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Creep behavior of sandstone under the coupling action of stress and pore water pressure using three-dimensional digital image correlation 利用三维数字图像相关技术研究应力与孔隙水压力耦合作用下砂岩的蠕变行为
2区 工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2023-11-03 DOI: 10.1177/10567895231209838
Cancan Chen, Heping Xie, Jiang Xu, Shoujian Peng, Cunbao Li, Minghui Li
Understanding the damage evolution and time-dependent property of rock creep is of great significance for predicting geohazards and evaluating the long-term stability of geotechnical structures. In this study, a three-dimensional digital image correlation system was adopted to investigate the creep behavior of sandstone under the coupling action of stress and pore water pressure. The apparent strain fields, deformation characteristics of the localization zone, and micromorphology of the fracture surface were analyzed. The results demonstrated that when the applied deviatoric stress level was above σ ci (crack initial stress) or σ cd (crack damage stress), the increase in pore water pressure promoted creep deformation evidently, improved the creep rate significantly and shortened the time-to-failure of the rock obviously. In the radial strain field, the localized development of substantial microcracks on the rock surface was concentrated in the steady-state creep, while the microcracks interconnected to form macroscopic shear cracks that dominated the accelerating creep, and this damage evolution characteristic can be used as a precursor and early warning of rock creep failure. Besides, increasing the pore water pressure also would cause the divergence point of strain curves inside and outside the localization zone to appear earlier at the secondary creep, and produce a wider localization zone at the tertiary creep. The creep fracture surface of the rock was dominated by intergranular microcracks. Increasing the pore water pressure would result in the deterioration of the cemented structure and breakage of the cemented matrix more seriously, thus stimulating the generation of more microcracks.
了解岩石蠕变的损伤演化和随时间变化的特性,对于预测地质灾害和评价岩土结构的长期稳定性具有重要意义。本文采用三维数字图像相关系统,研究了砂岩在应力和孔隙水压力耦合作用下的蠕变行为。分析了断口局部化区的视应变场、变形特征和断口表面的微观形貌。结果表明:当施加偏应力水平大于σ ci(裂纹初始应力)或σ cd(裂纹损伤应力)时,孔隙水压力的增加明显促进了岩石的蠕变变形,显著提高了岩石的蠕变速率,明显缩短了岩石的破坏时间;在径向应变场中,岩石表面大量微裂纹的局部发育集中在稳态蠕变中,而微裂纹相互联结形成宏观剪切裂纹以加速蠕变为主,这种损伤演化特征可作为岩石蠕变破坏的前兆和预警。此外,孔隙水压力的增大也会使二次蠕变局部化区内外应变曲线的发散点出现得更早,三级蠕变局部化区出现得更宽。岩石蠕变断口以晶间微裂纹为主。孔隙水压力的增加会导致胶结结构的恶化和胶结基体的破坏更加严重,从而刺激更多微裂纹的产生。
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引用次数: 0
Blast response and damage assessment of reinforced concrete slabs using convolutional neural networks 基于卷积神经网络的钢筋混凝土板爆炸响应与损伤评估
2区 工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2023-10-26 DOI: 10.1177/10567895231204640
Bilal Ahmed, Taehyo Park, Jong-Su Jeon
Concrete structures are essential for shelters, storage, transportation, and defense systems. However, they are vulnerable to terrorist attacks and explosions. The most exposed component of these structures is the reinforced concrete slab, which is also the primary force-transferring member. Therefore, the present study utilizes machine learning techniques to predict the maximum vertical displacement of reinforced concrete slabs subjected to air-blast loading. This can be achieved using 11 input parameters of the slab and TNT blast to predict the maximum displacement. The dataset comprises 146 samples from various experimental and numerical blast studies on reinforced concrete slabs in the open literature. Rather than presenting the data in a tabular format, each individual data sample is transformed into an image using distinct techniques: one uses a self-similarity matrix, and the other utilizes an image generator for the tabular data. Image generation transforms tabular data into images by assigning features to pixel positions. This results in spatial dependency of the input features. Using these images, various convolutional neural networks were adopted (ResNet-18, ResNet-50, ResNet-101, EfficentNet-b0, ShuffleNet, Xception, DarkNet-53, and DenseNet-20) and trained to predict the slab maximum displacement. Most models demonstrated promising results. The performance of the models was predicted based on the root mean squared error, mean absolute error, and coefficient of determination, and the impact of input features on the maximum displacement was examined. Along with this, the initial study of the blast damage assessment on reinforced concrete slabs is explained for future work to be performed based on the proposed method.
