Isotropic Damage Model Research Articles

Optimization of multiphase structures considering damage

The present contribution deals with a gradient based optimization strategy to improve the ductility of composite structures. In order to achieve the chosen optimization goal, stiff inclusions in a soft matrix are varied in shape and location controlled by the variation of implicit level-set functions. The eXtended Finite Element Method (XFEM) allows the use of a fixed structured mesh. For the non-linear constitutive behaviour an isotropic damage model is chosen for interface and matrix softening failure; the inclusions are assumed to be elastic. For the calculation of the required sensitivities the influence of the material interfaces, the related enrichment funcions of the X-FEM as well as the kinematic and constitutive relations have to be taken into account.

Finite Difference Energy Method for nonlinear numerical analysis of reinforced concrete slab using simplified isotropic damage model

This work presents a model to predict the flexural behavior of reinforced concrete slabs, combining the Mazars damage model for simulation of the loss of stiffness of the concrete during the cracking process and the Classical Theory of Laminates, to govern the bending of the structural element. A variational formulation based on the principle of virtual work was developed for the model, and then treated numerically according to the Finite Difference Energy Method, with the end result a program developed in Fortran. To validate the model thus proposed have been simulated with the program, some cases of slabs in flexure in the literature. The evaluation of the results obtained in this study demonstrated the capability of the model, in view of the good predictability of the behavior of slabs in flexure, sweeping the path of equilibrium to the rupture of the structural element. Besides the satisfactory prediction of the behavior observed as positive aspects of the model to its relative simplicity and reduced number of experimental parameters necessary for modeling.

Exact solutions for an elastic damageable hollow sphere subjected to isotropic mechanical loadings

In this paper, we first recall some available Eshelby-based homogenization schemes applied to microcracked materials. An emphasis is put on models accounting for interacting opened or closed microcracks and their spatial distribution. On the basis of these schemes, we briefly present a class of isotropic damage models. The main part of the study is devoted to the derivation of exact solutions for mechanical fields (damage distribution, displacement, stress fields) in a hollow sphere subjected to a radial loading and made up of an elastic damageable material. The solutions, discussed in link with the different homogenization schemes, may serve as a reference for assessment of numerical predictions of brittle damage models. Interestingly, it is shown that the existence of physically meaningful solutions strongly depends on the model under consideration. Finally, we establish explicit solution to the hollow sphere problem in unloading regime.

A micromechanical-based damage analysis of a cylindrical bar under torsion: Theoretical results, Finite Elements verification and application

We first present exact closed-form solutions to the problem of a cylindrical bar subjected to a torsion loading. The bar is made of a material whose behavior is modeled by means of a class of micromechanically based isotropic elastic damage models. It is shown that under an increasing torsion, the bar exhibits a global softening regime related to its progressive deterioration. The paper also provides explicit expressions of the mechanical fields as well as of the damage distribution in the bar. A careful attention is given to the response during an unloading step. Finally, after implementing the damage models in a Finite Element software, we simulate the bar response under the same torsion loading. Interestingly a full agreement is noted between the theoretical predictions and the numerical results, also in the softening regime. Finally, the proposed models are applied to a gray cast iron; the predictions compare well to experimental data.

A 3D mixed frame element with multi-axial coupling for thin-walled structures with damage

A 3D mixed beam finite element is presented, modeling the warping of the cross-sections as an independent kinematic field. The beam formulation is derived on the basis of the Hu-Washizu variational principle, expressed as function of four independent fields: the standard displacements, strains and stresses and the additional warping displacement. This is interpolated along the beam axis and on the cross-section, by placing on it a regular grid of interpolation points and adopting Lagrange polynomials. The warping degrees of freedom defined at the cross-section interpolation points are condensed, thus preserving the element matrix and vector sizes. A fiber discretization of the cross-sections is adopted. The constitutive relationship at the midpoint of each fiber is based on an isotropic damage model for brittle-like materials, distinguishing between the damage variables in tension and in compression to properly describe the unilateral effect. An efficient algorithm is formulated for the element state determination, based on a consistent linearization of the governing equations. A simple numerical application on a cantilever beam with torsion in the linear elastic range is presented and two torsion tests on plain concrete beams are performed, by comparing the numerical results with the experimental outcomes.

Three‐dimensional simulations of tensile cracks in geomaterials by coupling meshless and finite element method

SummaryFailure in geotechnical engineering is often related to tension‐induced cracking in geomaterials. In this paper, a coupled meshless method and FEM is developed to analyze the problem of three‐dimensional cracking. The radial point interpolation method (RPIM) is used to model cracks in the smeared crack framework with an isotropic damage model. The identification of the meshless region is based on the stress state computed by FEM, and the adaptive coupling of RPIM and FEM is achieved by a direct algorithm. Mesh‐bias dependency, which poses difficulties in FEM‐based cracking simulations, is circumvented by a crack tracking algorithm. The performance of our scheme is demonstrated by two numerical examples, that is, the four‐point bending test on concrete beam and the surface cracks caused by tunnel excavation. Copyright © 2014 John Wiley & Sons, Ltd.

