Continuum Damage Mechanics Theory Research Articles

An advanced continuum damage mechanics model for predicting the crack progress process based on the consideration of the influence of crack direction under quasi-static load

In reality the wrong crack path can be generally obtained in the case of arbitrary crack propagation by traditional continuum damage mechanics (CDM). In this paper a novel advanced continuum damage mechanics (ACDM) method is proposed, which can predict the crack propagation and fracture behavior correctly for the structures. The material property degradation method, which is usually used when simulating the structures within the framework of CDM, is advanced based on considering the influence of crack direction. The maximum tensile stress criterion is used to predict the damage initiation and crack propagation direction and the advanced CDM used to predict the damage evolution process in meso-level under the quasi-static load. It can directly evaluate the propagation process of the discrete crack and the fracture strength for structures using the continuum model as well as not using discontinuum model. The algorithm for the application of our advanced CDM theory in the numerical simulation based on finite element method (FEM) is presented. ACDM model is not only a simple and useful model which can easily be used in FEM framework but also a phenomenological model based on the concept of crack propagation. The simulation results by our ACDM are compared with the experiment results and the ones and from cohesive zone method and extended finite element method for good agreements to be achieved.

Simulation of coupled structural-acoustic response with dynamic damage evolution

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 exotic formulations. The overall solution method is staggered, solving for the dynamic damage evolution first with an explicit step, and then using the new values 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. Efforts toward fully coupled verification of the solution algorithm are presented, as are validation studies for cases 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. Special attention is given to brittle fracture. Examples of downstream usage of the evolving structural response are discussed in the concluding remarks.

A thermodynamics-based formulation for constitutive modelling using damage mechanics and plasticity theory

In this study, a generic formulation for constitutive modelling of engineering materials is developed, employing theories of plasticity and continuum damage mechanics. The development of the proposed formulation is carried out within the framework of thermodynamics with internal variables. In this regard, the complete constitutive relations are determined by explicitly defining a free energy potential and a dissipation potential. The focus is put on the rigour and consistency of the proposed formulation in accommodating the coupling between damage and plasticity, while keeping its structure sufficiently generic to be applicable to a wide range of engineering materials. In particular, by specifying the coupling between damage and plasticity in the dissipation function, a single generalised loading function that controls the simultaneous evolution of these dissipative mechanisms is obtained. The proposed formulation can be readily used for either enriching existing plasticity models with damage, or for the developments of new coupled damage-plasticity models. The promising features and the applications of the proposed formulation for describing the behaviour of different engineering materials are discussed in details.

Ex-situ X-ray tomography characterization of porosity during high-temperature creep in a Ni-based single-crystal superalloy: Toward understanding what is damage

Creep damage by void nucleation and growth limits the lifetime of components subjected to mechanical loads at high temperatures. For the first time, the porosity of a Ni-based single crystal superalloy subjected to high temperature creep tests (T≥1000°C) is followed by ex-situ X-ray computed tomography. A large experimental campaign consisting of nine temperature/stress conditions is carried out to determine the kinetics of the damage accumulation by voids. It is, indeed, essential to characterize their evolution to create internal variables describing properly the evolution of damage in a Continuum Damage Mechanics framework. Nonetheless, it is pointed out that the increase in the plastic strain rate during the tertiary creep stage is not necessarily related to the increase in the pore volume fraction for the alloy and temperature range explored (1000–1100°C). Therefore, it seems that the changes in the microstructure, i.e. precipitation coarsening and γ/γ′ topological inversion, and the shearing of the γ′ particles have to be considered further to properly describe the damage evolution. Thus, the Continuum Damage Mechanics theory is undermined and should be replaced by a transformative paradigm taken into consideration microstructural evolutions in order to improve the predictability of further damage models.

