Proposed Damage Model Research Articles

Compressive resistance of thin-walled pultruded GFRP profiles: The role of delamination examined through experiments and FE simulations

Significant efforts have been made in the last decades to develop design rules and guidelines for composite structures, meeting the increasing interest in pultruded glass fibre reinforced profiles (GFRP) by the construction industry. One aspect that has been difficult to address is the crushing resistance of these profiles, with previous research indicating that the design equations are not conservative, predicting much higher resistances than those obtained in experimental tests. This paper explores the possibility that crushing resistance is governed by tensile failure in the through-thickness direction of the laminates, by Poisson effect, and proposes modifications to a previously presented material damage model to account for this in finite element (FE) simulations. Compressive experimental tests were conducted in stub-column specimens, with 5 different open-section configurations, obtained from three different producers. The test results were compared to analytical and FE simulations, confirming that the former grossly overestimate the resistance, while the latter, with the proposed damage model, compare well with experimental results.

Prediction of mass adhesive damage based on the Rousselier model: Experimental and numerical analysis

The study of the mechanical strength of adhesives remains an important area of research for researchers. These adhesives must be prepared in the form of mass test pieces to characterize them under different mechanical stresses. However, during the preparation of the test pieces several defects are likely to be present, namely air bubbles, cavities, or impurities. The behavior of the adhesive differs depending on the presence of one of these defects and, in most cases, the real behavior of the adhesive is not precisely known. For this purpose, several tests are necessary to have a close estimate of the adhesive's behavior. To numerically model the behavior of the adhesive it is necessary to consider the presence of these types of defects. This paper proposes a damage criterion based on the Rousselier model, which describes the damage due to crack growth from the presence of cavities in an adhesive, assumed as a ductile material. The proposed damage model was developed and implemented in a user-defined subroutine in the ABAQUS finite element code. Other damage models integrated into ABAQUS were used. In addition, the extended finite element method (XFEM) was used in the numerical simulations to study automatic damage modelling by the appearance and propagation of cracks in highly stressed areas. The main objective of this work is an analysis by the finite element method to determine the elastoplastic behavior coupled with the damage in the mass adhesive, considering the size, position, and shape of the defect (porosities) by the proposed models. Initially, experimental tests were carried out on mass specimens of adhesive to characterize the tensile response and to determine their mechanical properties depending on the position and size of the defect, which may exist in the specimen following its fabrication. The numerical results were validated by uniaxial tensile tests on the mass adhesive. Comparisons with the damage models integrated into ABAQUS have proven their effectiveness in predicting the behavior of the adhesive in the presence of a cavity.

A novel statistical damage constitutive model of rock joints considering normal stress and joint roughness

The shear constitutive model of rock joints is of great significance to the stability analysis in rock engineering, and it is closely related to the normal stress ([Formula: see text]) and joint roughness coefficient ( JRC). However, the existing investigations seldom consider the influences of [Formula: see text] and JRC simultaneously. Therefore, a novel damage constitutive model considering the [Formula: see text] and JRC is developed in this work. In the presented model, it is assumed that the rock materials are composed of damaged and undamaged microunits, and the damage evolution law of the microunits conforms to the Weibull distribution in the shear process. Based on the proposed assumption, the constitutive relationship between shear stress and shear displacement is deduced. The evolutions of the mechanical parameters and damage variable versus [Formula: see text] and JRC are analyzed in detail. The proposed damage model that involves [Formula: see text] and JRC is verified by comparing theoretical values with the laboratory results. The results show that the damage constitutive model is in good agreement with the test results. Additionally, the influences of [Formula: see text] and JRC on the shear stress-displacement curves are studied. This work can provide a valuable theoretical method for analyzing the shear mechanical characteristics and damage evolution laws of rock joints.

A damage rock model considering shear failure by modified logistic growth theory

Localized rock failures, like cracks or shear bands, demand specific attention in modeling for solids and structures. This is due to the uncertainty of conventional continuum-based mechanical models when localized inelastic deformation has emerged. In such scenarios, as macroscopic inelastic reactions are primarily influenced by deformation and microstructural alterations within the localized area, internal variables that signify these microstructural changes should be established within this zone. Thus, localized deformation characteristics of rocks are studied here by the preset angle shear experiment. A method based on shear displacement and shear stress differences is proposed to identify the compaction, yielding, and residual points for enhancing the model's effectiveness and minimizing subjective influences. Next, a mechanical model for the localized shear band is depicted as an elasto-plastic model outlining the stress-displacement relation across both sides of the shear band. Incorporating damage theory and an elasto-plastic model, a proposed damage model is introduced to replicate shear stress-displacement responses and localized damage evolution in intact rocks experiencing shear failure. Subsequently, a novel nonlinear mathematical model based on modified logistic growth theory is proposed for depicting the shear band's damage evolution pattern. Thereafter, an innovative damage model is proposed to effectively encompass diverse rock material behaviors, including elasticity, plasticity, and softening behaviors. Ultimately, the effects of the preset angles, temperature, normal stresses and the residual shear strength are carefully discussed. This discovery enhances rock research in the proposed damage model, particularly regarding shear failure mode.

