International Journal of Engineering Science最新文献_第2页

On size-dependent mechanics of Mindlin plates made of polymer networks 聚合物网络明德林板的力学尺寸依赖性

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2024-11-15 DOI: 10.1016/j.ijengsci.2024.104164

Xiao-Jian Xu , Bo Wang

The recent advances of solid mechanics of polymer networks are that they can be well-modelled by a physically-based size-dependent constitutive relation via a simplified strain gradient elasticity theory. However, boundary value problems of plate models composed of polymer networks have not been reported, which limit wide applications of the models in the engineering science. In this paper, we systematically established a variationally consistent boundary value problems of Mindlin plate models for polymer networks leading to the framework of a simplified strain gradient elasticity. This study considers the strain energy produced by the strain gradient in the thickness direction and proposes a well-posed boundary value problem for a Mindlin plate with arbitrary boundaries, discussing possible boundary conditions, especially higher-order nonconventional ones. The senses of stress resultants and double stresses acting on the face of a volume element are firstly explained. Surprisingly, it is found that unexpected corner condition related to normal derivatives of shear force, bending moment, and twisting moment exists for plates with irregular boundaries—contradicting conventional mechanics notions of plates. For illustrative purpose, static bending analyses of a simply supported rectangular plate subjected to a uniformly distributed loading and a concentrated loading are provided. The effective Young's modulus predicted by this approach agrees well with reported result in the open literature. This work may be helpful in developing efficient numerical methods and offers new insights into the existence of corner condition in Mindlin plates within the context of a simplified strain gradient elasticity theory.

聚合物网络固体力学的最新进展是，可以通过简化的应变梯度弹性理论，利用基于物理的尺寸相关构成关系对其进行良好建模。然而，由聚合物网络组成的板模型的边界值问题尚未见报道，这限制了该模型在工程科学中的广泛应用。本文在简化应变梯度弹性的框架下，系统地建立了聚合物网络 Mindlin 板模型的变异一致性边界值问题。本研究考虑了厚度方向应变梯度产生的应变能，并提出了具有任意边界的 Mindlin 板的边界值问题，讨论了可能的边界条件，尤其是高阶非常规边界条件。首先解释了作用在体积元素面上的应力结果和双重应力的含义。令人惊讶的是，研究发现不规则边界的板材存在与剪切力、弯矩和扭转力的法向导数相关的意外转角条件，这与板材的传统力学概念相悖。为了说明问题，我们对承受均匀分布荷载和集中荷载的简单支撑矩形板进行了静态弯曲分析。这种方法预测的有效杨氏模量与公开文献中报告的结果非常吻合。这项工作可能有助于开发高效的数值方法，并在简化应变梯度弹性理论的背景下为明德林板中角条件的存在提供了新的见解。

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引用次数: 0

Eshelby's inhomogeneity model within Mindlin's first strain gradient elasticity theory and its applications in composite materials Mindlin 第一应变梯度弹性理论中的 Eshelby 不均匀性模型及其在复合材料中的应用

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2024-11-13 DOI: 10.1016/j.ijengsci.2024.104167

Koami P. DADABO, Napo BONFOH, Hafid SABAR, Rodrigue MATADI-BOUMBIMBA

Eshelby's inhomogeneity problem is solved within the second form of Mindlin's first strain gradient elasticity theory for the prediction of the effective elastic properties of composites. Considering Green's function technique, an integral equation is established for an ellipsoidal inhomogeneity embedded in a homogeneous elastic medium and subjected to non-uniform boundary conditions. Within isotropic elasticity, the mean strain inside a spherical inhomogeneity is detailed to provide analytical results. In addition to the elastic properties of the inhomogeneity and the matrix, the strain localization depends on five gradient elastic constants, introduced by the first strain gradient elasticity theory. The effective bulk and shear moduli of a two-phase composite are predicted through Mori-Tanaka's scheme. The strain localization and the effective elastic moduli are then expressed within some simplified gradient elasticity theories. To test the relevance of the developed model, its predictions are compared with those of some investigations and the effective elastic properties are analyzed for a metal matrix composite. Finally, some comparisons with experimental data are performed to estimate the characteristic length scale parameters and gradient elastic constants of local phases.

