International Journal of Damage Mechanics最新文献

{"title":"Microstructure-sensitive damage in dual-phase Ti-5553 alloy: Effects of stress state and α/β interfacial mechanics","authors":"M. Amir Siddiq, Giribaskar Sivaswamy, Salaheddin Rahimi, Brad Wynne","doi":"10.1177/10567895261453717","DOIUrl":"https://doi.org/10.1177/10567895261453717","url":null,"abstract":"This study presents a comprehensive microstructure-sensitive investigation of deformation and failure in dual-phase Ti-5Al-5Mo-5V-3Cr (Ti-5553) alloy using crystal plasticity finite element methods coupled with experimental characterisation. Material parameters governing elastic–plastic behaviour and damage evolution (void nucleation, growth, and coalescence) were calibrated via inverse modelling using stress–strain data and EBSD-informed microstructures from heat-treated samples. Representative volume elements systematically capture realistic <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" overflow=\"scroll\"> <mml:mi>α</mml:mi> <mml:mo>/</mml:mo> <mml:mi>β</mml:mi> </mml:math> </jats:inline-formula> morphologies, including embedded, grain boundary, triple junction, and elongated grain configurations. Simulations explore how stress triaxiality ( <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" overflow=\"scroll\"> <mml:mi>X</mml:mi> </mml:math> </jats:inline-formula> = 1/3 to 3), Lode parameter ( <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" overflow=\"scroll\"> <mml:mi>L</mml:mi> </mml:math> </jats:inline-formula> = −1 to 1), Burgers orientation relationship (BOR) variants, crystal orientation, <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" overflow=\"scroll\"> <mml:mi>α</mml:mi> </mml:math> </jats:inline-formula> phase volume fraction, and phase-boundary geometry govern slip localisation and damage evolution. Key findings reveal stress-state dependent optimal microstructural parameters: (1) at moderate triaxiality ( <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" overflow=\"scroll\"> <mml:mi>X</mml:mi> </mml:math> </jats:inline-formula> = 1/3), <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" overflow=\"scroll\"> <mml:mi>α</mml:mi> </mml:math> </jats:inline-formula> volume fractions near 10% suppress strain localisation and delay damage onset; (2) under elevated triaxiality ( <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" overflow=\"scroll\"> <mml:mi>X</mml:mi> </mml:math> </jats:inline-formula> = 1), lower <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" overflow=\"scroll\"> <mml:mi>α</mml:mi> </mml:math> </jats:inline-formula> fractions (∼5%) become more damage-resistant; (3) crystallographic compatibility across <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" overflow=\"scroll\"> <mml:mi>α</mml:mi> <mml:mo>/</mml:mo> <mml:mi>β</mml:mi> </mml:math> </jats:inline-formula> interfaces, determined by BOR variant selection and boundary orientation, directly controls interfacial stress concentrations and void nucleation sites; (4) orientati","PeriodicalId":13837,"journal":{"name":"International Journal of Damage Mechanics","volume":"62 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2026-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148287366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigation of the shear behavior and microscopic damage constitutive modeling of sulfate saline soils during the freeze–thaw process","authors":"Jian Liu, Laigui Wang, Han Gao, Huabin Zhang, Guochao Zhao, Hewan Li","doi":"10.1177/10567895261454729","DOIUrl":"https://doi.org/10.1177/10567895261454729","url":null,"abstract":"Influenced by the climatic conditions of seasonally frozen regions, sulfate saline soils exhibit salt expansion, frost heave, thaw settlement, and dissolution-induced collapse, which can cause severe damage to engineering structures. These failures are closely associated with the deterioration of macroscopic mechanical properties and the damage evolution of the soil microstructure. To investigate the mechanical response and damage characteristics of sulfate saline soils during the complete freeze–thaw process, macroscopic direct shear tests and microscopic scanning electron microscopy observations were conducted on sulfate saline soils with a salt content of 2% at several temperature points throughout the process. The results indicate that during the freeze–thaw process, the shear strength of sulfate saline soil first increases and then decreases. Correspondingly, the shear stress–shear displacement curves initially evolve from an ideal plastic or strain-weak hardening state to a strain-softening state and subsequently return to an ideal plastic or strain-weak hardening state. Further analysis reveals that sulfate primarily influences the degree of soil damage through crystallization–dissolution processes and by altering the critical temperature and intensity of the water–ice phase