Investigation on dynamic response of thin spherical shells impacted by flat-nose projectile based on a novel damage model

Thin-shell structures are widely used in various engineering applications. It is essential to investigate the impact resistance of thin-shell structures, to provide theoretical support for engineering applications. Numerous impact tests have been conducted on thin spherical shells using ballistic guns. The effects of the impact velocity and shell thickness on the deformation and fracture of thin spherical shells are summarized. Moreover, a novel damage model based on statistic damage mechanics is proposed to better predict dynamic responses of thin shells impacted by projectiles. Considering that fracture surfaces are formed by void evolution and are affected by the stress states, the damage level is defined as the ratio of the statistical cross-sectional area of the voids to the cross-sectional area of the representative elements. Utilizing statistical methods, the incorporation of continuous void nucleation, ellipsoidal void growth, and the acceleration of dynamic void evolution are introduced into the novel damage model. Subsequently, numerical investigations of the dynamic response of spherical shells under impact are conducted based on the proposed damage model. The numerical results are consistent with the experimental results in terms of the depression deformations and strain signals. The effects of shell thickness and double-layer structures on the dynamic response of spherical shells are investigated via numerical simulations considering the novel damage model in detail. The results demonstrate that the proposed model can accurately predict the dynamic response of spherical shells impacted by flat-nose projectiles, thus serving as a valuable reference for engineering design.

A corrosion cracking mechanism-based model with molten salt corrosion damage coupling the effect of chloride impurity and plastic deformation

The corrosion kinetic models, incorporating the effects of chloride impurity and plastic deformation were proposed. Molten salt corrosion (MSC) damage was quantitatively described using the corrosion kinetic and the distance of materials points from the corrosion surface. By employing the elastic-viscoplastic theory with a hyperbolic-sine flow rule and the proposed damage model, a corrosion cracking mechanism-based model was developed and implemented using finite element (FE) analysis method. The corrosion-assisted cracking ahead of crack tips in accordance with the corrosion cracking mechanism was simulated. Furthermore, the predicted corrosion depth, corrosion morphologies, and multi-site corrosion cracking behaviors showed good agreement with the experimental results.

Strain-Based damage model for ductile tearing simulation under combined tensile and shear modes

This paper proposes a strain-based damage model to simulate ductile tearing under combined tensile and shear modes. For tensile mode, the multiaxial fracture strain model depending only on the stress triaxiality is used, determined by analysing smooth bar tensile test and fracture toughness test data. For shear mode, a simple constant fracture strain model is used, determined by analysing smooth bar torsion test and torsion fracture test using a deep surface cracked cylinder specimen. The proposed damage model is applied to simulate circumferential surface cracked pipe made of SUS 304 under combined bending and torsion. Comparison with full-scale surface cracked pipe test data suggests that the use of the combined tensile and shear damage model with the linear interaction rule gives good and conservative prediction results.

Validation of a damage constitutive model based on logistic model dedicated to the mechanical behavior of the rock

The establishment of mechanical models of rocks can provide crucial guidance to the surrounding rocks stability analysis in the rock engineering. According to statistical damage theory and Mohr–Coulomb strength criterion, the Logistic model is used to yield the damage evolution equation and further establish statistical damage constitutive model for describing the whole failure process of rocks. Then, the rationality of the proposed damage model is proved by comparing with the different test curves, and damage evolution laws are summarized into four stages, including: slow-growth stage, rapid-growth stage, constant-speed-similar growth stage and speed-reducing growth stage. Physical meanings of model parameters r′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${r}{\\prime}$$\\end{document} and m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m$$\\end{document} are also discussed. Finally, to verify the application of this proposed model, this damage constitutive model is developed and implemented to simulate the tunnel excavation and analyze the stability of surrounding rocks by using Fortran, python and Abaqus. The displacement data on site is used to prove the superiority of proposed damage constitutive model compared with the existing ones in Abaqus. The research outcomes presented in this paper can also provide useful references for the theory and application of rock mechanics.