混凝土结构是必不可少的庇护所,储存,运输和防御系统。然而,他们很容易受到恐怖袭击和爆炸。这些结构中暴露最多的构件是钢筋混凝土板,它也是主要的传力构件。因此,本研究利用机器学习技术来预测受空气爆炸荷载作用下钢筋混凝土板的最大垂直位移。利用板坯和TNT炸药的11个输入参数来预测最大位移。该数据集包括146个样本,来自公开文献中对钢筋混凝土板的各种实验和数值爆炸研究。不是以表格格式表示数据,而是使用不同的技术将每个单独的数据样本转换为图像:一个使用自相似矩阵,另一个使用表格数据的图像生成器。图像生成通过为像素位置分配特征将表格数据转换为图像。这导致了输入特征的空间依赖性。利用这些图像,采用各种卷积神经网络(ResNet-18、ResNet-50、ResNet-101、EfficentNet-b0、ShuffleNet、Xception、DarkNet-53和DenseNet-20)进行训练,预测板的最大位移。大多数模型都显示出令人鼓舞的结果。基于均方根误差、平均绝对误差和决定系数对模型的性能进行了预测,并考察了输入特征对最大位移的影响。同时,对钢筋混凝土板爆炸损伤评估的初步研究进行了说明,为今后基于本文提出的方法开展的工作奠定基础。
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引用次数: 0
A novel meso-damage constitutive model of rock under true triaxial stress with three-dimensional cracking strength, threshold and closure effect 考虑三维开裂强度、阈值和闭合效应的真三轴应力下岩石细观损伤本构模型
2区 工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2023-10-17 DOI: 10.1177/10567895231204631
Zhi Zheng, Jiaju Zhou, Junhong Li, Honghui Tao, Xiaofeng Han, Hongyu Xu, Qiang Zhang
Deep underground engineering is in a true three-dimensional stress state, and the adjustment of the three-dimensional stress state caused by engineering excavation will induce the fracture or even instability of the surrounding rock. However, three-dimensional mechanical model research suitable for the stability analysis of deep surrounding rock is very scarce. Therefore, a series of tests under different true triaxial stresses on two rocks (rhyodacite and marble) were conducted, and the characteristic strength (crack stable propagation initiation stress, crack unstable propagation initiation stress and peak strength) and deformation characteristics were further analyzed. After that, using the Lemaitre strain equivalence hypothesis and rock statistical damage theory, a new statistical damage constitutive model at true triaxial stress states was proposed, which introduced the three-dimensional strength criterion Modified Wiebols Cook to characterize the three-dimensional strength of the rock microelement. Therefore, the intermediate principal stress can be reasonably considered. The damage threshold, initial compaction effect and residual strength of the rock microelement at different true triaxial stress conditions were also considered. Then the relationships between the proposed model parameters and σ 2 and σ 3 were analyzed. Furthermore, sensitivity analysis of the influence of parameters m and F 0 in proposed model on the shape of rock stress–strain curve and peak strength was also investigated. The comparison between the results predicted by proposed model and the experimental data shows that the new model established in this study can well simulate the prepeak and postpeak deformation characteristics of rock and the intermediate principal stress effect under true triaxial stress conditions.
