Computer Methods in Applied Mechanics and Engineering最新文献_第8页

A quadrilateral plate-type finite element to model stress singularities in no-tension materials 模拟无张力材料应力奇点的四边形板型有限元

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-09 DOI: 10.1016/j.cma.2024.117433

The assessment of masonry constructions and, in general, of only-compression structures requires accurate modelling of stress patterns activated by external loads and boundary settlements. To this aim, previous research introduced the continuous Airy-based stress singularities (CASS) method, a convex optimisation strategy that selects the solution of the boundary value problem in the space of admissible Airy-based stress states. In this sense, the stress tensor solution is evaluated as the curvature of the Airy stress potential. However, the CASS application range was limited to only rectangular elements.

This paper reformulates the CASS method to analyse domains with curved geometries, thus enabling the modelling of curved structures largely present in architectural heritage. Specifically, a novel approach to evaluating curvature in non-rectangular finite elements is introduced. Several benchmarks are proposed to validate the novel computational approach. First, the numerical strategy is validated against analytical solutions on a masonry panel subjected to lateral loads. In particular, the method’s accuracy is assessed by comparing the regular and irregular finite elements. After that, the method is benchmarked on a semicircular arch against well-known solutions represented by the minimum and maximum thrust conditions and the minimum thickness problem. Finally, its robustness and potential are showcased in a real case study represented by the church of Santa Maria Immacolatella della Pietà dei Turchini in Naples, Italy.

对砌体结构以及一般的纯压缩结构进行评估，需要对外部荷载和边界沉降引起的应力模式进行精确建模。为此，先前的研究引入了连续艾里应力奇异点（CASS）方法，这是一种凸优化策略，可在可接受的艾里应力状态空间中选择边界值问题的解决方案。从这个意义上说，应力张量解被评估为 Airy 应力势的曲率。然而，CASS 的应用范围仅限于矩形元素。本文对 CASS 方法进行了重构，以分析具有曲线几何形状的域，从而能够对建筑遗产中大量存在的曲线结构进行建模。具体而言，本文介绍了一种在非矩形有限元中评估曲率的新方法。为验证新颖的计算方法，提出了几个基准。首先，在承受侧向荷载的砌体面板上，根据分析解决方案对数值策略进行了验证。特别是，通过比较规则和不规则有限元，评估了该方法的准确性。之后，该方法在半圆拱上与最小和最大推力条件以及最小厚度问题所代表的著名解决方案进行了基准比较。最后，以意大利那不勒斯的 Santa Maria Immacolatella della Pietà dei Turchini 教堂为代表的实际案例研究展示了该方法的稳健性和潜力。

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引用次数: 0

Boosting crayfish algorithm based on halton adaptive quadratic interpolation and piecewise neighborhood for complex optimization problems 基于 halton 自适应二次插值和片断邻域的提升小龙虾算法，用于复杂优化问题

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-09 DOI: 10.1016/j.cma.2024.117429

The Crayfish Optimization Algorithm (CFish) is an innovative meta-heuristic approach that draws inspiration from the movements and behaviors of crayfish. CFish exhibits strong performance across many test sets and optimization issues, but it faces challenges with sluggish convergence, an uneven distribution between exploration and exploitation, and inadequate accuracy due to high-dimensional tasks. To tackle these concerns, this study presents an evolved version named QICFish, which integrates multiple sophisticated strategies to optimize performance. The CFish algorithm improves its population initialization by using the Halton sequence, resulting in a substantial enhancement of the exploration phase and an increase in population variety. Furthermore, the implementation of the adaptive quadratic interpolation approach enhances the algorithm's capacity to exploit its surroundings by eliminating individuals of worse quality and expediting the creation of solutions of superior quality. Furthermore, an adaptive mutation method is employed to improve the process of exploration and effectively locate more favorable areas inside the search space. Finally, the adaptive piecewise neighborhood strategy, enhances the pace of convergence and maintains a balanced transition between exploration and exploitation. Then, QICFish outperforms other cutting-edge algorithms across several dimensions of the CEC’17 and CEC’20 test sets, as shown by experimental comparisons. Furthermore, the efficacy and feasibility of the solution are confirmed by successfully addressing six intricate engineering problems and two truss topology optimization problems. The simulation findings demonstrate that QICFish exhibits robust competitive capabilities and shows great potential for engineering optimization challenges. Therefore, QICFish is a very efficient meta-heuristic approach for solving engineering optimization problems.

