International Journal of Damage Mechanics

Wang, Susheng; Ding, Changdong; Zhang, Qiang; Zhang, Jiuchang; Shen, Wanqing

doi: 10.1177/10567895261432394pmid: N/A

In underground rock engineering, the three-dimensional (3D) stress state governs the time-dependent behavior of surrounding rocks, thereby directly affecting the long-term safety and stability of engineering structures. This study presents a novel true triaxial time-dependent constitutive model that characterizes nonlinear creep behavior governed by coupling of viscoplastic deformation and time-dependent damage. The model advances the 3D Hoek-Brown yield function by incorporating the azimuthal orientation of cracks. The coupled model is implemented using a numerical procedure that features an explicit nonlinear integration algorithm for updating the time-dependent damage factor. The model's effectiveness is validated by its accurate prediction of true triaxial creep test results for Jinping marble. The comprehensive constitutive model advances continuum damage mechanics, providing a scientific basis for analyzing and evaluating the long-term safety and stability of deep hard rock engineering.

Wu, Luyuan; Wang, Haoran; Ma, Dan

doi: 10.1177/10567895261443173pmid: N/A

Rock materials exhibit complex mechanical responses due to their heterogeneity and anisotropy, while traditional stress–strain models can only partially describe their behaviour and encounter limitations in handling complex nonlinear relationships. This study proposes a multi-model stacking fusion framework integrating random forest, LightGBM, and Extreme Gradient Boosting with Bayesian optimisation for stress–strain relationship prediction across five rock failure stages. The Stacking ensemble framework relies on the noise resistance of random forest to address overfitting and integrates the advantages of Extreme Gradient Boosting and LightGBM in capturing complex feature interactions, effectively overcoming the poor generalisation of single models. A dual-validation scheme (five-fold out-of-fold cross-validation combined with an independent validation set) was employed to generate unbiased meta-features and robustly assess model generalisation. Selected meta-learners (linear model, Lasso, and ridge) further integrate these base learner outputs to more precisely capture the complex relationships of rock mechanical behaviour. The proposed framework was trained and validated using a dataset comprising over 218,000 data samples collected from sandstone and mudstone samples from the Yuanzigou coal mine. Taylor-diagram analysis demonstrated the Stacking ensemble framework's superior robustness and improved generalisation. The Stacking-Lasso hybrid model demonstrates outstanding predictive performance of stress–strain relationship with R2 of 0.942 (pre-peak) and 0.931 (post-peak), alongside mean absolute error of 0.0128/0.0565, mean squared error of 2.54 × 10−4/5.0 × 10−3, mean absolute percentage error of 0.051, and root mean square deviation of 0.0138/0.0707 in pre- and post-peak regimes, respectively. SHapley Additive exPlanations feature importance analysis reveals that axial stress (σz) and confining pressure (σx/y) constitute the most dominant features controlling rock mechanical behaviour. Additionally, a visual interactive tool for the Stacking ensemble is developed based on PyQt, enabling data upload, model training and result visualisation. This study confirms the framework as an innovative, reliable reference for advancing digital and intelligent rock mechanics modelling.

Guo, Junbin; Wang, Han; Wu, Liwei; Yu, Chuanqiang; Hou, Shuai

doi: 10.1177/10567895261440846pmid: N/A

To investigate the ricochet phenomenon and failure characteristics for PMMA (Polymethyl-methacrylate) plates subjected to oblique penetration, an improved peridynamic contact model is proposed in this study. The proposed model incorporates the dynamic friction coefficient and shank friction force, complemented by a hybrid contact search strategy that combines grid search and KD-tree methods to enhance computational efficiency. To validate the model and approach, numerical simulations for the oblique impact tests on PMMA are conducted, where the peridynamic results have a satisfactory agreement with the corresponding experimental data. The ricochet phenomenon is accurately reproduced in the peridynamic simulations, underscoring that the proposed model and approach have the capability to effectively capture the intricate failure characteristics in PMMA under oblique penetration. Additionally, a systematic analysis is performed to investigate the influence of critical parameters, including the incidence angle, initial velocity, and attack angle, on the overall oblique penetration performance. These findings highlight the robustness and practical applicability of the proposed model and approach in predicting and analyzing intricate failure responses in PMMA under dynamic loading conditions.