transition. In addition, the fractal-based microscopic statistical damage constitutive model can effectively characterize the shear stress–shear displacement behavior and the damage deterioration mechanism of sulfate saline soils during the freeze–thaw process. The findings provide a theoretical basis and useful reference for agricultural planning and engineering construction in sulfate saline soil regions.","PeriodicalId":13837,"journal":{"name":"International Journal of Damage Mechanics","volume":"72 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2026-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148287367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cracks dynamic propagation and permeability jump characteristics of gas-bearing coal–rock combinations under different strain rates","authors":"Bowen Dong, Dengke Wang, Jun Deng, Wenrui Li, Furu Kang, Shixing Fan, Weiyong Lu, Yanzhao Wei, Hongquan Zhou, Yuling Xia, Xiuzhu Yuan, Tanggen Cao, Fu Chen","doi":"10.1177/10567895261453718","DOIUrl":"https://doi.org/10.1177/10567895261453718","url":null,"abstract":"Crack propagation in gas-bearing coal–rock bodies under dynamic disturbance plays a crucial role in coal mine safety. Impact-induced damage can significantly alter the permeability of coal–rock strata, thereby increasing the risk of gas-related hazards. In this article, the dynamic crack propagation and permeability jump characteristics of gas-bearing coal–rock combinations under different strain rate loading conditions were systematically investigated. Triaxial dynamic compression experiments were conducted to obtain the stress–strain responses and permeability evolution patterns of the samples. Further analysis of the failure modes and crack types of the coal–rock combination was conducted using industrial computed tomography scanning equipment, and the three-dimensional crack network was reconstructed. On this basis, a fractal seepage model was developed by integrating the pore network modeling approach. And the intrinsic mechanism underlying the permeability jump in gas-bearing coal–rock combinations is clarified. The results indicate that the dynamic stress–strain curve of coal–rock combinations exhibits dual linear elastic characteristics and elastoplastic instability behavior. The dynamic mechanical response of coal–rock combinations demonstrates pronounced strain-rate dependence. The cracks in the coal–rock combination are induced by compressive-shear failure, tensile-strain failure, and unloading failure, respectively. The crack propagation and failure extent in coal–rock combinations become increasingly severe with rising strain rates. The continuously increasing crack spatial complexity directly leads to a permeability jump. Relative to quasi-static compression failure, the coal–rock combination subjected to dynamic compression failure exhibits gas seepage hysteresis prior to the permeability jump.","PeriodicalId":13837,"journal":{"name":"International Journal of Damage Mechanics","volume":"25 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2026-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148287365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A two-step damage model for analysis of recycled aggregate concrete beam on foundation: Displacement-based approach","authors":"Worathep Sae-Long, Suchart Limkatanyu, Piti Sukontasukkul, Tanakorn Phoo-ngernkham, Suraparb Keawsawasvong, Chanachai Thongchom, Nattapong Damrongwiriyanupap, Rut Su, Amorn Pimanmas","doi":"10.1177/10567895261452506","DOIUrl":"https://doi.org/10.1177/10567895261452506","url":null,"abstract":"This study presents a damage-inclusive analytical framework for the static bending analysis of recycled aggregate concrete (RAC) beams resting on elastic foundations. The principal contribution is not the rederivation of the previously published two-step RAC constitutive model itself, but its integration into new displacement-based beam-foundation formulations that enable a structural-level assessment of damage-informed stiffness degradation under different foundation idealizations. Three RAC homogenization schemes, namely the Voigt (parallel), Reuss (series), and generalized self-consistent models, are combined with Kerr-type, Winkler–Pasternak, and Winkler foundations within the Euler–Bernoulli beam framework. The governing differential equations, boundary conditions, and closed-form analytical solutions are derived assuming small deformations and linear, homogeneous, isotropic effective behavior. Parametric studies are then conducted to evaluate the effects of constituent volume fractions, foundation parameters, and foundation model type on beam deflection. The results show that increasing the recycled concrete aggregate content increases beam deflection, whereas increasing the natural coarse aggregate and cement paste contents reduces it. Increasing the shear-layer