Numerical investigation of the forming capability of bulge process by using rubber as a forming medium

A finite element simulation of flexible bulge forming of aluminum sheet metal is carried out. The effect of rubber pad on forming capability is studied by comparing flexible bulge to hydroforming. Based on the theory of Continuum Damage Mechanics (CDM), a local approach with fully coupling between ductile damage and an anisotropic elasto-plastic model with mixed nonlinear kinematic/isotropic hardening is introduced. The model is implemented into a user-defined material (VUMAT) subroutine for the commercial finite element code ABAQUS/Explicit. A Mooney-Rivlin theory is adopted for rubber material behavior. Comparisons between both processes in terms of thickness variation, damage occurrence, and sheet formability are conducted for different rubber shores and friction. Numerical findings are in a good correlation with experiments from literature.

A damage mechanics based method for fatigue life prediction of the metal graded materials

Based on the continuum damage mechanics theory, the fatigue life prediction for TC4-TC11 graded material was conducted. At first, the damage evolution equation was derived, then the method to calibrate material parameters for TC4-TC11 graded material was proposed, and all the material parameters were obtained. A beam model with TC4-TC11 graded material was established by using the stratified method and finite element method. Finally, the fatigue life of TC4-TC11 graded beam was predicted.

Ultrasonic goniometric immersion tests for the characterization of fatigue post-LVI damage induced anisotropy superimposed to the constitutive anisotropy of polymer composites

We study an ultrasonic experimental approach for the damage characterization of polymer composites. Our approach is based on the key concept that damage of polymer composites involves a damage induced anisotropy superimposed to the constitutive anisotropy of the material. Thus, we correlate the damage to the analysis of the change in the anisotropy of the acoustic response of the material, by using an innovative goniometric ultrasonic immersion device designed and built at our laboratory. The experiments are performed on a glass fiber–reinforced composite material (GFRP), damaged first by a low velocity impact (LVI), and then by fatigue load cycles. We first identify possible changes in symmetry axes (acoustic axes) and/or in the symmetry class of the material due to the damage; to this aim, we compare the velocity curves and the slowness curves of the composite before and after the damage. Then, starting from the velocity measurements acquired in goniometric ultrasonic immersion tests performed before and after the damage, we determine the variations of the elastic constants due to the damage. For a quantitative characterization of the damage, a suitable anisotropic damage model developed in the framework of the Continuum Damage Mechanics theory is employed. In this model, the damage is related to the relative variation of the elastic constants of the material. For the validation of the procedure, ultrasonic results are also compared with experimental data obtained by conventional mechanical tests. The obtained results show the effectiveness of the proposed approach for the damage characterization of polymer composites.

Elasto-plastic Damage Analysis Based on Strain-space Plasticity

Continuum Damage Mechanics (CDM) is an evolving area of Solid Mechanics. CDM has been found to have great potential. Most of the plastic damage models attempt to bring together the theories of plasticity and CDM. In this paper, the strain-space plasticity theory is implemented for elastic-plastic damage material model in the framework of non-linear finite element analysis. In the stress space plasticity models the yield surface, loading and unloading criteria, flow rule, and often hardening rules are defined in stress space. The research paper presents a set of systematic formulations for the theory of isotropic elasto-plastic ductile damage. Lemaitre's model is considered for the damage evolution growth. The plastic flow and damage flow are coupled within the potential function. In order to verify the formulations presented, numerical results are compared with the results available in literature.

Evaluation of damage anisotropy induced in GFRP composite materials by an innovative ultrasonic experimental approach

We present a theoretical and experimental approach for the characterization of the damage induced anisotropy superimposed to the constitutive anisotropy of fiber-reinforced composite materials. The theoretical model here employed has been developed in the framework of the Continuum Damage Mechanics theory and allows for determining a tensorial damage measure based on the change of the elastic moduli of the composite material. Moreover, the model is general since it is applicable independently of the fibers reinforcement nature, of the presence of cracks, interlaminar voids and delamination, of the geometry of this cracks, and from of failure mechanisms of the composite materials. We perform damage experiments by using an innovative goniometric device designed and built at our laboratory (Laboratorio “M. Salvati”), and aimed at the mechanical characterization of materials. In particular, by rotating the sample into a water tank, we measure the ultrasonic “natural” velocities of the undamaged composite material along suitable propagation directions. This allows us for classifying the degree of symmetry of the material and for determining the elastic constants, also in highly anisotropic materials. Then we measure the ultrasonic velocities of the artificially damaged composite and we determine again the elastic moduli. The comparison between the elastic moduli of the damaged and the undamaged composite allows us for the characterization of the above cited anisotropic tensorial damage measure.