Meng, Li; Lee, Hsiao Wei; Ashkpour, Alireza; Iqbal, Mohammad Irfan; Sales, Christopher M; Farnam, Yaghoob (Amir); Hubler, Mija H; Najafi, Ahmad R

doi: 10.1177/10567895261444787pmid: N/A

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 https://github.com/MCMB-Lab/StrengthBasedPhaseFieldModel.

Cheng, Aiping; Wu, Haonan; Huang, Shibing; Silupumbwe, Seth; Xie, Sihang; Ye, Zuyang

doi: 10.1177/10567895261427807pmid: N/A

With the increasing application of cemented ultrafine tailing filling method, the research on mechanical properties of cemented ultra-fine tailings backfill (CUTB) is becoming increasingly significant. The constitutive model and brittle–ductile index evaluation of CUTB as important components of mechanical properties have a significant impact on the safety and stability of backfill mining area. In this article, two indicators of the initial damage coefficient caused by different binders and the strain damage coefficient caused by different curing ages were proposed to construct the damage constitutive model considering initial damage and strain damage effect. Combined with the proposed damage constitutive model of CUTB and existed brittle–ductile index of rock, an improved brittle–ductile index of CUTB was presented. Finally, the proposed damage constitutive model and improved brittle–ductile index of CUTB was verified and discussed. The results show that (1) the different binders have a significant initial damage effect on CUTB. The initial damage of OPC-CUTB was increased with the increase in curing age, while the initial damage of WSB-CUTB was declined with the increase in curing age. (2) The different binders have a significant strain damage effect on CUTB. The strain damage of WSB-CUTB was increased with the increase in curing age, while the strain damage of OPC-CUTB was decreased with the increase in curing age. (3) The improved brittle–ductile index can well reflect the initial damage and strain damage effect of CUTB with different binders. The WSB-CUTB is more brittle than OPC-CUTB. (4) The proposed damage constitutive model and improved brittle–ductile index can fully characterize the mechanical properties of CUTB with different binders. The research results provided important theoretical guidance and had an essential engineering significance for mine safety mining.

Young, Colin J.; Rayaprolu, Sreekar; Subbarayan, Ganesh

doi: 10.1177/10567895261454730pmid: N/A

In this work, we performed extensive high-cycle fatigue testing of AS7GU-T64 cast aluminum alloy, which is primarily used as cylinder heads in automobiles, under load-controlled, axial tension–compression to understand its damage evolution. We begin with a small-strain finite deformation theory to derive a nonlinear constitutive relation. This relationship is shown to be a fourth-degree expression and not a general power series. The constitutive relations are then used to develop a damage metric, which captures the asymmetry in tension–compression responses. The metric measures the damage as a ratio of nonlinear to linear terms in a stress–strain behavior, signifying the deviation from linearity to nonlinearity. The cyclic loading–unloading response is measured through a least squares fit to the data. The measured fatigue data is demonstrated to very effectively capture the evolving damage prior to catastrophic fracture. Finally, we present the postfailure analysis of the fractured samples.