stiffness and subgrade stiffness decreases beam deflection, while the generalized self-consistent model consistently predicts responses between the Voigt and Reuss bounds. For the parameter range considered, the Kerr-type foundation yields the largest deflections among the three foundation idealizations. The proposed framework provides a useful analytical benchmark for serviceability-oriented assessment and preliminary design of RAC members supported by deformable media, such as ground beams, strip/slab-on-ground elements, sleepers, and pavement-related substructures.","PeriodicalId":13837,"journal":{"name":"International Journal of Damage Mechanics","volume":"15 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2026-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148289814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Key effects and selections of model parameters in a strength-based phase field model and applications","authors":"Li Meng, Hsiao Wei Lee, Alireza Ashkpour, Mohammad Irfan Iqbal, Christopher M Sales, Yaghoob (Amir) Farnam, Mija H Hubler, Ahmad R Najafi","doi":"10.1177/10567895261444787","DOIUrl":"https://doi.org/10.1177/10567895261444787","url":null,"abstract":"Conventional phase field models are widely used to simulate brittle fracture, but cannot independently control fracture strength beyond uniaxial tension. To address this limitation, strength-based phase field formulations that incorporate prescribed strength surfaces have been proposed. However, most existing studies primarily emphasize the role of the strength surface in fracture initiation, while the resulting constitutive response and its dependence on model parameters remain insufficiently examined. In this work, a systematic investigation of the key model parameters (i.e. length scale, scaling factor, degradation function, and a newly introduced compression enhancement factor) is conducted through homogeneous solutions and parametric analyses. The results reveal that improper selection or inconsistent coupling of these parameters can lead to physically incorrect strength surfaces and constitutive laws. In particular, an inappropriate parameter combination may cause the predicted strength surface in the biaxial tension region to shrink toward the origin, implying an artificial reduction of admissible stress states. Moreover, when the compression enhancement factor is set to 1, the formulation degenerates to the revisited model used in publications, in which the compressive stress does not decrease after the peak stress, contradicting the typical softening response observed in brittle materials. By varying the compression enhancement factor, the strength surface can be tuned from a cone-like critical shape to an ellipsoid-like envelope, enabling flexible calibration to different material behaviors. The numerical results demonstrate that a combined examination of both the strength surface and the constitutive law is essential for ensuring physically admissible predictions of fracture initiation and propagation. The source code is available at <jats:ext-link xmlns:xlink=\"http://www.w3.org/1999/xlink\" ext-link-type=\"uri\" xlink:href=\"https://github.com/MCMB-Lab/StrengthBasedPhaseFieldModel\">https://github.com/MCMB-Lab/StrengthBasedPhaseFieldModel</jats:ext-link> .","PeriodicalId":13837,"journal":{"name":"International Journal of Damage Mechanics","volume":"151 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2026-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147751749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling of the instantaneous subsurface damage mechanism of vibration cutting GH4169 based on strain gradient","authors":"Yihang Fan, Hang Xue, Zhaopeng Hao, Gangwei Cui","doi":"10.1177/10567895261443798","DOIUrl":"https://doi.org/10.1177/10567895261443798","url":null,"abstract":"Nickel-based superalloy GH4169 is widely used in key aircraft engine components due to its excellent thermal strength, stability, and fatigue resistance. However, it is difficult to machine, and ultrasonic vibration cutting is often employed to improve its processability. Sub-surface damage induced during cutting can significantly compromise the fatigue life and reliability of the workpiece. Considering the scale-dependent deformation mechanisms and dislocation behavior in materials, this paper develops an instantaneous sub-surface damage depth prediction model for vibration cutting of nickel-based superalloys based on strain gradient theory. A strain gradient-enhanced constitutive equation for vibration cutting is established with cutting time <jats:italic toggle=\"yes\">t</jats:italic> as the independent variable. By analyzing real-time cutting force and cutting heat, the coupled effect on sub-surface damage within each vibration cycle is investigated. The von Mises yield criterion is applied, and MATLAB is used to predict instantaneous