Eshelby 不均匀性问题是在明德林第一应变梯度弹性理论的第二种形式下求解的，用于预测复合材料的有效弹性特性。考虑到格林函数技术，建立了嵌入均质弹性介质并受非均匀边界条件影响的椭圆形不均匀性的积分方程。在各向同性弹性中，详细说明了球形非均质体内部的平均应变，从而提供了分析结果。除了非均质体和基体的弹性特性外，应变定位还取决于第一个应变梯度弹性理论引入的五个梯度弹性常数。通过 Mori-Tanaka 方案预测了两相复合材料的有效体积模量和剪切模量。然后在一些简化的梯度弹性理论中表达应变定位和有效弹性模量。为了检验所开发模型的相关性，将其预测结果与一些研究结果进行了比较，并分析了金属基复合材料的有效弹性特性。最后，通过与实验数据进行比较，估算了局部相的特征长度尺度参数和梯度弹性常数。

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引用次数: 0

An energy-based fracture criterion for quasi-brittle crack propagation in micropolar continuum: Analytical and numerical study 微连续体中准脆性裂纹扩展的基于能量的断裂准则：分析和数值研究

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2024-11-08 DOI: 10.1016/j.ijengsci.2024.104173

Meral Tuna , Patrizia Trovalusci , Nicholas Fantuzzi

The present study provides closed-form expressions of propagation (kinking) angles by generalizing maximum energy release rate criterion in linear elastic fracture mechanics (LEFM) within micropolar theory of elasticity to address the in-plane, brittle crack propagation phenomenon in size-dependent materials with the presence of particle rotations.

The accuracy and limitations of the derived formulation is checked by manually detecting the peak point of the energy release rate (ERR) through repetitive numerical simulations performed for arbitrary orientations of infinitesimal branch crack, modelled via magnifying the corresponding region with proper boundary conditions. In both approaches (analytical and numerical), the basic fracture parameters (i.e. stress and couple-stress intensity factors at the main or infinitesimal branch tip) are attained with the aid of micropolar/extended-FEM (micropolar/XFEM) model.

Through the parametric study, performed for numerous material properties and loading conditions, it is revealed that, as non-locality increases, the variation of propagation angle with the mode mixity ratio substantially diverges from that in Cauchy continuum. It is manifested as a change in the trend of angle-mode mixity ratio curve, and dominated by the stress related intensity factors in the absence of non-singular terms for the considered example. Having a branch orientation approaching to crack’s axis with increased non-locality indicates the practical importance of resorting to non-classical theories for materials with scale effects such as particulate composites, masonry walls, rock-like assemblages, etc. following their disposition to fracture type failure. Moreover, the proposed fracture criterion enables crack propagation simulations within the framework of LEFM by integrating the formulation into a numerical method.

本研究通过将线性弹性断裂力学（LEFM）中的最大能量释放率准则概括到弹性微波理论中，提供了传播（扭结）角的闭式表达式，以解决存在颗粒旋转的尺寸依赖性材料中的面内脆性裂纹传播现象。通过手动检测能量释放率（ERR）的峰值点，对无限小分支裂纹的任意方向进行重复数值模拟，检查推导公式的准确性和局限性。在这两种方法（分析法和数值法）中，基本断裂参数（即主裂纹或无限小分支顶端的应力和耦合应力强度因子）都是借助微波/扩展有限元（micropolar/XFEM）模型获得的。这表现为角度-模态混合比曲线趋势的变化，并且在所考虑的实例中，在没有非邢格项的情况下，由应力相关强度因子主导。随着非局部性的增加，裂纹的分支方向接近裂纹轴线，这表明对于具有尺度效应的材料，如颗粒复合材料、砌体墙、类岩石组合等，在其发生断裂型破坏后，采用非经典理论具有重要的实际意义。此外，所提出的断裂准则通过将公式整合到数值方法中，可在 LEFM 框架内进行裂纹扩展模拟。