Numerical Simulation of Rotational Behavior of Bolted Glulam Beam-to-Column Connections with Slotted-In Steel Plates

This paper presents the results of a numerical study on rotational behavior of bolted glulam beam-to-column connections. Since wood often exhibited complex failure behavior under different loading states, a three dimensional anisotropic damage analysis model of wood was initially developed based on continuum damage mechanics theory for progressive failure analysis of wood. The damage model basically consisted of two ingredients: the failure criterion proposed by Sandhaas was chosen to capture the damage onset; three independent damage variables were adopted to control the ductile and brittle damage evolution process of wood. This material model was implemented in a commercial available finite element method based code using a user-material subroutine. Finite element model of bolted connection coupled with the proposed material model was established to further investigate the failure modes and moment resistance of such connections. It was found that the damage evolution progress was very similar to the crack development from experimental tests. By comparing the experimental results and numerical predictions, a fair agreement of the initial stiffness and moment resistance was found with modeling error less than 3%, which implied that the finite element model was suitable to simulate the rotational behavior of such connections. This research could provide the reference for the design of bolted glulam connections in heavy timber structures.

Simulation of coupled structural-acoustic response with dynamic damage evolution

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 exotic formulations. The overall solution method is staggered, solving for the dynamic damage evolution first with an explicit step, and then using the new values 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. Efforts toward fully coupled verification of the solution algorithm are presented, as are validation studies for cases without evolving damage. Applications with evolving damage are presented, and present a first principles study of changes in the structural acoustic response to dynamically evolving damage in the structure. Special attention is given to brittle fracture. Examples of downstream usage of the evolving structural response are discussed in the concluding remarks.

Explicit multiscale modelling of impact damage on laminated composites – Part II: Multiscale analyses

This work describes a multiscale impact damage prediction methodology for laminated composite structures which is based on the HFGMC micromechanical model and the MMCDM damage formulation. The numerical approach is intended for application within explicit finite element analyses and has been employed for modelling of high-velocity impact damage in laminated composite structures. Structural-scale applications and the multiscale framework of the method are presented in this paper whereas introduction and validation of the methodology have been presented in Part I of the paper.By applying the described method, the micromechanical model calculates the local stress/strain fields within the unidirectional composite material, whereas the structural-scale computations have been performed employing Abaqus/Explicit. The Mixed Mode Continuum Damage Mechanics (MMCDM) theory has been utilised as to model the damage and failure modes of the composite material at the micromechanical level. As demonstrated in the Part I paper, the HFGMC and MMCDM model enable modelling of the microdamage nonlinearities at in-plane shear and transverse compressive loading of the composite plies. The micromechanical damage modelling approach has been employed at high-velocity soft-body impact on CFRP and GFRP composite plates in this work. Results of the multiscale damage model have been validated using available experimental data and by comparison with the numerical results obtained using the commonly used ply-level failure criteria and damage models.

Explicit multiscale modelling of impact damage on laminated composites – Part I: Validation of the micromechanical model

This work presents the development and verification of a multiscale methodology applicable for modelling of impact damage in laminated composite structures. The methodology employs the High Fidelity Generalized Method of Cells (HFGMC) micromechanical model for the prediction of local stress/strain fields within the unidirectional composite material. The micromechanical model has been coupled with Abaqus/Explicit, where the structural scale computations have been performed.The methodology utilises the Mixed Mode Continuum Damage Mechanics theory (MMCDM) as to model damage within the composite microstructure. Validation and application of the multiscale methodology have been presented in two separate papers. Part I presents an overview of the micromechanical model and validation of the micromechanical damage model, whereas the multiscale analyses have been demonstrated in Part II of the paper.The micromechanical damage model parameters have been determined by correlation with available experimental data of the nonlinear behaviour of the homogenised composite material at in-plane shear and transverse compressive loading. The obtained results demonstrate the ability of the micromechanical approach to model accurately the failure modes of the composite material, as well as the nonlinear behaviour of the composite plies at the in-plane shear and transverse compressive loading.