damage depth. The variation of damage depth with cutting time <jats:italic toggle=\"yes\">t</jats:italic> is studied, along with its underlying mechanisms. Results show that the maximum instantaneous damage depth occurs when the instantaneous cutting depth peaks. Experimental validation confirms good agreement between predicted and measured damage depths. The key contribution of this work is an instantaneous damage depth prediction model for elliptical vibration machining of GH4169, incorporating strain gradient theory. This model enables the determination of damage depth at different cutting instants, offering insight into damage evolution within each vibration cycle.","PeriodicalId":13837,"journal":{"name":"International Journal of Damage Mechanics","volume":"4 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2026-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147751751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A novel fatigue life prediction approach of a GH4169 superalloy-welded joint based on a physics-informed machine learning method","authors":"Zhicheng Liu, Sihui Yang, Songlin Peng, Bochuan Li","doi":"10.1177/10567895261440161","DOIUrl":"https://doi.org/10.1177/10567895261440161","url":null,"abstract":"Defects were usually inevitable during welding process, the equivalent size of the maximum initial welded defects that perpendicular to the loading direction was usually introduced as the initial crack, whereas, the influence of morphology feature of the defects could not be well considered, and the fatigue life prediction issue of welded joint was usually challengeable according to the dispersion of the morphology, size, location, and quantity of the welding defects. Therefore, a physics-informed machine learning approach was constructed in order to captured the action mechanism of morphology features of welding defects in this study, the introduction of the additional physics information not only extended the initial training datasets, but also enhanced the interpretability of the lifetime prediction results, influence of the morphology detail of the defects was well considered through a modified physics fatigue prediction model. The final fatigue life prediction results revealed that physics-informed long short-term memory network approach was the best one compared with physics-informed convolutional neural network and the physics-informed random forest method, which exhibited the highest coefficient of determination and the most robust generalization ability.","PeriodicalId":13837,"journal":{"name":"International Journal of Damage Mechanics","volume":"4 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147739659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Molecular dynamics simulation of deformation and failure in magnesium bicrystals containing preexisting voids","authors":"Tian Liang, Yongting Lan, Changrui Ke, Songtao Zhu, Mingyang Liang","doi":"10.1177/10567895261441286","DOIUrl":"https://doi.org/10.1177/10567895261441286","url":null,"abstract":"Magnesium and its alloys have broad application prospects due to their lightweight and high specific strength. However, their hexagonal close-packed crystal structure results in poor room-temperature ductility and low damage tolerance, which are critical bottlenecks limiting engineering applications. In actual magnesium crystals, initial defects such as micropores are commonly present. Yet the coupling effects between such defects and grain boundaries (GBs) on plastic deformation evolution and failure mechanisms at the atomic scale remain insufficiently understood. This study employs molecular dynamics simulations to construct magnesium bicrystal models with a preset void. The deformation and failure responses under uniaxial tension are systematically examined for five distinct GB angles, namely 14.52°, 34.54°, 53.14°, 71.74°, and 90° asymmetric boundary. The synergistic regulatory mechanisms of GB geometry and internal defects are revealed. The results demonstrate that the mechanical behavior is dominated by the GB angle. Low-angle symmetric tilt GB (14.52°) possess both high yield strength and favorable plastic stability, whereas high-angle and asymmetric GBs are prone to inducing stress concentration. Voids act as stress concentrators and interact differently with various GBs to regulate dislocation evolution, twin nucleation, and crack initiation. Particularly, the special GB angle of 53.14° can effectively retard crack propagation via twinning. This study elucidates the interaction mechanisms between GBs and preexisting defects at the atomic scale, revealing the dual role of voids as stress concentrators at the early deformation stage and damage nucleation sites during plastic deformation. The findings provide a theoretical foundation for GB engineering design and damage tolerance optimization of magnesium