小龙虾优化算法（CFish）是一种创新的元启发式方法，它从小龙虾的动作和行为中汲取灵感。CFish 在许多测试集和优化问题上都表现出很强的性能，但它也面临着收敛缓慢、探索和利用之间分配不均以及高维任务导致精度不足等挑战。为了解决这些问题，本研究提出了一种名为 QICFish 的进化版本，它集成了多种复杂策略来优化性能。CFish 算法通过使用 Halton 序列改进了种群初始化，从而大大加强了探索阶段，并增加了种群的多样性。此外，自适应二次插值方法的实施通过淘汰质量较差的个体和加速创建质量上乘的解决方案，增强了算法对周围环境的利用能力。此外，还采用了自适应突变方法来改进探索过程，并有效地在搜索空间内找到更有利的区域。最后，自适应分片邻域策略提高了收敛速度，并保持了探索和利用之间的平衡过渡。通过实验比较，QICFish 在 CEC'17 和 CEC'20 测试集的多个维度上都优于其他前沿算法。此外，通过成功解决六个复杂的工程问题和两个桁架拓扑优化问题，证实了该解决方案的有效性和可行性。仿真结果表明，QICFish 具有强大的竞争能力，在应对工程优化挑战方面具有巨大潜力。因此，QICFish 是解决工程优化问题的一种非常有效的元启发式方法。

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引用次数: 0

A novel active learning method based on matrix-operation RBF model for high-dimensional reliability analysis 基于矩阵运算 RBF 模型的新型主动学习法，用于高维可靠性分析

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-08 DOI: 10.1016/j.cma.2024.117434

In order to deal with high dimensional reliability analysis, an active learning method based on matrix-operation radial basis function (RBF) model is proposed in this paper. To accomplish active learning, the predicted mean and standard deviation of the RBF model need to be obtained with the help of leave-one-out cross validation (LOOCV). When dealing with high dimensional problems, by LOOCV, the calculation of RBF matrix between candidate points and the training points, and the prediction of the sub-models at candidate points will be very time-consuming. Therefore, in this paper, we propose a matrix-operation method for RBF matrix calculation and a matrix-operation method for sub-model prediction. Such a matrix-operation RBF model significantly reduces the computation time of LOOCV and makes active learning mechanism possible. On this basis, we propose a novel learning function according to the prediction information of RBF model. In addition, the error-monitor mechanism is introduced to timely terminate the learning process. Four high-dimensional complex examples are investigated to verify the performance of the proposed method.

为了处理高维可靠性分析，本文提出了一种基于矩阵运算径向基函数（RBF）模型的主动学习方法。为了实现主动学习，需要借助留空交叉验证（LOOCV）来获得 RBF 模型的预测均值和标准偏差。在处理高维问题时，通过 LOOCV 计算候选点与训练点之间的 RBF 矩阵以及候选点的子模型预测将非常耗时。因此，本文提出了一种矩阵操作 RBF 矩阵计算方法和矩阵操作子模型预测方法。这种矩阵运算 RBF 模型大大减少了 LOOCV 的计算时间，并使主动学习机制成为可能。在此基础上，我们根据 RBF 模型的预测信息提出了一种新的学习函数。此外，我们还引入了错误监测机制来及时终止学习过程。通过对四个高维复杂示例的研究，验证了所提方法的性能。

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引用次数: 0

Variational Bayesian surrogate modelling with application to robust design optimisation 变异贝叶斯代用建模在稳健设计优化中的应用

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-08 DOI: 10.1016/j.cma.2024.117423