Collapse of the clock tower in Finale Emilia after the May 2012 Emilia Romagna earthquake sequence: Numerical insight

The paper presents the final results of a wide numerical campaign conducted by the authors at the Technical University of Milan in cooperation with the Italian Cultural and Architectural Heritage Ministry (MiBAC) on the clock tower in Finale Emilia (Italy), collapsed during the main shock of the devastating May 20–29, 2012 seismic sequence. The analyses are aimed at better understanding the causes at the base of the collapse of the tower. The two main seismic events, occurred on May 20 and 29, were characterized by the presence of low frequency ground motions, with relevant vertical components. Consequently, structures having natural periods greater than those typical of ordinary buildings – such as the one analyzed – have been severely damaged.After the first tremor (on the 20th of May), the clock-tower was split in two, with one half collapsing into rubble and the other standing precariously. The subsequent strong aftershock caused the almost total failure of the structure.To investigate the behavior of the tower under seismic loads, a number of numerical analyses are performed, including simplified static analyses according to Italian Guidelines on architectural heritage, spectral response, non-linear static (pushover and kinematic limit analysis) and full non-linear dynamic analyses. In all cases, a full 3D detailed FE model is adopted. When dealing with the FEM non-linear dynamic analysis, a smeared crack isotropic damage model already implemented in ABAQUS is adopted.From the numerical results, both the role played by the actual geometry and the insufficient resistance of the constituent materials are envisaged, also in light of the actual failure mechanism. In all cases, the numerical analyses provide a valuable picture of all possible failure mechanisms, thus giving useful hints for the reconstruction of the tower.

Modelización numérica del comportamiento estructural cíclico de barras esbeltas de acero con pandeo restringido

This work presents a numerical model of the cyclic structural behavior of dissipative buckling-restrained braces, commonly used as an alternative to classical concentric braces for seismic protection of building frames and other structures. Such devices are usually composed of a slender steel core embedded in a stockiest casing that is intended to prevent its buckling when it is under compression. The casing is made either of mortar or steel, and a sliding interface is interposed between the core and the casing to prevent excessive shear stress transfer. The behavior of the steel core is described by a damage and plasticity model; the behavior of the mortar casing is described by an isotropic damage model and the sliding behavior of the interface is described by a contact penalty model. These 3 models are implemented in the Abaqus software package following an explicit formulation. In a previous article (published in an earthquake engineering journal) the model was briefly described, its ability to reproduce the cyclical behavior of buckling-restrained braces was preliminarily pointed out and their results were satisfactorily compared with those of experimental tests. The aim of this paper is to describe the model thoroughly and to present new judgments about its usefulness.

An anisotropic damage model based on microstructure of boom–panel for the fatigue life prediction of structural components

ABSTRACTBecause of their simplicity, many isotropic damage models have been used to approximately predict the fatigue life of metallic engineering components. However, experimental observations confirm that the anisotropic damage evolves at probable failure sites even for isotropic materials. In this study, a model of microstructure of boom–panel is constructed to simulate a representative volume element (RVE), and the anisotropic damage of the RVE is described by the independent isotropic damage of boom and panel. Firstly, the constitutive equation of the RVE in terms of stiffness of boom–panel is deduced by the principle of deformation and static consistency. Then the expressions of damage‐driving force for boom and panel based on the principle of thermodynamics are introduced, and the damage evolution equations are constructed. The parameters of boom and panel are identified from fatigue test data of uniaxial tension and pure torsion, respectively. Finally, the aforementioned method is applied to predict the fatigue life of two structures: one is Pitch‐Change‐Link, which is a kind of structure in helicopter, and the other is a specimen under tension–torsion. The prediction results all fit well with the experimental data.

A soil damage model expressed by a double scalar and its applications

Poroelasticity refers to the study of the mechanics of porous elastic materials that are saturated with compressible or incompressible fluids. When considering saturated poroelastic geomaterials, their consolidation response can be influenced by the evolution of damage in the porous skeleton. The objective of this paper is to examine the problem of consolidation response of damage-susceptible poroelastic geomaterials. Firstly, a new constitutive model of soft soils expressed by isotropic double scalar damage variables is developed and incorporated into Biot’s consolidation finite element equations via EDAPD program. Then, the EDAPD program is applied to analyze a soft subgrade reinforced by surcharge preloading technology. The comparison between the numerical predictions and the experimental data shows that the isotropic double scalar damage model presented in this paper is effective and feasible in analyzing the consolidation problem of damaged porous media.