深部地下工程处于真正的三维应力状态,工程开挖引起的三维应力状态的调整会诱发围岩断裂甚至失稳。然而,适合于深部围岩稳定性分析的三维力学模型研究非常匮乏。因此,对两种岩石(流纹石和大理岩)进行了不同真三轴应力下的一系列试验,并进一步分析了特征强度(裂纹稳定扩展起裂应力、裂纹不稳定扩展起裂应力和峰值强度)和变形特征。然后,利用Lemaitre应变等效假设和岩石统计损伤理论,提出了真三轴应力状态下的统计损伤本构模型,该模型引入了修正Wiebols Cook三维强度准则来表征岩石微单元的三维强度。因此,可以合理考虑中间主应力。同时考虑了不同真三轴应力条件下岩石微单元的损伤阈值、初始压实效应和残余强度。然后分析了模型参数与σ 2和σ 3的关系。此外,还对模型中参数m和f0对岩石应力-应变曲线形状和峰值强度的影响进行了敏感性分析。模型预测结果与试验数据的对比表明,所建立的新模型能较好地模拟真三轴应力条件下岩石峰前、峰后变形特征及中间主应力效应。
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引用次数: 0
A coda wave interferometry to characterize and evaluate the powder debonding damage of solid propellant: Experimental investigation and discrete element simulation 用尾波干涉法表征和评价固体推进剂粉末脱粘损伤:实验研究与离散元模拟
2区 工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2023-09-15 DOI: 10.1177/10567895231199482
Yu Pan, Deze Yang, Wenzhong Qu, Xihua Chu
The debonding of solid filler powder and binder matrix is the main form of damage for composite solid propellant. This study proposes a coda wave interference (CWI) analysis method to quantitatively characterize and evaluate the internal powder debonding damage of composite solid propellant by experiment and discrete element simulation. In order to verify the validity of numerical simulation, the discrete element method (DEM) samples to simulate the powder debonding damage of solid propellant are established, and the DEM simulation and micro-CT scanning experiment are carried out. The micro-experimental and DEM results prove the efficiency and accuracy of DEM samples in modeling the damage behaviors of solid propellant specimens. Furthermore, in order to quantitatively characterize and evaluate powder debonding damage of solid propellant, using CWI method to analyze the damage states of solid propellants in the experiment and DEM simulation of tension. Two coda evaluation parameters based on different damage states are proposed, and the relationship curves of coda evaluation parameters and tensile strain are obtained. Though the analysis of the curve results of experiment and DEM simulation, the validity of CWI is demonstrated. The coda evaluation parameters can quantitatively identify and judge the accumulation process of initial damage, the appearance of micro holes and the failure point of propellant.
固体填料粉与粘结剂基体的脱粘是复合固体推进剂的主要破坏形式。本文提出了一种尾波干涉(CWI)分析方法,通过实验和离散元模拟对复合固体推进剂内部粉末脱粘损伤进行定量表征和评价。为了验证数值模拟的有效性,建立了模拟固体推进剂粉末脱粘损伤的离散元法(DEM)样本,并进行了DEM模拟和微ct扫描实验。微观实验和数值模拟结果证明了数值模拟方法在模拟固体推进剂损伤行为方面的有效性和准确性。此外,为了定量表征和评价固体推进剂的粉末脱粘损伤,采用CWI方法对实验中固体推进剂的损伤状态进行了分析,并对张力进行了DEM模拟。提出了两种基于不同损伤状态的尾轴评价参数,得到了尾轴评价参数与拉伸应变的关系曲线。通过对实验曲线结果和DEM模拟结果的分析,验证了CWI的有效性。尾数评价参数可以定量地识别和判断初始损伤的积累过程、微孔的出现以及推进剂的失效点。
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引用次数: 0
Modeling temperature dependence of tensile fracture strength for rocks considering phase transition and the direct effect of thermal damage 考虑相变和热损伤直接影响的岩石抗拉断裂强度温度依赖性模型
2区 工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2023-09-12 DOI: 10.1177/10567895231196263
Ziyuan Zhao, Jianzuo Ma, Shifeng Zheng, Haibo Kou, Jun Qiu, Weiguo Li, Fangjie Zheng, Siyuan Lang
Accurately and conveniently acquiring the tensile fracture strength of rocks at different temperatures is vital no matter for the security or economical design of deep underground engineering projects. Extensive testing in the laboratory, assisted with fitting approaches, is the main method to obtain the high-temperature tensile fracture strength in the available literature. However, the high-temperature destruction test is difficult to conduct and requires numerous time and resources. In this work, considering the main physical mechanisms such as phase transition and thermal damage that affect the tensile fracture strength of rocks at high temperatures, theoretical models for predicting their temperature-dependent tensile fracture strength (TDTFS) are established based on the Force-Heat Equivalence Energy Density Principle. The presented models achieve great prediction on the different variation trends of tensile strength below and above the phase transition temperature, as well as the corresponding sudden change of strength. For rocks without phase transition, the presented model only needs some physical parameters tested at room temperature can get a good prediction capacity on the TDTFS. Moreover, a new theoretical characterization model of the equivalent thermal damage parameter was presented and take a comparison with the previous model. Finally, the potential applications and limitations of the TDTFS model are further discussed. The application threshold of the presented TDTFS models is relatively low, and they may therefore be suitable as a method for providing a rapid and preliminary evaluation of strength at a large temperature range for rock engineering.