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引用次数: 0

A generalized differential scheme for the effective conductivity of percolating microinhomogeneous materials with the Hall effect 利用霍尔效应计算渗流微均质材料有效电导率的广义微分方案

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2024-11-06 DOI: 10.1016/j.ijengsci.2024.104175

Anatoly Markov , Mikhail Markov , Valery Levin

In this paper, we propose a self-consistent scheme for the calculation of the components of the effective electrical conductivity tensor. The calculations were fulfilled for a microinhomogeneous material, the components of which have the Hall effect. The presence of the Hall effect leads to appearance of asymmetry of the components of the conductivity tensor and to dependence of these components on the magnitude of the magnetic field applied to the material. Our approach is based on the Generalized Differential Effective Medium (GDEM) method. This method generalizes the classical differential scheme (DEM) for the case of several inclusion types instead of one. In this case, the GDEM scheme leads to a system of matrix differential equations that were solved numerically. This solution was obtained for materials containing spherical or cylindrical inclusions (3D and 2D-problems). In the case of cylindrical inclusions, the results were obtained for inclusions with the symmetry axes orthogonal to the magnetic field. The application of the GDEM method allows us to consider the percolation effect for 2D and 3D-microheterogeneous materials. The results obtained are compared to the experimental data and the calculation results obtained by other self-consistent schemes.

在本文中，我们提出了一种计算有效电导张量成分的自洽方案。计算是针对具有霍尔效应的微均质材料进行的。霍尔效应的存在导致电导张量的分量出现不对称性，并且这些分量取决于施加到材料上的磁场大小。我们的方法基于广义微分有效介质（GDEM）方法。该方法是对经典微分方案（DEM）的概括，适用于包含多种类型而非一种类型的情况。在这种情况下，GDEM 方案会产生一个矩阵微分方程系统，并通过数值方法求解。这种解法适用于含有球形或圆柱形夹杂物的材料（三维和二维问题）。在圆柱形夹杂物的情况下，得到的结果是对称轴与磁场正交的夹杂物。应用 GDEM 方法，我们可以考虑二维和三维微均质材料的渗滤效应。我们将所得结果与实验数据和其他自洽方案的计算结果进行了比较。

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引用次数: 0

Dilatational disk and finite cylindrical inclusion in elastic nanowire 弹性纳米线中的扩张盘和有限圆柱包涵体

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2024-11-05 DOI: 10.1016/j.ijengsci.2024.104169

Anna L. Kolesnikova , Nguyen Van Tuyen , Mikhail Yu. Gutkin , Alexey E. Romanov

For the first time, strict analytical solutions for the elastic fields and the strain energies of an infinitely thin dilatational disk (DD) and a dilatational cylindrical inclusion (CyI) of finite length coaxially embedded in an infinite elastically isotropic cylinder with free surface are given and analyzed in detail. The solutions are represented in an integral form that is suitable for further analytical use and numerical study. The screening effect of the cylinder free surface on the elastic fields and the strain energies of the DD and the CyI is discussed. It is shown that this effect is significant for both the axial displacement and stress fields when the DD and CyI radii are comparable with the cylinder radius, however it is rather weak for the DD strain energy (the energy release does not exceed ∼10%). In contrast, for the CyI strain energy, the screening effect can be very strong. It is also shown that the hydrostatic stress is inhomogeneous and exists not only inside the CyI, as is the case with this stress for inclusions in an infinite medium, but also outside it. This stress is concentrated on the free surface at the points that are closest to the CyI boundary. Inside the CyI, the hydrostatic stress is much higher in magnitude than outside it.

