Proposed Damage Model Research Articles

A damage model for masonry structures

In this paper a brittle damage model for masonry structures characterized by a unit cell composed of mortar, blocks and a finite number of fractures is proposed. Initially, a micromechanically consistent binary representation of the damage variable is proposed for regular heterogeneous media, and a discrete damage kinetic law is developed. Then, a typical masonry material is considered and a specific damage model is derived from the previous one by employing the classical cohesive Coulomb failure criterion and by taking into account the specific microstructure of the masonry. This damage model is used to formulate the nonlinear quasistatic problem of masonry structures subject to assigned loading paths. Then, a numerical procedure based on the finite element method is implemented in a computer code. Finally, some applications are developed to analyze the nonlinear behavior of simple masonry structures and to show the capability of the proposed damage model to capture the differences of behavior by varying the microstructure and the physical properties of the masonry.

A comprehensive description for damage of concrete subjected to complex loading

The damage of concrete subjected to multiaxial complex loading involves strong anisotropy due to its highly heterogeneous nature and the geometrically anisotropic characteristic of the microcracks. A comprehensive description of concrete damage is proposed by introducing a fourth-order anisotropic damage tenser. The evolution of damage is assumed to be related to the principal components of the current states of stress and damage. The unilateral effect of damage due to the closure and opening of microcracks is taken into account by introducing projection tensors that are also determined by the current state of stress. The proposed damage model considers the different kinds of damage mechanisms that result in different failure modes and different patterns of microdefects that cause different unilateral effects. This damage model is embedded in a thermomechanically consistent constitutive equation in which hardening and the triaxial compression caused shear-enhanced compaction can also be taken into account. The validity of the proposed model is verified by comparing theoretical and experimental results of plain and steel fiber reinforced concrete subjected to complex triaxial stress histories.

Anisotropic Damage of Fiber-Reinforced MMC Using Overall Damage Analysis

An anisotropic damage model is proposed for fibrous metal matrix composites (MMC) with a ductile matrix. The model incorporates damage mechanics with micromechanical behavior. An overall damage tensor, M for the whole composite is used in this analysis. This formulation allows the proposed damage model to directly use the elastoplastic stiffness tensor obtained for the undamaged effective configuration. An explicit expression is obtained for the elastoplastic stiffness tensor for the damaged composite material. Numerical solutions are obtained for different types of laminate layups compared with experimental results.

Low-Cycle Variable Amplitude Fatigue Modeling of Top-and-Seat Angle Connections

A set of variable amplitude tests was performed on a commonly used type of semi-rigid connection: the top-and seat angle. Variable amplitude tests included incremental decremental and step tests to investigate the sequence effects on cyclic and low-cycle fatigue behavior for this class of beam column connection. The concept of an effective equi-amplitude plastic rotation is introduced as the characteristic measure of rotation history. It is shown that effective rotation is independent of load path when compared to companion constant amplitude test results. An energy based cumulative damage model is characterized in terms of energy-life and energy-rotation relationships. The proposed damage model is employed in fatigue damage prediction analysis and compared with the classical Miner's linear damage accumulation model coupled with the rainflow cycle counting method. The proposed energy based damage model implicitly incorporates the memory effects of the previous loading history and precludes the necessity of performing explicit cycle counting, and it is easily implemented into non-linear time-history analysis for seismic design and evaluation purposes.

Continuum Damage Mechanics, Anisotropy and Damage Deactivation for Brittle Materials Like Concrete and Ceramic Composites

The main lines of a Continuum Damage Mechanics Modelling are reviewed, for applications to brittle materials treated as elastic damageable ones. The proposed damage models consider in the same framework the cases of initially isotropic materials like concrete and anisotropic composites. Attention is focused on the damage deactivation effects and on the possibility to describe irreversible strains directly associated to the damaging processes without any additional dissipation. Finally, the model is applied to two particular SiC/SiC and C/SiC composites.

On a microstructural model of damage in solids

The aim of the paper is to outline and discuss some ideas and preliminary results concerning microstructural modelling of brittle-like damage in solids. We argue that the basic premises of the simple microelastic theory (independent micro-dilatation of particles), developed by S. Cowin et al. and the author, are a natural starting point in developing certain continuum damage mechanics models. In the brittle-like case under study, with the assumption of isotropic deterioration, the damage rate is added to the arguments (strain, damage and damage gradient) of the elastic energy density. The additional field quantity of the theory—the damage parameter in our context—leads to the appearance of hyperstresses and a balance equation for them. It is shown that the latter can be conveniently identified with the well-known Kachanov's law of damage growth. Thus this law, traditionally introduced through purely phenomenological arguments, finds a natural place in the herein proposed damage model as an equation expressing hyperstress equilibrium.