准确、方便地获取岩石在不同温度下的抗拉断裂强度,对于深部地下工程的安全设计和经济设计至关重要。在现有文献中,在实验室中进行大量的测试,并辅以拟合方法,是获得高温拉伸断裂强度的主要方法。然而,高温破坏试验很难进行,需要大量的时间和资源。本文考虑了影响岩石高温拉伸断裂强度的相变和热损伤等主要物理机制,基于力-热等效能量密度原理建立了岩石高温相关拉伸断裂强度(TDTFS)理论模型。所提出的模型对相变温度以下和以上的拉伸强度变化趋势以及相应的强度突变有较好的预测效果。对于没有相变的岩石,该模型只需要在室温下测试一些物理参数,就可以获得较好的TDTFS预测能力。提出了一种新的等效热损伤参数理论表征模型,并与已有模型进行了比较。最后,进一步讨论了TDTFS模型的潜在应用和局限性。所提出的TDTFS模型的应用门槛较低,因此可以作为一种快速、初步评估岩石工程大温度范围强度的方法。
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引用次数: 0
A resilience assessment framework for microencapsulated self-healing cementitious composites based on a micromechanical damage-healing model 基于微力学损伤-愈合模型的微囊化自愈胶凝复合材料弹性评估框架
2区 工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2023-09-11 DOI: 10.1177/10567895231197237
Kaihang Han, Jiann-Wen Woody Ju, Chengping Zhang, Dong Su, Hongzhi Cui, Xing-Tao Lin, Xiangsheng Chen
In this paper, a resilience assessment framework for microencapsulated self-healing cementitious composites is proposed based on a micromechanical damage-healing model. A 3D micromechanical analytical model is constructed to analyze the performance evolution during the damage-healing process of self-healing concrete. The resilience assessment of microencapsulated self-healing concrete is defined by virtue of the residual stiffness, self-healing effect on stiffness and damage cumulative on stiffness, which corresponds to three main features of resilience; namely, the robustness, recoverability and adaptability. The assessment results indicate that the release of healing agents within microcapsules and healing process of extended microcracks allows the microencapsulated self-healing concrete to have higher resilience than conventional concrete. Moreover, a parameter sensitivity analysis is conducted to investigate the influence of the healing efficiency, the applied initial damage and the fracture toughness of the repaired microcrack on resilience of microencapsulated self-healing concrete. The results indicate that higher healing efficiency and applied initial damage leads to high resilience, and fracture toughness of the repaired microcrack makes less difference to the results. The findings of this paper lay a theoretical foundation for the resilience design of self-healing material layer of underground structures.