Wu, Jian-Ying

doi: 10.1177/10567895261429154pmid: N/A

We address in this work unified analysis of phase-field models for cohesive fracture in order to alleviate the difficulty in selecting proper models and for further improvement. Aiming to regularize the Barenblatt's cohesive zone model, all the discussed models are distinguished by three characteristic functions, that is, the geometric function dictating the crack profile, the degradation function for the constitutive relation and the dissipation function defining the crack driving force. The latter two functions coincide in the associated formulation, while in the non-associated one they are designed to be different. Distinct from the counterpart for brittle fracture, in the phase-field model for cohesive fracture the regularization length parameter has to be properly incorporated into the dissipation and/or degradation functions such that the failure strength and traction–separation softening curve are both well-defined. Moreover, the resulting crack bandwidth needs to be non-decreasing during failure in order that imposition of the crack irreversibility condition does not affect the anticipated traction–separation law (TSL). With a truncated degradation function that is proportional to the length parameter, the Conti-Focardi-Iurlano model and the latter improved versions can deal with crack nucleation only in the vanishing limit and capture cohesive fracture only with a particular TSL. Owing to a length scale dependent degradation function of rational fraction, these deficiencies are largely overcome in the phase-field cohesive zone model (PF-CZM). Among many variants in the literature, only with the optimal geometric function, can the associated PF-CZM apply to general non-concave softening laws and the non-associated PF-CZM to (almost) any arbitrary one. Some mis-interpretations are clarified and representative benchmarks are presented.

Li, Dong; Wang, Ziqian; Zhang, Renbo; Jin, Liu; Du, Xiuli

doi: 10.1177/10567895261448792pmid: N/A

To better study the mesoscopic mechanical behavior of fiber-reinforced recycled aggregate concrete, an efficient modeling method of a three-dimensional mesoscopic numerical model is proposed. For mesoscopic composition, based on the traditional concrete structure of “aggregate-ITZ-mortar,” recycled aggregate is further subdivided into “aggregate core-old ITZ-old mortar” to accurately characterize its heterogeneous nature. For random placement of aggregates and fibers, corresponding random placement methods are established according to their respective geometric characteristics. This ensures uniform and random distribution of aggregates and fibers in three-dimensional space. For mesh generation and property assignment of the concrete matrix, a mapping rule based on geometric inclusion relationships is established. It efficiently assigns complex mesoscopic component properties to homogeneous background mesh elements, solving the problem of property allocation for multiphase materials. Subsequently, a corresponding numerical model is established with reference to real specimens in physical tests, and a uniaxial compression simulation is carried out. It is found that under the same load conditions as physical tests, the failure mode and stress–strain curve of the numerical model established by this method are largely consistent with the actual situation. Finally, the influence of recycled aggregate replacement ratio on the compressive performance of specimens is studied through numerical simulation. The results show that with the increase of recycled aggregate replacement ratio, the compressive strength of specimens decreases continuously. After adding 1% steel fibers to the specimens, their strength and ductility increase compared with before, but the strength still decreases with the increase of recycled aggregate replacement ratio.

Zhang, Yiming; Ren, Xiaodan

doi: 10.1177/10567895261449620pmid: N/A

In this study, a plastic damage constitutive model for ultra-high performance concrete (UHPC) is developed to facilitate the nonlinear analysis and performance assessment of UHPC structures. Based on the principles of irreversible thermodynamics and internal variable theory, the model systematically integrates plasticity and damage within a unified energy framework. The explicit form of the elastoplastic Helmholtz free energy potential is derived, and the damage energy release rate, defined as the thermodynamic conjugate to the damage variable, is introduced as the driving force for damage evolution. Uniaxial cyclic tests are employed to establish the evolution criteria of the internal variables under uniaxial stress states. Furthermore, the concept of energy equivalent strain is introduced to bridge the theoretical gap between uniaxial and multiaxial constitutive models, enabling the formulation of evolution criteria for internal variables under general multiaxial stress conditions. Finally, the applicability and accuracy of the proposed constitutive model are validated through a series of material tests and structural member experiments. The results demonstrate that the proposed model accurately captures the development of plastic deformation and the process of damage evolution in UHPC, providing a reliable theoretical foundation for the nonlinear analysis of UHPC structures.

Liu, Zhicheng; Yang, Sihui; Peng, Songlin; Li, Bochuan

doi: 10.1177/10567895261440161pmid: N/A

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.