Damage zones based on Dugdale model for materials

In this paper, an infinite sheet with a crack is studied using continuum damage mechanics technique. The formulation is based on the hypothesis of incremental complementary energy equivalence model for damage evaluation. Damage distributions in the region of a macrocrack tip are calculated for an elastic-perfectly plastic material. The size of the damage zone is also derived via the Dugdale model with damage which considers the interactions between the macrocracks and microcracks. To assess the results, comparisons are made between proposed damage model, Dugdale plastic model and finite element solutions. Good agreement is observed.

An incremental stress-based constitutive modeling on anisotropic damaged materials

An ‘incremental form’ of anisotropic damage constitutive equation is proposed both for brittle and ductile materials. Based on the concept of irreversible thermodynamics that damage processes are history independent coupled with irreversible energy dissipation, two types of definition for damage representation are established, known as damage tensor D and damage strain tensor εd, to describe constitutive responses of damaged materials. A state variable coupled with damage and other observable state variables, i.e. εd, is formulated separately from other internal variables and defined as an equivalent damage variable. A constitutive relation due to damage is finally formulated by introducing ‘damage flow potential function’ employing the theory of irreducible integrity bases. A clear physical representation based on theoretical foundations and rigorous mathematical arguments of the conventional damage models defined in terms of ‘damage effect tensor M(D)’ is also elucidated. Validity of the proposed model is verified by comparing with the formulations of conventional damage effect tensor. A plastic potential function coupled with damage is also introduced by employing the anisotropic plastic flow theory, so that the proposed damage model can be applied to characterize a wide range of damage problems of practical engineering interest.

Failure analysis of a cracked plate based on endochronic plastic theory coupled with damage

An anisotropic model of damage mechanics for ductile fracture incorporating the endochronic theory of plasticity is presented in order to take into account material deterioration during plastic deformation. An alternative form of endochronic (internal time) theory which is actually an elasto-plastic damage theory with isotropic-nonlinear kinematic hardening is developed for ease of numerical computation. Based on this new damage model, a finite element algorithm is formulated and then employed to characterize the fracture of thin aluminum plate containing a center crack. A new criterion termed as Y R-Criterion is proposed to define both the crack initiation angle and load. Experiments have been conducted to verify the validity of the proposed damage model and it is found that the theoretical crack initiation loads correspond closely with the measured values.

Pre-Hardening Effect on Low Cycle Fatigue

A continuum damage mechanics model which accounts for the coupling effect among plastic damage, fatigue damage and creep damage is proposed. The model is capable of identifying the beneficial effects of pre-hardening on fatigue life of metals. It is shown that the proposed damage model can predict the fatigue lifetime of RS50 steel subjected to single pre-hardening load and double pre-hardening load yielding satisfactory agreement with experimental results. The model can also be applied to analyze the non linear damage accumulation behavior of two-level fatigue tests.

A continuum damage mechanics model for low-cycle fatigue failure of metals

A continuum damage mechanics model for low-cycle fatigue is presented. The rupture time of hot rolled type RS50 steel is predicted by the damage model and compared with those measured with excellent agreement. It is shown that the proposed damage model can predict the rupture time of material more reasonably when stress variation is infinitesimal, or when the stress ratio R approaches unity.

A damage mechanics model of fatigue crack initiation in notched plates

A damage model is proposed to characterize fatigue crack initiation in notched plates. This is accomplished by assuming a damage fracture criterion and effective instantaneous tangent moduli matrix which accounts for damage accumulation. A finite element package is used to perform the numerical analyses for an edge-notched plate specimen made of Al alloy 2024-T3 under cyclic loading of varying constant amplitudes. The estimated fatigue crack initiation life agrees satisfactorily with those determined experimentally. An important observation from the results of the proposed damage model is its ability to identify the phenomenon of stress redistribution due to material degradation in two-dimension specimens during fatigue loading.

Sequence Effects on Stochastic Fatigue of Welded Joints

The influence of small stress ranges on a recently proposed sequencedependent fatigue damage model is examined. The damage model is capable of including sequence effects by taking into account the interaction of neighboring cycles in predicting the fatigue damage accumulation. The parameters necessary for use of the damage model are obtained using a combined experimental and empirical approach. The model is modified here to ignore stress cycles below a truncation level that is consistent with the endurance limit of the specimens under constant amplitude loads. It is shown that with this modification, the damage model gives fatigue life predictions that compare very well with experimental results for a wide variety of stochastic loads. Additional experimental investigation with different specimen geometry and material is needed to further examine the validity of the proposed damage model and the extent to which the parameters needed to use this model are geometry‐ and material‐dependent.

A continuum damage mechanics model for crack initiation in mixed mode ductile fracture

This paper presents the development of a fracture criterion based on the postulation that the threshold condition of crack initiation in mixed mode ductile fracture is satisfied when the overall damage w in an element at the prospective direction of crack path reaches its critical value wc. The validity of the proposed criterion is checked by predicting the fracture loads of thin aluminium plates containing an isolated crack inclined at the angle of β=30, 45, 60 and 75 degrees and the predicted loads are compared satisfactorily with those determined experimentally. The analysis is performed based on the anisotropic model of continuum damage mechanics theory proposed earlier by the authors, thus providing additional proof of the consistency, applicability and versatility of the model. When the fracture loads of the mixed mode plates calculated using conventional fracture mechanics are compared with those determined using the proposed damage model, a maximum close to 30 percent over-estimation of the loads from the conventional approach is observed as opposed to within 7 percent discrepancy between the computed and measured fracture loads using the damage approach. The observation reveals the importance of including damage consideration in any ductile fracture analysis.