基于微力学损伤-愈合模型,提出了微囊化自愈胶凝复合材料的弹性评估框架。建立了三维细观力学分析模型,分析了自愈混凝土损伤-愈合过程中的性能演变过程。微囊化自愈混凝土的回弹性评价是根据剩余刚度、自愈对刚度的影响和损伤累积对刚度的影响来定义的,对应于回弹性的三个主要特征;即鲁棒性、可恢复性和适应性。评价结果表明,微胶囊内愈合剂的释放和扩展微裂缝的愈合过程使得微胶囊化自愈混凝土具有比常规混凝土更高的回弹性。通过参数敏感性分析,研究了修复后微裂纹的修复效率、外加初始损伤和断裂韧性对微囊化自愈混凝土回弹的影响。结果表明,较高的修复效率和施加的初始损伤导致修复后的微裂纹具有较高的回弹率,修复后微裂纹的断裂韧性对修复结果影响较小。研究结果为地下结构自愈材料层的回弹设计奠定了理论基础。
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引用次数: 0
Seepage-stress combined experiment and damage model of rock in different loading and unloading paths 不同加卸载路径下岩石渗流-应力组合试验及损伤模型
IF 4.2 2区 工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2023-09-05 DOI: 10.1177/10567895231193056
Zhi Zheng, Hongyu Xu, Wei Wang, Qiang Zhang, Yujie Wang, Qiancheng Sun, Honghui Tao, Xiaofeng Han
In the excavation of water-related underground projects such as hydropower and energy reserves, the surrounding rock surfers complex stress path and stress state redistribution, resulting in damage and failure under the hydro-mechanical coupling condition. However, the rock hydro-mechanical coupling characteristics under complex stress paths are unclear and corresponding theoretical models are scarce. In this study, a series of tests such as triaxial compression, unloading confining pressure and cyclic loading and unloading were carried out to study the effects of different stress paths, stress levels and seepage pressure on rock deformation, strength, failure and permeability. Based on test results, the damage evolutions under three different testing paths were analyzed, a new seepage-stress coupling statistical damage model which can better simulate the compaction stage is proposed. The prediction results of the proposed model under different stress paths are in good agreement with the experimental results. Under different stress paths, the fitting relationship between parameters R0 and n and σeff is similar and has good correlation.
在水电、能源储备等与水有关的地下工程开挖中,围岩在水-力耦合条件下产生复杂的应力路径和应力状态重分布,造成破坏破坏。然而,复杂应力路径下岩石的水-力耦合特性尚不清楚,相应的理论模型也很少。本研究通过三轴压缩、卸载围压、循环加卸载等一系列试验,研究了不同应力路径、应力水平和渗流压力对岩石变形、强度、破坏和渗透率的影响。在试验结果的基础上,分析了三种不同试验路径下的损伤演化规律,提出了一种能更好地模拟压实阶段的渗流-应力耦合统计损伤模型。该模型在不同应力路径下的预测结果与实验结果吻合较好。在不同应力路径下,参数R0、n与σeff的拟合关系相似,具有较好的相关性。
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引用次数: 0
An entropy-based failure prediction model for the creep process 基于熵的蠕变过程失效预测模型
IF 4.2 2区 工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2023-09-04 DOI: 10.1177/10567895231194654
Zohreh Shirazi, Bijan Mohammadi
The creep process is a life-limiting degradation mechanism for many parts. Consequently, it should have been considered throughout the design process. This study aimed to assess the creep curve of Inconel 718 by designing a fixed blade profile. The finite element model has been done using ABAQUS software. The temperature distribution of the vane was calculated to assess the thermal stress on the vane. For temperature analysis, the film subroutine code was written. The creep life prediction model was evaluated using creep subroutine. This model included an entropy model based on the Boltzmann theory and continuum damage mechanics. Stress and temperature were applied at a range from 100 to 900 MPa and from 620 to 800°C, respectively. Finally, an accumulation damage parameter was computed. In this investigation, all three parts of the creep curve can be achieved simultaneously. There was good agreement between the simulations performed on a vane based on this method and the samples studied in previous research.