Surrogate models provide a quick-to-evaluate approximation to complex computational models and are essential for multi-query problems like design optimisation. The inputs of current deterministic computational models are usually high-dimensional and uncertain. We consider Bayesian inference for constructing statistical surrogates with input uncertainties and intrinsic dimensionality reduction. The surrogate is trained by fitting to data obtained from a deterministic computational model. The assumed prior probability density of the surrogate is a Gaussian process. We determine the respective posterior probability density and parameters of the posited statistical model using variational Bayes. The non-Gaussian posterior is approximated by a Gaussian trial density with free variational parameters and the discrepancy between them is measured using the Kullback–Leibler (KL) divergence. We employ the stochastic gradient method to compute the variational parameters and other statistical model parameters by minimising the KL divergence. We demonstrate the accuracy and versatility of the proposed reduced dimension variational Gaussian process (RDVGP) surrogate on illustrative and robust structural optimisation problems where cost functions depend on a weighted sum of the mean and standard deviation of model outputs.

代用模型为复杂的计算模型提供了可快速评估的近似值，对于设计优化等多查询问题至关重要。当前确定性计算模型的输入通常是高维和不确定的。我们考虑用贝叶斯推理来构建具有输入不确定性和内在降维的统计代用模型。通过拟合从确定性计算模型中获取的数据来训练代用模型。假设代用指标的先验概率密度是一个高斯过程。我们使用变异贝叶斯确定各自的后验概率密度和假设统计模型的参数。非高斯后验近似于带有自由变异参数的高斯试验密度，两者之间的差异用 Kullback-Leibler (KL) 分歧来衡量。我们采用随机梯度法，通过最小化 KL 分歧来计算变异参数和其他统计模型参数。我们在成本函数取决于模型输出的均值和标准偏差的加权和的示例性稳健结构优化问题上，证明了所提出的降维变分高斯过程（RDVGP）代理的准确性和多功能性。

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引用次数: 0

Adding friction to Third Medium Contact: A crystal plasticity inspired approach 为第三介质接触增加摩擦力：受晶体可塑性启发的方法

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-08 DOI: 10.1016/j.cma.2024.117412

This paper presents the first method to enable friction in the Third Medium Contact (TMC) method. TMC embeds a solid in a highly compliant medium, which becomes infinitely stiff under ultimate compression, thus allowing forces to be transferred between the solids when the medium between the solids is compressed. This approach is increasingly adopted for integrating internal contact in structural design processes, owing to its continuous, fully implicit characteristics, simplicity, and its stability when applying regularisation to the third medium regions. The lack of friction has previously restricted the use of the TMC method in simulating real-world contact conditions. Here, we address this issue by (1) integrating an anisotropic term into a Neo-Hookean material model to provide shear resistance, and (2) employing a framework inspired by crystal plasticity that includes a yield criterion specifically designed to replicate the effects of Coulomb friction.

The effectiveness of the method is demonstrated through two examples: (1) a smooth sliding contact problem and (2) a non-smooth C-shaped structure. Results demonstrate a close agreement with reference solutions obtained by a conventional Lagrange multiplier approach. While the method, for now, requires user-defined slip directions, it represents a significant advancement by enabling the integration of friction into TMC, thereby broadening its applicability to problems involving realistic frictional contact. Future research should focus on restoring the fully implicit nature of TMC in the presence of friction, and on developing automated slip direction definitions to enhance usability and expand the method’s versatility.

本文首次提出了第三介质接触法（TMC）中实现摩擦的方法。TMC 将固体嵌入高顺应性介质中，该介质在极限压缩下会变得无限坚硬，因此当固体之间的介质被压缩时，力可以在固体之间传递。由于这种方法具有连续、完全隐含、简单以及在第三介质区域应用正则化时的稳定性等特点，因此越来越多地用于在结构设计过程中整合内部接触。由于缺乏摩擦力，TMC 方法在模拟实际接触条件时受到限制。在这里，我们通过以下方法解决了这一问题：（1）将各向异性项整合到新胡克材料模型中，以提供剪切阻力；（2）采用一个受晶体塑性启发的框架，其中包括一个专门用于复制库仑摩擦效应的屈服准则：(1) 平滑滑动接触问题和 (2) 非光滑 C 形结构。结果表明，该方法与通过传统拉格朗日乘法器方法获得的参考解非常接近。虽然该方法目前还需要用户定义滑动方向，但通过将摩擦力整合到 TMC 中，它代表了一项重大进步，从而扩大了其对涉及现实摩擦接触问题的适用性。未来的研究应侧重于恢复 TMC 在存在摩擦力时的完全隐式性质，以及开发自动滑移方向定义，以提高可用性并扩展该方法的多功能性。