Fatigue damage propagation models for ductile fracture of ultrahigh toughness cementitious composites

Ultrahigh toughness cementitious composites are a kind of high-performance cementitious material with a characteristic of ductile fracture. Based on the continuum damage mechanics theory and flexural fatigue damage model, two damage propagation models of ultrahigh toughness cementitious composites are built. One is a linear bilogarithmic model with J-integral range as its independent variable, while the other one is a linear model on a semilogarithmic scale with fatigue stress level as its independent variable. However, according to former research, the J-integral depends strongly on specimens’ geometry, so the first damage propagation model is deeply influenced by material dimension. As a result, the second damage propagation model is more convenient in application, shows the material fatigue property in comparison with the first model. In order to prove these two models and obtain the parameters, a three-point flexural fatigue experiment on single-edge-notched fracture specimens is carried out. The results shows that the two models fit better with the experimental results, rather than the crack propagation law of ultrahigh toughness cementitious composites.

Influence of different sources of microstructural heterogeneity on the degradation of asphalt mixtures

The response and degradation of the hot mix asphalt (HMA) materials used in pavement structures are affected by their inherent heterogeneity. The objective of this work is to study the impact of two different sources of HMA heterogeneity in the uncertainty of the mechanical moisture degradation of HMA. The first source of heterogeneity is the spatial variability of the properties of the bulk fine aggregate matrix (FAM) of the mixture, and the second is the location and shape of the coarse aggregate particles. The heterogeneity of the bulk FAM phase was modelled using a random field technique, while that of the coarse aggregates was accounted for by randomly generating realistic probable sets of aggregate particles. Thus, ‘computational replicates’ of HMA microstructures were generated and subjected to moisture diffusion and mechanical loading using a finite element approach. In the mechanical simulations, a non-linear viscoelastic moisture damage constitutive relationship based on continuum damage mechanics theory was selected to characterise the response of the bulk FAM phase. The results show that conducting computational simulations with realistic HMA microstructures that properly capture the heterogeneity of the material is useful to quantify the mean values and dispersion (i.e. uncertainty) associated with the response and degradation of the mixture. This information, which cannot be easily obtained in the field or in the laboratory due to the difficulty of acquiring a sufficient amount of data, is useful to conduct structural reliability analysis and to predict the life cycle behaviour of the material.

Finite element modelling of the low velocity impact response of composite plates with block copolymer nano-reinforcements

The use of composite materials in passive safety structures has increased significantly due to their low specific mass and high energy absorption capacities. The purpose of this study is to develop and validate a macroscopic numerical model to simulate the impact response of composite laminates with nano-reinforcements. The impact resistance of laminate with Kevlar fibre reinforced epoxy resin embedded with Nanostrength®, an acrylate triblock copolymer that self-assembles in the nanometer scale is investigated. Low velocity impact experiments were performed on square plates clamped by means of a circular fixture using an instrumented drop tower. Images of the composite laminate during impact were recorded by a high-speed video camera fixed underneath the plate. An approach for modelling these composites in the commercial finite element code LS-Dyna using constitutive model based on the theory of continuum damage mechanics developed by Matzenmiller, Lubliner and Taylor - called MLT model - is presented. LAMINATED COMPOSITE FABRIC material model, available in the LS-Dyna material model library as (MAT58), was chosen for modelling the low velocity impact of the Kevlar composite plate. The model requires input of material properties in shear, tension, and compression to define stress-strain behaviour within the laminate. The parameters needed for the model are determined using a combination of experimental tests and parametric analysis. The macroscopic response of the Kevlar composite with and without nanoparticles in the resin subjected to impact loading are simulated in LS-Dyna with the phenomenological material model, and is validated by comparison with experiments. It was found that the Kevlar epoxy composite material with Nanostrength M52N had better resistance to perforation compared to the lamiante with neat resin.

