Continuum Damage Mechanics Theory Research Articles

Application of a coupled elasto-acoustic-damage system to acoustic emissions from sea ice fracture

Sea ice fracture and the resultant acoustic emissions have been studied extensively through observation, experiments, and theoretical analysis. This work demonstrates the applicability of a novel time-domain method for simulating dynamic damage evolution in a coupled structural-acoustic system for the prediction of acoustic emissions from sea ice fracture. The primary aim of this study is to employ first principles modeling of acoustic emissions from failure, as derived via the theory of continuum damage mechanics, including the transition of the acoustic waves from solid to fluid domains. The overall solution method is designed to be compatible with modern high-performance computing environments. The algorithm is staggered, where first the solution for the dynamic fracture evolution is found with an explicit step, and then the coupled computation of the structural-acoustic system response is computed using the new values of the damage and modified geometry. Code and solution verification of the fully coupled solution algorithm are presented, as are comparison to laboratory experiments and field observations for sea-ice fracture.

A simplified continuum damage mechanics based modeling strategy for cumulative fatigue damage assessment of metallic bolted joints

Fatigue damage and consequent failure account for the majority of the failure in metallic bolted joints of aerospace and mechanical engineering applications. In this paper, we present a cumulative fatigue damage evaluation approach for metallic bolted joints based on a combined continuum damage mechanics (CDM) theory and the critical plane approach. The analysis approach is applicable to both proportional and non-proportional multiaxial loading conditions. A cycle jumping based algorithm with a fixed damage evolution rate is adopted for efficient numerical approximation. To further increase the computational efficiency, a simplified modeling strategy is developed to avoid the expensive calculation of the full loading-unloading cyclic stress history. The proposed approach is established based on the assumption that a linear relation can be established between the minimum and maximum stress tensors in high-cycle fatigue analysis and is thus only dependent on the maximum stress states. A set of examples including a notched specimen and a metallic bolted joint with pre-tension are simulated to demonstrate the simplified approach.

A novel constitutive modelling approach measured under simulated freeze–thaw cycles for the rock failure

In this study, we derived a computational modelling relation between the model parameters and characteristic parameters of rock deformation and failure via total differentials. We construct a damage model of rock under simulated freeze–thaw cycles and loading based on continuum damage mechanics theory that considers the influence of confining pressure and the random characteristics of rock material defects. This model reflects the variation in regulation between the internal mechanism of freeze–thaw damage and selected physical variables, making it more adaptable. We further analyze the evolution of microdamage and induced material mechanical properties of the rock using our proposed model, producing a total damage evolution curve under freeze–thaw cycles and loading that reflects the closure, initiation, propagation and coalescence of internal microcracks, as well as the subsequent appearance of macrocracks and rock failure. As the number of freeze–thaw cycles increases, rock damage intensifies, as demonstrated by the material’s deteriorating micromechanical properties. However, in later stages of deformation, both the strain and plasticity of the rock increase. With increasing confining pressure, rock damage and the damage accumulation rate, peak damage evolution ratio and descending segment after the peak decrease which manifest in the enhanced resistance of the rock to failure and increased macroscopic plastic deformation. Finally, we perform triaxial compression tests of rock under freeze–thaw cycles to validate our model. The macroscopic rock deformation and failure predicted by our model’s damage characteristics analysis are consistent with our experimental result.

Research on the Damage Evolution Process of Steel Wire with Pre-Corroded Defects in Cable-Stayed Bridges

A numerical simulation method is presented in this paper to study the damage evolution and failure process of high-strength steel wires with pre-corrosion defects in cable-stayed bridges under fatigue loads. This method was based on the mechanism of crack nucleation accelerated by corrosion pits, in which cellular automata (CA) and finite element (FE) simulation methods were used. First, based on the continuum damage mechanics (CDM) theory, a fatigue damage model suitable for steel wire with pre-corroded defects was established to describe the evolution process of the microscopic damage of steel wires, and a user-defined material subroutine (UMAT) was written using formula translator (FORTRAN) language. Then, in MATLAB, the shape and position of random pitting defects on the steel wire surface were generated using 3D CA technology. Afterwards, a pitting defect model was successively inputted into AutoCAD, Rhino and ABAQUS software to obtain the FE model of steel wire with initial pitting defects or initial damage. Finally, the life-and-death element method and the UMAT program were used to simulate the fatigue damage evolution process of the steel wire with initial defects in ABAQUS software, and the fatigue life of the steel wire was obtained. The results show that the proposed strategy and algorithm can effectively describe the fatigue damage evolution process of the steel wire with initial pitting defects under the action of a fatigue load, and the simulated fatigue life is in good agreement with the experimental results. The obtained stress-life (S-N) curves of the steel wire with different corrosion degrees show that the influence of pit corrosion on fatigue life is much greater than that of the mass loss caused by corrosion. By comparing the irregular pit model with regular pit models, it can be found that the irregular shape angle is the main reason for the smaller fatigue life and the larger stress concentration in the irregular pit model than in the regular pit model.