首次给出并详细分析了同轴嵌入具有自由表面的无限弹性各向同性圆柱体中的无限薄扩张圆盘（DD）和有限长扩张圆柱包体（CyI）的弹性场和应变能的严格解析解。解以积分形式表示，适合进一步分析和数值研究。讨论了圆柱体自由表面对 DD 和 CyI 的弹性场和应变能的屏蔽效应。研究表明，当 DD 和 CyI 的半径与圆柱体半径相当时，这种效应对轴向位移和应力场都有显著影响，但对 DD 应变能的影响较弱（能量释放不超过 ∼10%）。相反，对于 CyI 应变能，屏蔽效应可能非常强。研究还表明，静水应力是不均匀的，它不仅存在于 CyI 内部（这与无限介质中夹杂物的应力情况相同），也存在于 CyI 外部。该应力集中在自由表面上最靠近 CyI 边界的点上。在 CyI 内部，静水应力的大小远高于外部。

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引用次数: 0

On quasi-brittle static fracture analysis of micropolar plates via XFEM model 通过 XFEM 模型对微极板进行准脆性静态断裂分析

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2024-11-04 DOI: 10.1016/j.ijengsci.2024.104168

Meral Tuna , Patrizia Trovalusci , Nicholas Fantuzzi

The main objective of this study is to implement extended finite element method (XFEM) to two-dimensional (2D) micropolar structures in order to extract basic fracture parameters required in linear elastic fracture mechanics (LEFM) in a computationally efficient manner, and thus to provide basis to explore the crack propagation phenomenon within this framework. The stress and couple-stress intensity factors (SIF and CSIF) are detected with the aid of interaction integral, I-integral, and compared with the ones in the literature for validation purposes while an engineering problem of practical importance; plate with an oblique edge crack, is investigated to demonstrate the applicability of the developed methodology. The approach presents considerable simplification in modeling process owing to ability of XFEM to treat discontinuities and singularities appeared in the cracked domains, and offers a new, and different perspective to available methods (e.g. phase field method and peridynamics), each with their own advantages and limitations, extended to deal with crack and its growth in micropolar structures.

本研究的主要目的是将扩展有限元法（XFEM）应用于二维（2D）微极结构，以便以计算效率高的方式提取线性弹性断裂力学（LEFM）所需的基本断裂参数，从而为在此框架内探索裂纹扩展现象提供基础。借助交互积分（I-integral）检测应力和耦合应力强度因子（SIF 和 CSIF），并与文献中的应力和耦合应力强度因子进行比较，以进行验证。由于 XFEM 能够处理裂纹域中出现的不连续性和奇异性，因此该方法大大简化了建模过程，并为现有方法（如相场法和周动力学）提供了一个新的不同视角，这些方法各有其优势和局限性，可扩展用于处理微极性结构中的裂纹及其生长问题。

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引用次数: 0

Parameter certainty quantification in nonlinear models 非线性模型中的参数确定性量化

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2024-11-04 DOI: 10.1016/j.ijengsci.2024.104163

Amit Ashkenazi, Dana Solav

Estimating model parameters from experimental data is a common practice across various research fields. For nonlinear models, the parameters are estimated using an optimization algorithm that minimizes an objective function. Assessing the certainty of these parameter estimates is crucial to address questions such as “what is the probability the estimation error is smaller than 5%?”, “is our experiment sensitive enough to estimate all parameters?”, and “how much can we change each parameter while still fitting the data accurately?”. Typically, the certainty levels are quantified using a linear approximation of the model. However, we show that in models that are highly nonlinear in their parameters or in the presence of large experimental errors, this method fails to capture the certainty levels accurately. To address these limitations, we present an alternative method based on the Hessian approximation of the objective function. We show that this method captures the certainty levels more accurately and can be derived geometrically. We demonstrate the efficacy of our approach through a case study involving a nonlinear hyperelastic material constitutive model and an application on a nonlinear model for the conductivity of electrolyte solutions. Despite its higher computational cost, we recommend adopting the Hessian approximation when accurate certainty levels are required in highly nonlinear models.