Flexural fatigue damage model of ultra-high toughness cementitious composites on base of continuum damage mechanics

Ultra-high toughness cementitious composite is a fiber reinforced cementitious material, with the characteristics of strain hardening and multiple cracking under uniaxial tension. It could be applied in some structures to sustain complicated loading conditions, such as fatigue loads. This paper presents an experimental and theoretical investigation on the flexural fatigue damage property of ultra-high toughness cementitious composites. Based on continuum damage mechanics and elastic-plastic isotropic damage model, a flexural fatigue damage model of ultra-high toughness cementitious composites is developed. The parameter of starting damage Ds is introduced, which equals to the damage amount happening in fatigue stage I. Meanwhile, the plastic strain ɛp on the bottom surface of the standard specimen is employed to calculate fatigue damage, D. The fitted parameters of the damage model are obtained with the experimental data. The research result shows that the starting damage amount and the cumulative damage degree drop with the decrease of stress levels. It is proved that this fatigue damage model is applicable to calculate the fatigue damage of ultra-high toughness cementitious composites.

Influence of Patch Shape and Size on Adhesively Bonded Composite Repair

Compared with the traditional mechanical repair technology, the adhesively bonded repairs in composites have the obvious advantages of less increment of structure weight, strong design ability, easy forming and low cost. Therefore, the technology of adhesively bonded repairs in composites has been successfully applied to some damaged structures of military and civilian aircraft. Based on the three-dimensional progressive damage theory, the models of adhesively bonded repairs are respectively established with different shapes of the patches by using the software of ANSYS. Motherboard and patch are established with the orthogonal anisotropic damage model, and adhesive is established with the isotropic damage model. Under uniaxial tensile load, at the same time, considering the damage form and the trends of expansion of the laminates and adhesive, the ultimate failure load is determined. The validity of the method is proved by comparing with previous references. The calculation results of damage model show that the patch shape and size, which have a great effect on the ultimate failure load of composite laminates, are important design parameters of adhesively bonded repairs. The effect of repair with tilted square patch is better than others. When the round-corner process of tilted square patch is conducted, the load-bearing capacity of damaged laminates is improved.

801 損傷モデルによる異形鉄筋まわりの3次元内部ひび割れの再現解析(OS8-(1),OS8 オーガナイズドセッション《複合材料の変形と破壊およびマルチスケール計算技術》)

The isotropic damage model applied in this study is based on fracture mechanics for concrete, and is capable of simulating quasi-brittle fracture and crack propagation with the fracture energy. The internal cracks affect the mechanical behavior of reinforced concrete subjected to tensile. But internal cracks cannot observed from the surface of concrete. For maintenance management and life prediction of the structure, it's important that we observe invisible internal cracks from surface of concrete. Therefore, we simulate 3D internal crack propagations formed in concrete around deformed bar using the damage model. Finally we assess the validity of the result of our crack simulation by comparing that of laboratory experiment.

Coupled hydromechanical modelling of the mine-by experiment at Meuse-Haute-Marne underground rock laboratory France

Abstract At the Meuse-Haute-Marne underground rock laboratory, France, a mine-by experiment was performed in the niche GCS by ANDRA. A 3D coupled hydraulic and mechanical (HM) continuum model was applied to understand the coupled HM mechanisms in the Callovo–Oxfordian claystone. Features such as transverse isotropy, shrinkage phenomena and permeability change induced by mechanical deformation were considered using the numerical code RockFlow. Intensive parameter studies in comparison with measured deformation and pore pressure data reduced model uncertainties. Fully saturated models showed very precise calculation results for the far-field zone sensors, but rapidly decreased pore pressure and continuously increased deformation in the near-field zone cannot be interpreted adequately even considering shrinkage and partially saturated flow models. A 2D isotropic damage model taking stiffness degradation into account was applied and acceptable calculation results were obtained for pore pressure evolution. However, the time-dependent deformation cannot be evaluated by the current model.

An isotropic damage model to simulate collapse in reinforced concrete elements

A damage model with different failure surface in tension and compression is formulated, implemented and validated to study reinforced concrete elements under actions which induce their collapse. The constitutive behaviour of concrete considers the softening deformation after reaching a failure surface, whereas the hardening of the reinforcing steel is represented by a plasticity von Mises surface. The developed damage model does not exhibit the problem of stress locking as the smeared cracking model does; this guaranties an adequate energy release as the material fails. Numerical examples are presented showing the validity of the developed damage model for modelling the behaviour of reinforced concrete elements up to their collapse.