Finite element analysis of controlled low strength materials

Controlled low strength materials (CLSM) are flowable and self-compacting construction materials that have been used in a wide variety of applications. This paper describes the numerical modeling of CLSM fills with finite element method under compression loading and the bond performance of CLSM and steel rebar under pullout loading. The study was conducted using a plastic-damage model which captures the material behavior using both classical theory of elasto-plasticity and continuum damage mechanics. The capability of the finite element approach for the analysis of CLSM fills was assessed by a comparison with the experimental results from a laboratory compression test on CLSM cylinders and pullout tests. The analysis shows that the behavior of a CLSM fill while subject to a failure compression load or pullout tension load can be simulated in a reasonably accurate manner.

Continuum Damage Modeling of Hydraulic Fracture from Perforations in Horizontal Wells

The perforations play an important role in determining the near-wellbore fracture geometry during the stimulation phase. To address the impact of perforations on fracture geometry in horizontal wells, a 3D coupled hydromechanical finite element model is developed and employed. Based on the theory of continuum damage mechanics, scalar damage variable governs the degradation of the stiffness of the solid. Damage affects the crack element modeling that is used to consider crack behavior and construct a crack-tracking algorithm to simulate propagation. The model was validated against the analytical solutions and perforation fracture experiments. The results indicate that perforation can be used to control the fracturing pressure and propagation behavior of the initial fracture, which has a further effect on the fracture geometry of near-wellbore region in horizontal wells. Optimizing perforation parameters can direct the propagation of the initial fracture toward the preferred fracture plane. The results demonstrate an improved capability to depict the 3D near-wellbore fracture geometry and fracture propagation with a continuum damage model. The model enables the optimization of orientations and perforation parameters, so that most efficient perforating completions can be designed for hydraulic fracture stimulation.

Failure damage mechanical properties of thoracic and abdominal porcine aorta layers and related constitutive modeling: phenomenological and microstructural approach.

Despite increasing experimental and analytical efforts to investigate the irreversible effects of arterial tissue failure, the underlying mechanisms are still poorly understood. The goal of this study was to characterize the failure properties of the intact wall and each separated layer (intima, media, and adventitia) of the descending thoracic and infrarenal abdominal aorta and to test the hypothesis that the failure properties of layer-separated tissue depend on the location of the aorta. To test this hypothesis, we performed uniaxial tests to study the mechanical behavior of both intact and layer-separated porcine aortic tissue samples taken from descending thoracic and infrarenal abdominal aorta until complete failure. The fracture stress is higher in the infrarenal abdominal aorta than in the equivalent descending thoracic aorta. It was also found that the extrapolation of the elastic mechanical properties from the physiological to the supra-physiological regime for characterizing the mechanical response of the aorta would be inappropriate. Finally, we report values of constitutive parameters using phenomenological and microstructural damage models based on continuum damage mechanics theory. The phenomenological damage model gives an excellent fit to the experimental data compared to the microstructural damage model. Although the fitting results of the phenomenological model are better, the microstructural models can include physically motivated aspects obtained from experiments.