alloys.","PeriodicalId":13837,"journal":{"name":"International Journal of Damage Mechanics","volume":"20 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2026-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147733632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cross-scale prediction of macroscale viscoelasticity and fatigue of asphalt mixtures from meso-scale material compositions","authors":"Li’an Shen, Juntao Wang, Xue Luo, Yuqing Zhang","doi":"10.1177/10567895261435789","DOIUrl":"https://doi.org/10.1177/10567895261435789","url":null,"abstract":"Cross-scale prediction enhances the efficiency and reliability of performance prediction by linking macroscale performance to meso-scale material compositions. However, existing cross-scale models calibrated under specific meso-scale conditions can only predict macroscale viscoelastic responses at the same conditions, limiting extensibility across materials and load conditions. The cross-scale prediction of macroscale viscoelastic fatigue based on meso-scale coefficients remains insufficiently explored. This study aims to address this transferability issue within the investigated domain and predict asphalt mixtures’ viscoelastic and fatigue performance at the macroscale from meso-scale material compositions. First, uniaxial compressive dynamic modulus tests were conducted on asphalt mortar to extract meso-scale viscoelastic parameters. Discrete element models of asphalt mixtures incorporating these parameters and realistic aggregate distributions reconstructed via digital image processing were established for two gradations (AC-16 and AC-25). The models accurately predicted macroscale dynamic moduli within the tested temperature–frequency range, with differences within 8% compared with experiments. Then, a discrete element fatigue model (DEFM) was developed by implementing a J-integral based Paris’ law to model particle-to-particle crack growth at the meso-scale. Using a single set of Paris’ law coefficients (A and n) calibrated at a specific loading condition, the model can predict fatigue life across various stress levels and loading regimes within the investigated domain. Results demonstrate that, for the studied mixtures, the Paris’ law coefficients A and n at the meso-scale are independent of stress level and frequency but depend on temperature and gradation: higher temperatures increase A and decrease n, while coarser gradation lowers A and raises n.","PeriodicalId":13837,"journal":{"name":"International Journal of Damage Mechanics","volume":"66 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147708690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Establishing rock stress–strain relationship through analysis of damage growth rate","authors":"Shaohong Li, Qiyuan Zhang, Ming Wei","doi":"10.1177/10567895261440713","DOIUrl":"https://doi.org/10.1177/10567895261440713","url":null,"abstract":"Establishing constitutive relationships that describe the deformation behaviour of rocks remains a central focus in rock mechanics. With the introduction of growth laws, adoption of distinct assumptions for the damage evolution rate under loading, and incorporation of a new parameter termed the maximum damage degree to represent the practical characteristic that the load-bearing capacity of rocks does not vanish completely with progressive deformation, three damage constitutive relations are derived, namely, linear, logarithmic and quadratic forms. The proposed models include two damage evolution parameters. These parameters can be determined analytically through closed-form expressions based on conventional mechanical properties, thereby ensuring the practicality and applicability of the models. Validation is performed using existing compression test data for granite and marble. Additionally, the effect of damage evolution parameters on the stress–strain response is examined. The results show that for identical strain conditions, the damage degree predicted by the quadratic damage constitutive relationship is greater than that obtained from the linear and logarithmic relationships in sequence. Error statistics show that the quadratic damage constitutive relationship exhibits the best performance, followed by the linear and logarithmic models. Furthermore, both the quadratic and linear relationships outperform the existing damage relationship employing the Weibull function. In the proposed models, the two damage evolution parameters respectively govern the size and shape of deformation curve. By incorporating the variation of conventional mechanical parameters with confining pressure, the proposed model can predict the deformation response of rocks under various confining pressures.","PeriodicalId":13837,"journal":{"name":"International Journal of Damage Mechanics","volume":"65 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147684503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}