles of varying amplitude, to residual strength under sudden overload and damage under nonproportional strain tensor variation. Application to size effect in fatigue is relegated to a follow-up paper, while a cycle-jump algorithm for extrapolation high-cycle fatigue with millions of cycles remains to be researched.