Strain based approach in fatigue damage modeling of brittle material-application to concrete

Due to very good compressive strength of concrete, it is used widely in all over the world during three decades. The Formulation of Concrete is through combination of Cement, stone aggregate, sand and water according to their design mix based on the ultimate strength required for the structural component. The Mixing of concrete is as mortar, the layer of cement, sand and water is wrapped around the aggregate. When the load is applied to the concrete, the weaker zone i.e. mortar of cement, sand is weaker than stone aggregate, damage by formulation of crack before crack in aggregate. The Damage behavior of Concrete is thus to be analyzed according to their fatigue behavior. Strain Based approach in Fatigue Damage Modelling of Brittle Material in Concrete is presented to describe the behavior and failure of con-crete by utilizing Damage Mechanics approach. Stiffness degradation and inelastic deformation are the essential features of concrete that develop due tothe formation of multitude of microcracks in the fatigue environment. Microcracking, which is anisotropic in nature, destroys the bond between material grains, and affects the elastic properties resulting in the reduction of material stiffness in elastic as well as plastic stage. This paper presents an anisotropic fatigue damage model for plain concrete subjected to cyclic tension. The model is developed, in strain space, using the general framework of internal variable theory of continuum thermodynamics and Damage Mechanics. It is argued that within the damage surface of given strain states the unloadingreloading cycles (fatigue loading) stimulate the nucleation and growth microcracks in concrete, which will result in stiffness degradation and inelastic deformation, and hence material is termed as damaged. Damage is reflected through the fourthorder stiffness tensor involving a damage parameter whose increment is governed by the consistency equation associated with a cycle dependent damage surface in strain space. The model is capable of predicting stiffness degradation, inelastic deformation and strength reduction under fatigue loading and compared against experimental result. By increasing the number of loading cycles, the strength of concrete gradually decreases and the limit surface is allowed to contract and form new curves representing residual strengths. The magnitude of loading, load range, and the load path are known to influence the fatigue life and hence are addressed in this formulation. In this paper, a strength softening function is proposed in order to address the re-duction in the strength of concrete due to fatigue. Separate softening functions are also proposed to account for the deformation characteristics in concrete under cyclic loading. Numerical simula-tions predicted by the model in both uniaxial and biaxial stress paths show a good correlation with the experimental data available in the literature.

Simulation of Alkali-Silica Reaction Model in a Concrete Gravity Dam at the Macroscale and Mesoscale

Abstract Alkali-silica reaction causes major problems in concrete structures due to the rapidity of its deformation. Factors that affect ASR include the alkali and silica content, relative humidity, temperature and porosity of the concrete, making the relationship a complex phenomenon to be understood. In investigating the mechanical deformation of the structure, the theory of continuum damage mechanics proves to be a suitable method. Damage mechanics can be used to predict the physical and chemical behavior of a structure, making it an appropriate method to study the behavior of the structure under the influence of alkali-silica reactivity. Therefore solution of the damage model is critically needed to overcome the concrete deformation problem. In this research, an engineering example of a thermo-chemo-hygro-mechanical model of a concrete gravity dam at the macroscale and coupled with the mesoscale will be studied for varying environmental conditions of temperature and relative humidity. The simulation was developed using the stochastic finite element software. Investigations found that temperature, as well as relative humidity influences the latency and characteristic time constants, which dictate the rapidity of ASR expansion into the structure, rendering heterogeneous values across the cross-section of the structure according to the relative humidity and temperature distribution.

Damage constitutive model of single flaw sandstone under freeze-thaw and load

The deterioration of mechanical properties subjected to freeze-thaw action is a determining factor for natural rock masses in cold region engineering. Taking four cases of flaw sandstone as the research object, freeze-thaw cycles experiments and triaxial compression tests were conducted to analyze the mechanical properties after 0, 20, 40 and 60 freeze-thaw cycles. The damage evolution equation of freeze-thaw sandstone under load is established based on the Lemaitre strain equivalent principle and continuum damage mechanics theory. In this regard, the damage model was developed to predict the degradation of triaxial compression strength for single flaw sandstone samples, it takes into account pre-existing cracks, confining pressure, freeze-thaw action and load. The results show that the sandstone damage consists of factors mentioned above, the coupled damage variable acquired from the proposed method well agree with the actual condition, and the damage constitutive model validations are given through comparisons between the calculated and the measured.

Damage related material constants in continuum damage mechanics for unidirectional composites with matrix cracks

Application of a continuum damage mechanics formulation rests on the ease with which the material constants involved in the formulation can be determined. For an initially linear elastic material, the changes in elastic constants induced by damage depend on certain damage related material constants that are commonly determined by experiments in addition to those required to determine the initial properties. This additional experimental task can render the continuum damage mechanics theory less attractive. The present paper will only deal with those associated with damage representation. We propose here a procedure for analytically determining seven out of eight damage related material constants for unidirectional composites assumed initially transversely isotropic and containing a parallel array of matrix cracks along fibres. The remaining constant can be determined experimentally or by a numerical experiment proposed here for the purpose. The analytical expressions derived are in terms of initial elasticity constants of a unidirectional composite and are verified for their accuracy by numerical experiments. Since a unidirectional composite forms a building block in composite laminates, the results obtained here can be naturally used for damage in laminates.