Influence of Aggregate Stiffness on Fracture-Mechanical Properties of Lime-Based Mortars

Addition of relatively stiff aggregates into lime-based mortars is responsible for an increase of the effective mortar stiffness and stress concentrations around aggregates during mechanical loading. To observe the damage development during the three-point bending and splitting tests a 2D plane-stress nonlinear finite element analysis utilizing isotropic damage model was carried out and the results were validated against experimentally obtained data. The study revealed that the finite element model is able to capture the trends observed during the experimental investigation. The results of the numerical modeling and experimental investigation show the advantages of the use of relatively compliant crushed brick aggregates in ancient structures.

Modelling reinforced concrete beams under mixed shear-tension failure with different continuous FE approaches

The paper presents quasi-static numerical simulations of the behaviour of short reinforced concrete beams without shear reinforcement under mixed shear-tension failure using the FEM and four various constitutive continuum models for concrete. First, an isotropic elasto-plastic model with a Drucker-Prager criterion defined in compression and with a Rankine criterion defined in tension was used. Next, an anisotropic smeared crack and isotropic damage model were applied. Finally, an elasto-plastic-damage model was used. To ensure mesh-independent FE results, to describe strain localization in concrete and to capture a deterministic size effect, all models were enhanced in a softening regime by a characteristic length of micro-structure by means of a non-local theory. Bond-slip between concrete and reinforcement was considered. The numerical results were directly compared with the corresponding laboratory tests performed by Walraven and Lehwalter (1994). The advantages and disadvantages of enhanced models to model the reinforced concrete behaviour were outlined.

Delamination in laminated plates using the 4-noded quadrilateral QLRZ plate element based on the refined zigzag theory

A numerical method based on the Refined Zigzag Theory (RZT) to model delamination in composite laminated plate/shell structures is presented. The originality of this method is the use of 4-noded quadrilateral plate finite elements whit only seven variables per node to discretize the plate/shell geometry. The ability to capture the relative displacement between consecutive layers in fracture mode II and III is the more important advantage of this element, denoted QLRZ [1].A continuum isotropic damage model [2] is used to model the mechanical behavior of the plies. The material non-lineal problem is solved with the modified Newton–Raphson method.The RZT plate theory, the QLRZ finite element and the isotropic damage model are described in this work. Also, the implicit integration algorithm is presented. The performance of the numerical model is analyzed by studying the delamination in a rectangular plate for two different laminates, using the 3D analysis as the reference solution.

A regularized Lagrangian meshfree method for rainfall infiltration triggered slope failure analysis

A two-level Lagrangian strain smoothing regularized meshfree formulation based on the stabilized conforming nodal integration is developed for analyzing the rainfall infiltration triggered large deformation slope failure. The regularization is fulfilled by developing two-level smoothed nodal gradients of the meshfree shape function in the Lagrangian meshfree discretization of the weak form of the coupled soil-rainfall infiltration equations. The two-level smoothed nodal gradients of the meshfree shape function are successively constructed based on the one-level smoothed meshfree nodal gradients which are obtained through a Lagrangian gradient smoothing operation on the deformation gradient and the rate of deformation tensor. The slope failure initiation and evolution is realized by a coupled isotropic damage and pressure-dependent plasticity model. Numerical results demonstrate that the present method is very effective for modeling large deformation slope failure process induced by rainfall infiltration.

Study of Ground Response Curve (GRC) Based on a Damage Model / Badanie Krzywej Odpowiedzi Gruntu (Grc) W Oparciu O Model Pękania Skał

Abstract Analysis of stresses and displacements around underground openings is necessary in a wide variety of civil, petroleum and mining engineering problems. In addition, an excavation damaged zone (EDZ) is generally formed around underground openings as a result of high stress magnitudes even in the absence of blasting effects. The rock materials surrounding the underground excavations typically demonstrate nonlinear and irreversible mechanical response in particular under high in situ stress states. The dominant cause of irreversible deformations in brittle rocks is damage process. One of the most widely used methods in tunnel design is the convergence-confinement method (CCM) for its practical application. The elastic-plastic models are usually used in the convergence-confinement method as a constitutive model for rock behavior. The plastic models used to simulate the rock behavior, do not consider the important issues such as stiffness degradation and softening. Therefore, the use of damage constitutive models in the convergence-confinement method is essential in the design process of rock structures. In this paper, the basic concepts of continuum damage mechanics are outlined. Then a numerical stepwise procedure for a circular tunnel under hydrostatic stress field, with consideration of a damage model for rock mass has been implemented. The ground response curve and radius of excavation damage zone were calculated based on an isotropic damage model. The convergence-confinement method based on damage model can consider the effects of post-peak rock behavior on the ground response curve and excavation damage zone. The analysis of results show the important effect of brittleness parameter on the tunnel wall convergence, ground response curve and excavation damage radius.