根据实验数据估算模型参数是各个研究领域的常见做法。对于非线性模型，参数估计采用优化算法，使目标函数最小化。评估这些参数估计的确定性对于解决以下问题至关重要，例如 "估计误差小于 5%的概率是多少？"、"我们的实验是否足够敏感，可以估计出所有参数？"以及 "我们可以在精确拟合数据的同时改变每个参数多少？"。通常情况下，确定性水平是通过模型的线性近似来量化的。然而，我们的研究表明，在参数高度非线性或存在较大实验误差的模型中，这种方法无法准确捕捉确定性水平。为了解决这些局限性，我们提出了一种基于目标函数 Hessian 近似值的替代方法。我们证明，这种方法能更准确地捕捉确定性水平，并能以几何方式推导出来。我们通过涉及非线性超弹性材料构成模型的案例研究和电解质溶液电导率非线性模型的应用，证明了我们方法的有效性。尽管计算成本较高，但当高度非线性模型需要精确的确定性水平时，我们建议采用赫塞斯近似法。

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引用次数: 0

Machine learning for crack detection in an anisotropic electrically conductive nano-engineered composite interleave with realistic geometry 各向异性导电纳米工程复合材料交错层中裂纹检测的机器学习，具有逼真的几何形状

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2024-11-01 DOI: 10.1016/j.ijengsci.2024.104171

Iskander S. Akmanov, Stepan V. Lomov, Mikhail Y. Spasennykh, Sergey G. Abaimov

Engineering interleaves of composite laminates with carbon nanotubes (CNTs) improves interlaminar fracture toughness, creating also conductivity, which can be employed for damage identification. The paper explores machine learning (ML) solution of the inverse problem of the defect identification for interleaves with anisotropic conductivity (aligned CNTs). The electrical and geometrical properties of the interleave are assigned based on the synchrotron X-ray computer tomography of glass fibre / epoxy laminates with nanostitch. Several machine learning (ML) models are applied (XGBoost, fully connected (FCNN) and convolution neural (CNN) networks). XGBoost and FCNN algorithms performed poorly, failing to detect smaller defects and giving significant errors for larger ones. CNN algorithm detects defects well: It predicts the geometric characteristics of the defect with error below 16 %.

使用碳纳米管（CNTs）对复合材料层压板的交错层进行工程设计，不仅能提高层间断裂韧性，还能提高导电性，可用于损伤识别。本文探讨了各向异性导电性（排列的碳纳米管）交错层缺陷识别逆问题的机器学习（ML）解决方案。交错层的电气和几何特性是根据具有纳米缝隙的玻璃纤维/环氧树脂层压板的同步辐射 X 射线计算机断层扫描来确定的。应用了多种机器学习（ML）模型（XGBoost、全连接（FCNN）和卷积神经（CNN）网络）。XGBoost 和 FCNN 算法表现不佳，无法检测到较小的缺陷，而对较大的缺陷则误差很大。CNN 算法能很好地检测出缺陷：它能预测缺陷的几何特征，误差低于 16%。

引用次数: 0

Indentation of a piezoelectric FGM-coated half-space by a conical conductive punch: Approximated analytical solution 锥形导电冲头对压电 FGM 涂层半空间的压痕：近似解析解

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2024-10-30 DOI: 10.1016/j.ijengsci.2024.104161

Andrey S. Vasiliev, Sergei S. Volkov, Andrey L. Nikolaev, Sergei M. Aizikovich

Indentation of the coated piezoelectric transversely isotropic half-space by a conical conductive punch is modeled. The coating is assumed to be functionally-graded (continuously inhomogeneous in depth) with all group of electromechanical properties varying independently in depth according to arbitrary continuous functions or piecewise homogeneous. The problem is described mathematically in terms of linear electroelasticity and reduced to solution of a system of dual integral equations using the Hankel’s integral transformations. Closed-form approximated analytical solution of this system is obtained using the bilateral asymptotic method taking into account asymptotic properties of the kernel transforms. Expressions for the contact pressure, electric induction are obtained in an analytical form suitable for engineering analysis as well as the relations for the indentation force, total electric charge, indentation depth, contact radius and electric potential. Analytical form of results clearly demonstrates the contribution of mechanical and electric loading to the total solution and influence of the coating’s thickness and its properties on contact characteristics. Numerical results for homogeneous and two types of functionally-graded coatings illustrate features of the theoretical results in a wide range of values of relative coatings thickness.