Softening properties and damage evolution of the preloaded building sandstone after exposure to high-temperature

In practical engineering, cyclic stress caused by underground excavation, blasting or seismic waves leads to initial damage to rocks, and the high temperature caused by fire will lead to changes in the mechanical and physical parameters of the initially damaged rock. Therefore, a series of experiments were carried out to research rock properties and damage evolution of the preloading sandstone after exposure to high temperatures. The results demonstrate that the mass decreases gradually at a constant rate when the temperature ranges from 25 °C to 600 °C, but above 600 °C, the quality decreases quickly. As the exposed temperatures and stress amplitude of cyclic preloading rise, the p-wave velocity gradually decreases. At exposure temperatures of up to 800 °C, the p-wave decreases by 27.8%, and it is reduced by 0.93% at the largest pre-stressed condition. Furthermore, the peak strength and elastic modulus decrease with the rise of the preloading stress amplitude and treated temperatures. The area of hysteresis loops increases with the increase of the cyclic preloading stress amplitude, and the plastic deformation of hysteresis loops results in the continuous deterioration of the secant modulus. The preloading stress amplitude and the temperature gradually increase, and the damage factor increases. Meanwhile, to compare the performance of the proposed damage model, the constitutive damage model of the preloading treatment sandstone exposure to high temperatures is established. The model has a good fitting effect for the sandstone subjected to the thermal-mechanical effect.

On the gradient-enhanced damage model for a hyperelastic material

An approach for modeling damage in the material in a geometrically nonlinear setting is studied. We consider a gradient-enhanced damage approach where the damage variable is taken as an independent variable, and the fluxes conjugated to the damage gradient are computed. The concept of maximum dissipation is used to derive the global Kuhn–Tucker conditions. The total free energy function consists of two nonlocal terms corresponding to referential gradient of the nonlocal damage variable and a penalty term to bridge the local damage variable and the nonlocal damage variable. Based on the principle of minimum total potential energy, a coupled system of Euler–Lagrange equations is obtained and solved in weak form. These nonlinear system of equations is solved by a standard Newton–Raphson-type solution scheme. The regularization capabilities, as well as the accuracy and efficiency of the proposed damage models are demonstrated by some standard benchmark examples.

Performance enhancement of damaged RC structures with viscoelastic dampers: Damage assessment and optimal placement

Evaluating the performance degradation of the earthquake-damaged structure and optimizing the placement of dampers is important for retrofitting post-earthquake structures. In this study, a damage evolution model is developed to evaluate the degradation of strength, stiffness, and energy dissipation capacity for earthquake-damaged structures. The proposed damage model is validated using previous experimental results based on the nonlinear finite element analysis. Then, research on the optimal design of damper parameters and quantity is carried out. Considering the optimization range of earthquake-damaged structures, a genetic algorithm with multi-objective functions is developed to determine the optimal placement of viscoelastic dampers in damaged structures. The results demonstrate that the proposed damage model can effectively describe the performance degradation of damaged structures. The control effects of the acceleration response increase exhibited a maximum enhancement of 3.38 times after accounting for the optimization range of earthquake-damaged structures. The optimization results of the multi-objective function with the optimization range are better aligned with the objectives of designers.

Estimation and analysis of the cumulative energy damage model for precast concrete nonrectangular column frame structures

A detailed characterization of structural damage progress is essential to performance-based seismic design for precast concrete nonrectangular column (PCNC) frame structures. The paper presents an experimental investigation into the damage behavior of the PCNC frame structures under reverse cyclic loading, including specimens PCFS1 and PCFS2 in bay and specimen PCFS3 in depth of a new precast residential building. Based on the experimental results, the damage mechanism of the PCNC frame structures was further discussed with the cumulative energy damage model proposed in this paper, and the influence of key structural parameters on the damage of the PCNC frame structures was examined, including energy dissipation adjusted factor, the residual deformation rate and the stiffness degradation rate. Available results indicated that the experimental damage curves of test specimens increased with the loading progress and acted with nonlinear damage characteristics, and PCNC frame structural damage behavior was sensitive to the axial compression ratio. For the proposed damage model, the calculation results were in good agreement with the experimental results. On the basis, the damage degree of the PCNC frame structures was divided into five performance levels including normal use, temporary use, use after repair, life safety and prevent collapse in the defined damage range of (0, 1). Elastic layer drift ratio limit was suggested to relax for PCNC frame structures. Final test results could provide a basis for the aseismic design and damage assessment of such structures after earthquake.