Quantitative analysis of QSI and LVI damage in GFRP unidirectional composite laminates by a new ultrasonic approach

Abstract Our work is focused on a new experimental approach for the comparison between Quasi Static Indentation (QSI) damage and Low-Velocity Impact (LVI) damage in polymer composites starting from the results of ultrasonic goniometric immersion tests. In particular, the comparison is performed through the analysis of the additional anisotropy induced by the damage in unidirectional Glass Fiber-Reinforced Polymer (GFRP) composites due to QSI and LVI damage tests performed with a low level of the employed energy. To this aim, we ultrasonically reconstruct the acoustic curves (velocity curves and slowness curves) before and after the damage. Ultrasonic experiments are performed by using a goniometric ultrasonic immersion device designed and built at our laboratory, aimed at the mechanical characterization of anisotropic materials. We highlight differences and similarities between QSI and LVI damage starting from the analysis of the variations of the acoustic behavior and by using a suitable anisotropic damage model developed in the framework of the Continuum Damage Mechanics theory. The proposed experimental approach can be suitably developed for in situ investigations on low-velocity impact damage in polymer composite components.

An explicit periodic nonlinear model for evaluating dynamic response of damaged slab track involving material nonlinearity of damage in high speed railway

For evaluating the vibration response of the damaged slab track efficiently, a novel explicit periodic nonlinear model for the damaged slab track in high speed railway involving material nonlinearity of damage is presented based on the theory of continuum damage mechanics and the constitutive relationship of concrete under uniaxial tension, where the infinite periodically supported composite beam for the track on the elastic foundation is truncated into a beam section with the length of a single vehicle by introducing periodic boundary conditions. The vibration equations of the nonlinear model are discretized into ordinary differential equations (ODEs) in space domain by the periodic spectral method, and then by applying the explicit central difference method these ODEs are solved with time-domain difference ultimately. The validity of the model is verified by the comparison of the results from the periodic model, finite element method (FEM) and the field test, and the reasonable values of the key computational parameters are recommended. Moreover, the influence of track structural parameters on the vibration response and damage evolution of CRTS II slab track of China’s high speed railway is investigated with the periodic nonlinear model. And some practical conclusions for design and construction are acquired.

Verification and validation of a coupled elasto-acoustic-damage system

A novel time-domain method for simulating dynamic damage evolution in a coupled structural-acoustic system is presented. The system is derived via the theory of continuum damage mechanics, and incorporates standard damage evolution models, but is readily extendible to more complex formulations. The overall solution method is staggered, first solving for the dynamic damage evolution with an explicit step, and then using the new values of damage in the coupled computation of the structural-acoustic system. The spatial domain is discretized using a mixed finite element method, and the temporal domain is discretized with a higher-order implicit time discretization scheme. Code and solution verification of the fully coupled solution algorithm are presented, as are validation studies for cases with and without evolving damage. Applications with evolving damage are presented, and present a novel first principles study of changes in the structural acoustic response to dynamically evolving damage in the structure....

An insight into the low-velocity impact behavior of patch-repaired CFRP laminates using numerical and experimental approaches

In this paper, the low-velocity impact response of patch-repaired CFRP laminates is investigated experimentally and numerically. This study considers various patches of different shapes and sizes placed on the single side of the parent laminate plates. In the low-velocity impact simulation, damage development and the failure process of the repaired laminate plates are analyzed based on continuum damage mechanics (CDM) theory which is derived from 3D Hashin failure criteria, and a cohesive zone model (CZM). In order to validate the proposed numerical approach, impact response such as impact force and energy are predicted from simulation. Moreover, the corresponding drop weight impact tests have been performed, and the numerical prediction is in a good agreement with the experimental measurements. Finally, the influence of patch parameters on repair performance has been analyzed according to the delamination surface area and absorbed energy of the repaired laminates from the low-velocity impact simulation. And, an optimal impact-resistance design of the patch repair is obtained based on the finding results.