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引用次数: 0

An efficient mixed finite element formulation for 3D strain gradient elasticity 三维应变梯度弹性的高效混合有限元公式

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-08 DOI: 10.1016/j.cma.2024.117422

Mixed finite element formulations enable the use of simple

C^{0}

continuous interpolation functions and standard finite element meshes for the numerical solution of (nonlocal) gradient elasticity problems. Yet, so far they are faced with the challenge of being costly due to the introduction of additional mixed solution variables. Furthermore, stability is not always observed in numerical benchmark tests, often necessitating stabilization terms. Since existing formulations lack second gradients in the weak form, consistency of the corresponding Euler–Lagrange equations with the surface flux equations of the original problem is not guaranteed, which does not always enable the application of arbitrary Neumann and Dirichlet boundary conditions of first and second order limiting practical applications. Therefore, in the present contribution a formulation is proposed, which is shown to be consistent for any kind of boundary conditions by adding suitable additional surface integrals. Furthermore, by incorporating the strains instead of the displacement gradient as a mixed variable and using simple interpolation functions that enable the condensation of the Lagrange multiplier, we arrive at an element that has less degrees of freedom than e.g. a standard P3 element for local elasticity. In numerical tests, it is shown that e.g. Hermite elements do not converge already in a simple benchmark problem, whereas the proposed formulation does not lack convergence, independent from the value of the length scale. In addition to that, the proposed element is shown to lead to a significantly reduced computing time compared to competitive formulations while maintaining advantageous convergence rates.

混合有限元公式可以使用简单的 C0 连续插值函数和标准有限元网格对（非局部）梯度弹性问题进行数值求解。然而，迄今为止，由于引入了额外的混合求解变量，它们面临着成本高昂的挑战。此外，在数值基准测试中并不总能观察到稳定性，往往需要稳定项。由于现有公式缺乏弱形式的第二梯度，因此无法保证相应的欧拉-拉格朗日方程与原始问题的表面通量方程的一致性，从而无法应用限制实际应用的一阶和二阶任意诺依曼和迪里夏边界条件。因此，本文提出了一种公式，通过添加适当的附加曲面积分，证明该公式与任何类型的边界条件都是一致的。此外，通过将应变而不是位移梯度作为混合变量，并使用简单的插值函数来实现拉格朗日乘数的浓缩，我们得到了一种自由度小于局部弹性标准 P3 元素的元素。数值测试表明，在一个简单的基准问题中，Hermite 元素已经无法收敛，而所提出的计算公式并不缺乏收敛性，与长度标度值无关。此外，与其他同类公式相比，所提出的元素在保持收敛速度优势的同时，还能显著缩短计算时间。

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引用次数: 0

Data-driven prediction of extreme value distributions of finite-length random processes with application to fiber strength statistics 数据驱动的有限长度随机过程极值分布预测，应用于纤维强度统计

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-08 DOI: 10.1016/j.cma.2024.117431

The maximum and/or minimum values of random processes over a finite sample length or duration are relevant to a wide variety of engineering applications, such as the strength of fibers in which the minimum local strength dictates overall strength, or flood applications in which the maximum instantaneous water level dictates levee reliability. While extreme value distributions can be derived, or at least estimated, for random processes with known marginal probability distribution functions (PDF) and correlation function (or spectral density function), this full characterization of the underlying random process may be unavailable. Instead, one may only have information about the PDF of the maximum or minimum values of such processes for given sample length(s) or duration(s). This paper leverages a relationship between the cumulative distribution function (CDF) describing maximum/minimum values of a random process and the length or duration of the sample, in order to provide an estimate of the maximum/minimum value CDF of the process associated with one given length/duration, based solely on the data associated with other sample lengths/durations. This way, detailed information about the underlying random process is not required. The results are verified using Monte Carlo simulation, and the approach is applied to data on fiber strength.