Orthotropic damage model for composite structures using the 3D Tsai-Wu failure criterion

This paper presents a novel approach concerning the development of an orthotropic damage model based on the original 3D Tsai-Wu failure criterion. In its original formulation, the Tsai-Wu criterion is only capable of identifying the existence of damage at a certain point in the material. However, it is not capable of identifying if the damage is located in the fiber, matrix or interlaminar zone. This work plans to fill this gap in knowledge by providing a simple method, based on equivalent stresses and strains, that identifies the failure modes when the Tsai-Wu failure criterion is near the on-set of damage. Using this novel method, it is possible to implement classical damage evolution laws based on the formulation of Matzenmiller. The proposed damage model is implemented in the commercial finite element software ABAQUS using user-subroutine UMAT, and the numerical results are compared with experimental data obtained earlier by other authors for different applications of glass fiber reinforced polymer (GFRP) structures. The numerical stabilization is achieved by using a new implicit to explicit material time step algorithm.

Damage properties of basaltic rocks under multilevel stress loading and microwave irradiation

The deterioration of mechanical strength and damage characteristics of rock under microwave is the primary focus in evaluating the applicability of microwave-efficient rock-breaking technology. This study analyzed the mechanical strength deterioration and damage characteristics of basalt under microwave irradiation and performed an X-ray digital radiography (DR) image analysis of the damage process of basalt under a multilevel stress loading (MSL) path. The research results show that basalt with a large porosity had a better thermal effect on microwave irradiation and significantly enhanced the resistance to deterioration. The microwave thermal effect of polar minerals is critical to plastic failure behavior. This study also proposes a rock damage characteristic evaluation model based on X-ray DR image quantitative analysis and X-ray absorption dose threshold segmentation. The image analysis model can accurately describe the evolution process of rock damage characteristics. A modified model for basalt damage characteristic analysis is provided. The elastic–plastic damage model based on the Cast3M finite element software was compared with the proposed damage model based on X-ray DR images. The calculated results show that the change in the damage zone was consistent with the damage crack propagation process of basalt. Therefore, the proposed damage evaluation model can provide guidance for the scientific evaluation of the adaptability of microwave-assisted tunnel boring machine (TBM) efficient rock-breaking technology.

A progressive damage model for quasi-static tension of 2D woven composites and FEM implementation

We tested the quasi-static tension behavior of the high-strength glass fiber four-Harness stain woven composite, Kevlar fiber plain woven composite, and their laminated hybrid composite. Their representative volume element models are established based on mesoscopic cross-section photographs combined with voxel mesh. A progressive damage model for predicting the damage initiation and evolution of the 2D woven composites is proposed. The crimping effect of plain-woven composites has been considered. The 3D Hashin and the maximum stress criterion are used as the fiber yarn and matrix's damage initiation criterion, respectively. The exponential model is used as the damage evolution model of the fiber yarn. A combination of exponential and reverse tangential damage models has been proposed to describe the damage evolution of the matrix. The proposed damage model is realized using user-defined subroutine UMAT and VUMAT. Abaqus/Standard performs the uniaxial tensile simulation of the two kinds of 2D woven composites with UMAT. Abaqus/Explicit solver simulates the laminated hybrid composite with VUMAT. The simulation results highly agree with the experiment results.

A mesoscopic damage model for the low-cycle fatigue of an extruded magnesium alloy

This paper presents a novel mesoscopic damage model to characterize the low-cycle fatigue damage evolution of an extruded AZ31 magnesium (Mg) alloy, taking into account the effect of twinning. The damage caused by the slip bands (SBs)–twin boundaries (TBs) and SBs–grain boundaries (GBs) interactions is treated based on the Tanaka–Mura model and the Eshelby inclusion theory. Strain energy values at the TBs and GBs are defined as the TB and GB damage variables, respectively. Explicit formulae for the TB and GB damage evolution are derived from the characteristics of the {101¯2} extension twin and the basal texture. A fracture energy-based crack initiation criterion is established, and the proposed damage model is validated against the existing experimental results. The model demonstrates its ability to reproduce the damage evolution processes, and the predictions of the crack initiation life are within the twice error band.