模拟了锥形导电冲头对涂层压电横向各向同性半空间的压痕。假设涂层是功能分级的（在深度上连续不均匀），其所有机电特性组在深度上根据任意连续函数独立变化或片状均质。该问题用线性电弹性进行数学描述，并利用汉克尔积分变换简化为二元积分方程组的求解。考虑到核变换的渐近特性，利用双边渐近法获得了该系统的闭式近似解析解。以适合工程分析的解析形式获得了接触压力和电感应的表达式，以及压痕力、总电荷、压痕深度、接触半径和电动势的关系式。分析结果清楚地表明了机械负载和电负载对总解决方案的贡献，以及涂层厚度及其特性对接触特性的影响。均质涂层和两种功能分级涂层的数值结果说明了理论结果在涂层相对厚度的广泛数值范围内的特点。

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引用次数: 0

Initially stressed strain gradient elasticity: A constitutive model incorporates size effects and initial stresses 初始应力应变梯度弹性：包含尺寸效应和初始应力的构成模型

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2024-10-30 DOI: 10.1016/j.ijengsci.2024.104166

Weiting Chen, Xianfu Huang, Quanzi Yuan, Ya-Pu Zhao

Unlike ordinary solid materials, underground nano-materials such as kerogen, have relatively small dimensions and suffer from unavoidable in-situ stresses. The coexistence of size effects and initial stresses poses a great challenge to the constitutive modeling of deeply buried nano-inclusions. Despite the theories of strain gradient elasticity (SGE) and initially stressed elasticity (ISE) have been separately developed, the phenomenological model that fully considers the impact of the two ingredients remains unexplored. This paper proposes a strain gradient elasticity constitutive model for kerogen with size effects and in-situ stresses. Based on the decomposition of strains and strain gradients, the initially stressed strain gradient elasticity (ISSGE) framework is established. Then, a new form of the volumetric response function for kerogen is derived utilizing the density and porosity independence of the Poisson ratio. On this basis, we construct the corresponding hyperelastic and higher-order strain energy densities embedded with the given initial stress. The new constitutive model is applied to investigate the spherical pore contraction problem. Theoretical analysis and experimental results indicate that combining the in-situ stress and the size effect strengthens the elastic stiffness. Such enhancement cannot be comprehensively described by the existing theories. The model presented here provides the first constitutive relation of initially stressed strain gradient elasticity and lays the foundation for further incorporating more mechanical behaviors of underground nano-materials.

与普通固体材料不同，地下纳米材料（如角质）具有相对较小的尺寸，并受到不可避免的原位应力的影响。尺寸效应和初始应力的共存给深埋纳米夹杂物的构造建模带来了巨大挑战。尽管应变梯度弹性（SGE）和初始应力弹性（ISE）理论已被分别提出，但全面考虑这两种成分影响的现象学模型仍未被探索。本文提出了具有尺寸效应和原位应力的角质层应变梯度弹性构造模型。基于应变和应变梯度的分解，建立了初始应力应变梯度弹性（ISSGE）框架。然后，利用泊松比的密度和孔隙度独立性，推导出一种新形式的角质层体积响应函数。在此基础上，我们构建了嵌入给定初始应力的相应超弹性和高阶应变能密度。新的构造模型被用于研究球形孔隙收缩问题。理论分析和实验结果表明，结合原位应力和尺寸效应可增强弹性刚度。现有理论无法全面描述这种增强。本文提出的模型首次提供了初始应力应变梯度弹性的构成关系，为进一步纳入更多地下纳米材料的力学行为奠定了基础。

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引用次数: 0