随机过程在有限样本长度或持续时间内的最大值和/或最小值与多种工程应用相关，例如，在纤维强度应用中，最小局部强度决定了整体强度；在洪水应用中，最大瞬时水位决定了堤坝的可靠性。虽然对于具有已知边际概率分布函数（PDF）和相关函数（或频谱密度函数）的随机过程，可以推导出或至少估计出极值分布，但可能无法获得基本随机过程的完整特征。取而代之的是，对于给定的样本长度或持续时间，人们可能只能获得此类过程的最大值或最小值的 PDF 信息。本文利用描述随机过程最大/最小值的累积分布函数（CDF）与样本长度或持续时间之间的关系，仅根据与其他样本长度/持续时间相关的数据，就能估算出与一个给定长度/持续时间相关的过程的最大/最小值 CDF。这样，就不需要关于基本随机过程的详细信息了。使用蒙特卡罗模拟验证了结果，并将该方法应用于纤维强度数据。

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引用次数: 0

Intrinsically selective mass scaling with hierarchic plate formulations 采用分层平板配方的本征选择性质量缩放

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-08 DOI: 10.1016/j.cma.2024.117430

The critical time step in explicit time integration methods depends on the highest natural angular frequency of the discretized problem. For shear deformable beam, plate and shell formulations, efficiency is therefore typically limited by the highest transverse shear frequencies, which are mostly of minor importance for the structural response. Direct parametrization using transverse shear variables within hierarchic structural element formulations allows a selective scaling of transverse shear frequencies in a simple manner, while bending frequencies remain practically unaffected. In particular, the novel concept of intrinsically selective mass scaling (ISMS) results in an efficient method that features high accuracy and preserves both linear and angular momentum for both consistent and lumped mass matrices. In addition, ISMS preserves the diagonal structure of lumped mass matrices. Similar to the underlying intrinsically locking-free, hierarchic concept for shear deformable structural element formulations, ISMS retains its beneficial properties for any smooth discretization scheme. In this contribution, we extend recent research on ISMS for beam formulations to the case of shear deformable plate formulations. We test our novel concept with respect to accuracy and efficiency by means of selected numerical experiments. We study both frequency spectra and the transient behavior in explicit time integration. To demonstrate the generality of ISMS, exemplarily both isogeometric discretizations based on B-splines and meshfree discretizations using local maximum-entropy approximants are investigated.

显式时间积分法的临界时间步长取决于离散化问题的最高固有角频率。因此，对于可剪切变形的梁、板和壳的计算方法，效率通常受到最高横向剪切频率的限制，而这些频率对结构响应的重要性大多不大。在分层结构元素公式中使用横向剪切变量直接进行参数化，可以简单地选择性地缩放横向剪切频率，而弯曲频率几乎不受影响。特别是，本征选择性质量缩放（ISMS）这一新颖概念产生了一种高效方法，其特点是精度高，并能同时保留一致质量矩阵和叠加质量矩阵的线性动量和角动量。此外，ISMS 还保留了叠加质量矩阵的对角线结构。与剪切变形结构元素公式的基本无锁定分层概念类似，ISMS 对任何平滑离散化方案都能保持其有益特性。在这篇论文中，我们将最近对梁公式 ISMS 的研究扩展到剪切变形板公式。我们通过选定的数值实验来检验我们的新概念的准确性和效率。我们研究了频率谱和显式时间积分中的瞬态行为。为了证明 ISMS 的通用性，我们对基于 B-样条线的等距离散和使用局部最大熵近似值的无网格离散进行了研究。

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引用次数: 0

Enabling large-scale and high-precision fluid simulations on near-term quantum computers 在近期量子计算机上实现大规模高精度流体模拟

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-04 DOI: 10.1016/j.cma.2024.117428