Evolution law of small strain shear modulus of expansive soil: From a damage perspective

It is of great significance to study the nonlinear evolution law of the small strain shear modulus of expansive soil for analyzing the deformation behavior of soil or geotechnical structure and the seismic site response. Existing studies rarely discuss the damage mechanism of the small strain shear modulus of expansive soil, and the corresponding damage model describing the small strain stiffness decay law is lacking. In this study, a series of resonance column tests were carried out to investigate the effects of mean effective stress, loading and unloading stress paths and vibration cycles on the nonlinear decay law of small strain shear modulus of expansive soil, and the damage mechanism was discussed in detail. Subsequently, a novel damage model describing the decay law of small strain shear modulus of expansive soil was proposed and verified by the results of resonant column tests. The results show that the decay process of the small strain shear modulus with the shear strain is essentially the damage of the soil structure, which can be characterized mathematically by damage model. The mean effective stress and the larger overconsolidation ratio caused by the unloading process can inhibit the damage, while the vibration cycles can cause small reduction in small strain shear modulus and promote the damage. The proposed damage model with clear physical meaning can well describe the evolution law of small strain shear modulus of expansive soil, and has higher accuracy than the traditional model.

Unveiling the damage evolution of SAC305 during fatigue by entropy generation

Low-cycle thermal-mechanical fatigue loadings induce progressive and permanent degradation of mechanical properties of lead-free solder materials, and thus reduce the fatigue life of electronic devices. In this study, damage evolution and accumulation of Sn-3.0Ag-0.5Cu (SAC305), the most successfully commercialized lead-free solder material, was investigated by performing strain-controlled fatigue tests at different temperatures (288–373 K) and strain rates (0.001–0.004 s−1). Unlike existing empirical models, a fatigue damage model was proposed based on entropy generation related to the thermodynamic nature of fatigue damage. To be intrinsic to entropy generation, the proposed model was calibrated with the peak stress degradation at different temperatures and strain rates. Our findings showed that the damage parameter is closely related to temperature and strain rate and monotonically increases from 0 to 1 during the low-cycle fatigue loading, which unveiled the fact regarding the irreversibility of the internal entropy generation. For the first time, the damage evolution is found to be more associated with the applied strain rate than the temperature. By observations using an optical microscopy, the physical damage mechanism is elucidated for SAC305 solder by correlating microstructures and damage evolutions. The evolving dendritic β-Sn phase and the surrounding Sn-Ag-Cu ternary eutectic network also explained the effects of temperature and strain rate based on the energy dissipation. Our proposed damage model reconciled the damage accumulation of SAC305 solder subjected to the low-cycle fatigue loading, which is readily adopted to predict the fatigue life of the electronic packaging structures.

A Constitutive Model of Time-Dependent Deformation Behavior for Sandstone

Considering sandstone's heterogeneity in the mesoscale and homogeneity in the macroscale, it is very difficult to describe its time-dependent behavior under stress. The mesoscale heterogeneity can affect the initiation and propagation of cracks. Clusters of cracks have a strong influence on the formation of macroscale fractures. In order to investigate the influence of crack evolution on the formation of fractures during creep deformation, a time-dependent damage model is introduced in this paper. First, the instantaneous elastoplastic damage model of sandstone was built based on the elastoplastic theory of rock and the micro-heterogeneous characteristics of sandstone. A viscoelastic plastic creep damage model was established by combining the Nishihara model and the elastoplastic damage constitutive model. The proposed models have been validated by the results of corresponding analytical solutions. To help back up the model, some conventional constant strain rate tests and multi-step creep tests were carried out to analyze the time-dependent behavior of sandstone. The results show that the proposed damage model can not only reflect the time-dependent viscoelastic deformation characteristics of sandstone, but also provide a good fit to the viscoelastic plastic deformation characteristics of sandstone's creep behavior. The damage model can also reproduce the propagation process of mesoscopic cracks in sandstone upon the damage and failure of micro-units. This research can provide an effective tool for studying the propagation of microscopic cracks in sandstone.

A new unified creep‐plasticity constitutive model coupled with damage for viscoplastic materials subjected to fatigue loading

AbstractA new unified creep‐plasticity (UCP) constitutive model coupled with damage is proposed for Sn–3.0Ag–0.5Cu (SAC305), one of the most successfully commercialized Pb‐free solders. By calibrating the proposed damage model based on entropy generation, the fatigue issues are elucidated for SAC305 solder at different temperatures and strain rates. After implementing a user‐defined material subroutine, finite element simulations with the proposed UCP‐damage model are capable of predicting the strength deterioration as the macroscopic response in terms of load‐deformation curves. More importantly, the UCP‐damage model reveals the damage accumulation and evolution of viscoplastic materials sensitive to fatigue deformation at different temperatures and strain rates. By comparing the predictions with and without damage, the equivalent plastic strains are obviously different when evaluating the thermal cycling fatigue life of electronic packaging structures, which confirms the significance of the UCP model reasonably coupled with the intrinsic description of damage by the concept of entropy generation.