蠕变过程对许多零件来说是一种限制寿命的退化机制。因此,在整个设计过程中都应该考虑到这一点。本研究旨在通过设计固定叶片型线来评估Inconel 718的蠕变曲线。利用ABAQUS软件建立了有限元模型。计算叶片的温度分布,以评估叶片上的热应力。对于温度分析,编写了薄膜子程序代码。利用蠕变子程序对蠕变寿命预测模型进行了评估。该模型包括基于玻尔兹曼理论和连续损伤力学的熵模型。施加的应力和温度分别为100 ~ 900 MPa和620 ~ 800℃。最后,计算了累积损伤参数。在本研究中,蠕变曲线的三个部分可以同时得到。基于该方法的叶片模拟结果与以往的研究结果吻合较好。
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引用次数: 0
An encoder-decoder model with embedded attention-mechanism for efficient meshfree prediction of slope failure 一种具有嵌入式注意机制的编码器-解码器模型,用于边坡破坏的有效无网格预测
IF 4.2 2区 工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2023-09-01 DOI: 10.1177/10567895231193053
Jun Chen, Dongdong Wang, Like Deng, Jijun Ying
The particle-based meshfree methods provide an effective means for large deformation simulation of the slope failure. Despite the advances of various efficient meshfree algorithmic developments, the computational efficiency still limits the application of meshfree methods for practical problems. This study aims at accelerating the meshfree prediction of the slope failure through introducing an encoder-decoder model, which is particularly enhanced by the attention-mechanism. The encoder-decoder model is designed to capture the long sequence character of meshfree slope failure analysis. The discretization flexibility of meshfree methods offers an easy match between the meshfree particles and machine learning samples and thus the resulting surrogate model for meshfree slope failure prediction has a quite wide applicability. In the meantime, the embedding of the attention-mechanism into the encoder-decoder neural network not only enables a significant reduction of the number of meshfree model parameters, but also maintains the key features of meshfree simulation and effectively alleviates the information dilution issue. It is shown that the proposed encoder-decoder model with embedded attention mechanism gives a more favorable prediction on the meshfree slope failure simulation in comparison to the general encoder-decoder formalism.
基于颗粒的无网格方法为边坡破坏的大变形模拟提供了有效手段。尽管各种高效的无网格算法取得了进展,但计算效率仍然限制了无网格方法在实际问题中的应用。本研究旨在通过引入一种编码器-解码器模型来加速边坡失稳的无网格预测,该模型特别得到了注意机制的增强。为了捕捉无网格边坡破坏分析的长序列特征,设计了编码器-解码器模型。无网格方法的离散化灵活性使得无网格粒子与机器学习样本之间的匹配更加容易,由此得到的替代模型对于无网格边坡破坏预测具有相当广泛的适用性。同时,将注意机制嵌入到编码器-解码器神经网络中,不仅可以显著减少无网格模型参数的数量,而且保持了无网格仿真的关键特征,有效缓解了信息稀释问题。结果表明,与一般的编码器-解码器形式相比,该嵌入注意机制的编码器-解码器模型对无网格边坡破坏模拟具有更好的预测效果。
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引用次数: 0
Theory and methods of constructing equations for the evolutionary damageability of materials 材料演化损伤性方程的理论与方法
IF 4.2 2区 工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2023-08-01 DOI: 10.1177/10567895231191149
V. Fedorov
The theory and methods for constructing equations (functions) of evolutionary damage and rupture of materials in the Kachanov model (creep rupture and fatigue rupture) are presented. In general, it is proved that the factorized Kachanov model is identical to the Palmgren-Miner rule, which is often not confirmed experimentally. To construct damageability functions adequate to the experimental data, new mathematical objects (potential and normalized potential) are introduced. If the entire history of changes in the damage variable is known in experiments, then the use of the potential makes it possible to construct a damageability function of any complexity without integrating the evolutionary equation (explicit method). For cases where only rupture moments are recorded in experiments, a criterion for the adequacy of the normalized potential is formulated and an implicit method for its construction is developed. It is supplemented with a recursive algorithm that generates an unlimited number of such potentials. The implicit method is illustrated by examples, following which the reader can construct a damageability equation for his material without a thorough study of the theory.
介绍了在Kachanov模型(蠕变断裂和疲劳断裂)中构造材料演化损伤和断裂方程(函数)的理论和方法。通常,已经证明了因子化的Kachanov模型与Palmgren-Miner规则是相同的,这通常没有得到实验的证实。为了构造适合实验数据的损伤函数,引入了新的数学对象(势和归一化势)。如果损伤变量的整个变化历史在实验中是已知的,那么使用势能可以在不集成进化方程的情况下构建任何复杂度的损伤函数(显式方法)。对于在实验中只记录断裂力矩的情况,制定了归一化电势充分性的标准,并开发了其构造的隐式方法。它补充了一个递归算法,可以生成无限数量的这种势。通过实例说明了隐式方法,读者可以在不深入研究该理论的情况下,为其材料构建一个可损伤性方程。
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引用次数: 0
期刊
International Journal of Damage Mechanics
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