Shakedown-ratcheting analysis of Bree's problem by anisotropic continuum damage mechanics coupled with nonlinear kinematic hardening model

In the present research, Bree's diagram, which has been used for ratcheting assessment of pressurized equipment in ASME III NH, has been developed when the pressure vessel contains discontinuities such as voids and microcracks. Nature of these defects leads to an anisotropic damage. Anisotropic Continuum Damage Mechanics (CDM) is considered to account effects of these discontinuities on the behavior of the structure. Shakedown – ratcheting response of a hollow sphere under constant internal pressure and cyclic thermal loadings is studied by using anisotropic CDM theory coupled with nonlinear kinematic hardening of Chaboche. Return mapping method is used to solve numerically the developed relations. Elastic, elastic shakedown, plastic shakedown and ratcheting regions are illustrated in the modified Bree's diagram. Influence of anisotropic damage due to the plastic deformation, is studied and it was shown that the plastic shakedown region is diminished because of the developed damage.

A modified damage law with the fuzzy neural network method for crack initiation life prediction of notched specimen

It is difficult to predict the fatigue life of notched specimen due to the complexity of notch effect. Based on the continuum damage mechanics theory of Lemaitre, a modified damage law for fatigue life prediction of notched specimen combined with the fuzzy neural network method is proposed to obtain a more reliable life. According to the fatigue experimental data, the material parameters in the damage evolution equation are demarcated. Then the fatigue life prediction of notched specimen is conducted. At last, after the stage pf experiment data collection and NN training , the established NN model will be able to reduce the relative error from 20.85% to about %7.12 in the verification test. Although the life prediction after being modified may not be accurate in every local region, the combination between the theoretical method and the fuzzy neural network method will obtain a more reliable material life in the whole. DOI: http://dx.doi.org/10.5755/j01.mech.23.6.14862

Thermo-mechanical behaviour of dovetail timber joints under fire exposure

This paper presents a 3D finite element model to analyse the thermo-mechanical behaviour of dovetail timber joints under standard fire exposure. The mechanical model of timber is based on Yamada-Sun failure criterion and continuum damage mechanics (CDM) theory. The thermal model considers the classical heat transfer and temperature-dependent properties of material to predict the charring rates and evolution of temperature fields. The thermo-mechanical model is validated by comparing the fire resistance and displacement-time curves with experimental results. Novel numerical failure criterion based on the kinetic energy-time curves were proposed. The numerical models show a good capacity to simulate the thermo-mechanical behaviour of dovetail timber joints under fire exposure.

On the fracture toughness of bulk metallic glasses under Berkovich nanoindentation

Measurements of fracture toughness from the crack tip opening displacement (CTOD) testing methods are complex and paramount important for a range of bulk metallic glasses (BMGs). In this work, we attempted to propose an indentation protocol to evaluate indentation fracture toughness based on two key considerations: First, the plastic deformation induced damage to the characteristic fracture initiation point calculated from integrating the indentation load-displacement curves is obtained and used to estimate indentation fracture toughness. Second, the continuum damage mechanics theory has been adopted to identify the characteristic fracture initiation point. To verify the applicability of the suggested approach, fracture toughness values of BMGs were estimated and compared with those from CTOD tests in the literature. The estimated fracture toughness values KC obtained from the indentation tests agreed well with those KQ from the CTOD tests within an approximately relative difference of 10%. We also found that KQ linearly correlates with KC (KQ=1.1KC−3.7). The value of KQ in Al-based BMG is predicted to be ~35MPa√m.

Hybrid micromechanical-phenomenological modelling of anisotropic damage and anelasticity induced by micro-cracks in unidirectional composites

In this paper, a new damage modelling approach is presented to describe the mechanical response of unidirectional composites under the small strain assumption. The proposed constitutive equations inherits from the phenomenological theories of Continuum Damage Mechanics (CDM) but brings out a micromechanical description of the damaged Representative Volume Element (RVE) while being formulated in a proper thermodynamical framework. The model is provided with an implicit numerical scheme based on the so-called “return mapping algorithm” as well as the formulation of the tangent operator. The identification and the prediction capabilities of the model are validated using experimental data including off-axis tensile tests. Finally, to provide a better understanding of the model, a multi-axial non-proportional simulation is performed and analysed.