Alteration in electrical and infrared switching properties of vanadium oxides due to proton irradiation

The effects of proton irradiation on the electrical and infrared switching properties of vanadium oxides were studied. Bombardments are carried out to fluences typical of long-term space missions. Proton bombardment significantly alters semiconductor phase resistivity, infrared transmissivity, transition temperature and hysteresis width. It is concluded that amorphization, hydrogen doping, and strain-related effects are not operative in the changes observed. Vanadium and oxygen vacancies and/or interstitials remain the likely cause for these changes. Implications of these results on proposed damage models are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Energy‐Based Coupled Elastoplastic Damage Models at Finite Strains

Energy‐based continuum damage‐elastoplasticity theories at finite strains are proposed within the framework of damage mechanics. The proposed damage models are based on the effective stress concept, damage threshold loading/unloading conditions, and the multiplicative split of finite kinematics. The models are linked to the history of “damage energy release rate” within representative volumes. The elastoplastic damage constitutive theories feature a thermodynamic basis, characterization of damage, coupling of damage and plasticity, as well as an anisotropic microcrack opening/closing mechanism. Both spatial and material descriptions are discussed. A simple and efficient computational integration algorithm is also given. In particular, a three‐step operator split algorithm is developed within the present framework. A numerical experiment of a notched specimen involving damage coupled with plastic flow is presented to illustrate the capability of the proposed method.

Impact damage model for ceramic materials

The fracture process in ceramic materials upon impact loading is complex in nature. Most often, the brittle ceramic deforms inelastically due to microcracking under shock (compression) loading. At high-velocity impact, the shock generated microcracks rapidly open and extend under subsequent tension (due to the release waves from the stress-free boundaries) leading to complete pulverization of the ceramic materials. The main objective of this paper is to model the damage process in ceramics due to impact loading. A computationally oriented continuum damage-based constitutive model is considered. Several modifications incorporating strain rate and damage effects on the compressive strength have been introduced into the model. Results are presented in terms of numerical simulations of a plate-impact test configuration. Effects of the model parameters on the compressive strength and spall strength are described. The proposed damage model has been used successfully to match the measured stress history from a plate-impact experiment on AD-85 (85% aluminum oxide) ceramic target material.

On energy-based coupled elastoplastic damage theories: Constitutive modeling and computational aspects

Novel energy-based coupled elastoplastic damage theories are presented in this paper. The proposed formulation employs irreversible thermodynamics and internal state variable theory for ductile and brittle materials. At variance with Lemaitre's work on damage-elastoplasticity, the present formulation renders rational thermodynamic potential and damage energy release rate. In contrast to previous work by Simo and Ju (featuring an additive split of the stress tensor), current formulation assumes an additive split of the strain tensor. It is shown that the “strain split” damage-elastoplasticity formulation leads to more robust tangent moduli than the “stress split” formulation. The plastic flow rule and hardening law are characterized in terms of the effective quantities; viz. the effective stress space plasticity. This mechanism is both physically well-motivated and computationally efficient. Further, a fourth-order anisotropic damage mechanism is proposed for brittle materials. Rational mechanisms are also presented to account for the microcrack opening and closing operations as well as the strain-rate dependency of microcrack growth.Efficient computational algorithms for proposed elasloplaslic damage models are subsequently explored by making use of the “operator splitting” methodology. In particular, new three-step operator split algorithms are presented Application is made to a class of inviseid and rate-dependent cap-damage models for concrete and mortar. Experimental validations are also given to illustrate the applicability of the proposed damage models.

Seismic damage assessment and basis for damage-limiting design

A seismic damage model is developed for reinforced concrete structures in which the structural damage is expressed as a linear combination of the maximum deformation and the hysteretic energy dissipation. From an extensive damage analysis of various reinforced concrete buildings, an intensity scale is derived to describe the potential destructiveness of ground motion. It is a simple function of the rms acceleration and strong-motion duration. The proposed damage model is calibrated with observed building damages from past earthquakes. On this basis, a design procedure is developed accordingly to limit the potential structural damage to a tolerable level.

Mechanistic Seismic Damage Model for Reinforced Concrete

A model for evaluating structural damage in reinforced concrete structures under earthquake ground motions is proposed. Damage is expressed as a linear function of the maximum deformation and the effect of repeated cyclic loading. Available static (monotonic) and dynamic (cyclic) test data were analyzed to evaluate the statistics of the appropriate parameters of the proposed damage model. The uncertainty in the ultimate structural capacity was also examined.