Quantum computational fluid dynamics (QCFD) offers a promising alternative to classical computational fluid dynamics (CFD) by leveraging quantum algorithms for higher efficiency. This paper introduces a comprehensive QCFD method, including an iterative method “Iterative-QLS” that suppresses error in quantum linear solver, and a subspace method to scale the solution to a larger size. We implement our method on a superconducting quantum computer, demonstrating successful simulations of steady Poiseuille flow and unsteady acoustic wave propagation. The Poiseuille flow simulation achieved a relative error of less than 0.2%, and the unsteady acoustic wave simulation solved a 5043-dimensional matrix. We emphasize the utilization of the quantum–classical hybrid approach in applications of near-term quantum computers. By adapting to quantum hardware constraints and offering scalable solutions for large-scale CFD problems, our method paves the way for practical applications of near-term quantum computers in computational science.

量子计算流体动力学（QCFD）利用量子算法提高效率，为经典计算流体动力学（CFD）提供了一种前景广阔的替代方法。本文介绍了一种全面的 QCFD 方法，包括一种可抑制量子线性求解器误差的迭代法 "迭代-QLS"，以及一种可将求解扩展到更大尺寸的子空间法。我们在超导量子计算机上实现了我们的方法，成功地模拟了稳定的普伊塞耶流和非稳态声波传播。Poiseuille流模拟的相对误差小于0.2%，非稳态声波模拟求解了5043维矩阵。我们强调在近期量子计算机的应用中利用量子-经典混合方法。通过适应量子硬件限制并为大规模 CFD 问题提供可扩展的解决方案，我们的方法为近期量子计算机在计算科学领域的实际应用铺平了道路。

引用次数: 0

Stress triaxiality and Lode angle parameters driven phase field coupled finite deformation plasticity formulation of ductile fracture 韧性断裂的应力三轴性和洛德角参数驱动相场耦合有限变形塑性配方

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-03 DOI: 10.1016/j.cma.2024.117435

The effect of stress triaxiality and Lode angle parameters on crack initiation and propagation is investigated using the phase field coupled elasto-plasticity formulation. To accomplish this, a multi-invariants, i.e., first invariant of stress tensor and second and third invariants of deviatoric stress tensor, dependent finite deformation hyperelasto-plasticity is coupled with phase field theory of ductile fracture. The novel ideas include a proposition of a phase field coupled multi-invariants dependent yield function by including the Hosford equivalent stress in the Drucker–Prager yield function in order to accurately predict the ductile response of the material prior to initiation of the failure and the postulation of the threshold energy in the phase field evolution equation defining a measure of the ductility of materials. The measure of ductility is reported in the form of damage initiation surface in terms of threshold plastic energy as a function of stress triaxiality and normalized Lode angle parameters using the Mohr–Coulomb fracture initiation criterion. The model parameters are calibrated based on the available experimental results in the literature considering the stress triaxiality and Lode angle parameters dependent responses of different specimens. The crack initiation and propagation paths predicted by the proposed model under the different states of stress triaxiality and Lode angle parameters, such as axisymmetric tension, plane strain condition, and axisymmetric compression, match with those predicted experimentally in the literature.

采用相场耦合弹塑性公式研究了应力三轴性和洛德角参数对裂纹产生和扩展的影响。为了实现这一目标，将依赖于有限变形超弹性塑性的多变量（即应力张量的第一变量和偏差应力张量的第二和第三变量）与韧性断裂相场理论相结合。新颖的观点包括通过在德鲁克-普拉格屈服函数中加入霍斯福德等效应力，提出了相场耦合多变量依赖屈服函数，以准确预测材料在失效开始前的延性响应，并在相场演化方程中假设了阈值能量，定义了材料延性的量度。延展性的衡量标准是以阈值塑性能作为应力三轴性和归一化洛德角参数的函数，采用莫尔-库仑断裂起始准则，以损伤起始面的形式报告的。考虑到不同试样的应力三轴度和 Lode 角参数相关响应，根据文献中现有的实验结果对模型参数进行了校准。在轴对称拉伸、平面应变条件和轴对称压缩等应力三轴性和 Lode 角参数的不同状态下，所建模型预测的裂纹起始和扩展路径与文献中的实验预测结果相吻合。

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引用次数: 0