Multiaxial fatigue life modelling using hybrid approach of critical plane and genetic algorithm

AbstractThis paper presents a new hybrid approach for multiaxial fatigue life estimation, based on continuum damage mechanics theory and a genetic algorithm with critical plane model formulation. The hybrid model employs a genetic algorithm based setup for calibration with standard proportional and non‐proportional profiles to predict fatigue life for complex loading profiles. The model is evaluated using experimental fatigue life data for SS304 steel. Calibration using simplified profiles is in agreement with the requirement for cost‐effective experimental fatigue life testing. In‐phase and out‐of‐phase loads are used for calibration, and fatigue life is predicted for more complicated profiles. The results show good agreement between the estimated and experimental fatigue life, and calibration through simple loading histories to predict fatigue life for complex histories appears to be an effective solution using the proposed model. A brief comparison is presented with fatigue life estimation performance of the proposed model with models available in commercial codes. Proposed model found to be more consistent in fatigue life prediction against various loading conditions.

A generalized finite‐strain damage model for quasi‐incompressible hyperelasticity using hybrid formulation

SummaryA new generalized damage model for quasi‐incompressible hyperelasticity in a total Lagrangian finite‐strain framework is presented. A Kachanov‐like reduction factor (1 − D) is applied on the deviatoric part of the hyperelastic constitutive model. Linear and exponential softening are defined as damage evolution laws, both describable in terms of only two material parameters. The model is formulated following continuum damage mechanics theory such that it can be particularized for any hyperelastic model based on the volumetric–isochoric split of the Helmholtz free energy. However, in the present work, it has been implemented in an in‐house finite element code for neo‐Hooke and Ogden hyperelasticity. The details of the hybrid formulation used are also described. A couple of three‐dimensional examples are presented to illustrate the main characteristics of the damage model. The results obtained reproduce a wide range of softening behaviors, highlighting the versatility of the formulation proposed. The damage formulation has been developed to be used in conjunction with mixing theory in order to model the behavior of fibered biological tissues. As an example, the markedly different behaviors of the fundamental components of the rectus sheath were reproduced using the damage model, obtaining excellent correlation with the experimental results from literature. Copyright © 2015 John Wiley & Sons, Ltd.

Análise Não Linear Estática de Treliça Plana Utilizando a Mecânica do Dano

<div><p class="SPabstract">As treliças possuem um vasto campo de aplicação na Engenharia de Estruturas, sendo muito utilizadas na construção de pontes - rodoviárias e ferroviárias, em estruturas de cobertura de edificações, em torres de transmissão de energia, entre diversos outros usos. Em geral são relativamente leves e especialmente indicadas para superar grandes vãos ou suportar carregamentos elevados. Nesse contexto, as treliças tornam‐se uma solução econômica e prática. Este artigo tem como objetivo avaliar o comportamento estrutural de treliças planas via Método dos Elementos Finitos considerando a não linearidade física. A relação constitutiva do material é descrita por um modelo baseado na teoria da Mecânica do Dano Contínuo. As análises não lineares são efetuadas por meio do método de Comprimento de Arco com o processo iterativo tipo Newton - Raphson. A partir dos resultados numéricos, a modelagem proposta apresenta potencialidade na análise de treliças planas devido a sua reduzida complexidade e baixo custo computacional.</p></div>

Evaluation of Cumulative Damage of RC Members under Repeated Impact Loading

In the civil and structural engineering field, there are so many problems regarding act of impact loading against some structures due to natural disaster. So it is important to evaluate the damage condition of them after impact loading, and to estimate the residual performance of them. This study is focused on a reinforced concrete (herein after called RC) structure such as caisson breakwater and rock-shed. In order to quantitatively evaluate the dynamic behavior and cumulative damage of RC members under low-velocity single and repeated impact loading, we conducted numerical approach by using the theory of Continuum Damage Mechanics (herein after called CDM). At the result, we clarified not only impact behavior of the members but also the relationship between cumulative kinetic energy of repeated impact loading and cumulative damage of the members. In addition, applicability limit of our model based on scalar damage modeling was clarified.