European Journal of Mechanics A-Solids最新文献_第6页

Vibration mitigation in piezoelectric sandwiched nanocomposite beam-like structures considering Bouc-Wen hysteresis: An adaptive fuzzy sliding mode control approach 考虑Bouc-Wen迟滞的压电夹层纳米复合材料类梁结构振动抑制：一种自适应模糊滑模控制方法

IF 4.2 2区工程技术 Q1 MECHANICS

European Journal of Mechanics A-Solids

Pub Date : 2026-05-01 Epub Date: 2025-11-26 DOI: 10.1016/j.euromechsol.2025.105961

Hadi Arvin , Maryam Shahriari-kahkeshi , Hossein Ghahhari , Ömer Civalek

In this study, an adaptive fuzzy sliding mode controller is proposed to mitigate the vibrations of a hysteretic sandwiched piezoelectric nanocomposite beam regarding system uncertainties, accounting for the intrinsic hysteresis behavior of the actuator layer. The core consists of a graphene sheet-reinforced composite, while the piezoelectric facesheets operate as both sensors and actuators. The actuator's hysteresis is modeled using a Bouc-Wen formulation with uncertain parameters. To compensate for this uncertain nonlinearity and suppress vibrations, an adaptive fuzzy sliding mode controller is developed, with stability guaranteed via Lyapunov's direct method. The results demonstrate the controller's high effectiveness in mitigating mechanical vibrations. The robustness of the proposed controller against parameter uncertainties allows it to manage small variations in structural stiffness and mass resulting from changes in the distribution pattern of the nanocomposite and the piezoelectric thickness ratio. As a result, the controlled deflection of the nanocomposite beam remains unaffected by these two parameters. The most important parameter affecting the controlled response is the type of boundary condition. Decreasing the piezoelectric layer thickness enhances the controller's effort. Due to the hysteresis behavior of the actuator, a steady-state controller effort remains in the system, which is more pronounced for the clamped-clamped nanocomposite beam. The corresponding hysteretic loop shows a similar observation for this boundary condition.

在本研究中，考虑到执行器层的固有迟滞行为，提出了一种自适应模糊滑模控制器来缓解迟滞夹层压电纳米复合材料梁在系统不确定性下的振动。核心由石墨烯增强复合材料组成，而压电片同时作为传感器和执行器。采用具有不确定参数的Bouc-Wen公式对作动器的滞回进行建模。为了补偿这种不确定的非线性并抑制振动，设计了一种自适应模糊滑模控制器，该控制器通过李雅普诺夫直接法保证其稳定性。结果表明，该控制器在抑制机械振动方面具有良好的效果。所提出的控制器对参数不确定性的鲁棒性使其能够管理由纳米复合材料分布模式和压电厚度比变化引起的结构刚度和质量的微小变化。结果表明，纳米复合材料梁的可控挠度不受这两个参数的影响。影响控制响应的最重要参数是边界条件的类型。减小压电层厚度可以增加控制器的工作量。由于执行器的迟滞行为，稳态控制器的工作仍然存在于系统中，这对于夹紧-夹紧纳米复合梁来说更为明显。相应的滞回环对该边界条件显示了类似的观察结果。

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引用次数: 0

Unveiling the role of peak load in the stability and growth of interlaminar fatigue damage in composite structures 揭示峰值荷载在复合材料结构层间疲劳损伤稳定性和发展中的作用

IF 4.2 2区工程技术 Q1 MECHANICS

European Journal of Mechanics A-Solids

Pub Date : 2026-05-01 Epub Date: 2025-12-18 DOI: 10.1016/j.euromechsol.2025.106001

Angela Russo, Rossana Castaldo, Aniello Riccio

Understanding the stability of delamination growth is essential for ensuring the reliability of composite structures under compressive fatigue loading. In post-buckling regimes, where crack propagation can become highly unstable and nonlinear, even small variations in the applied load may drastically alter damage evolution and residual strength. Despite its critical role, the stability of interlaminar crack growth under cyclic compression remains poorly understood, demanding refined numerical strategies to capture its complex behaviour. This work addresses this gap by investigating how the peak compressive load influences the stability and progression of delamination in composite structures.

A dedicated numerical approach has been developed to study these effects. The methodology, named SMART LOOP, couples the Virtual Crack Closure Technique (VCCT) with the Paris Law-based damage accumulation model. Such method employs an adaptive timestep strategy to ensure precise load control and mesh-independent predictions. SMART LOOP transforms force-controlled fatigue simulations into a sequence of displacement-controlled static analyses, where the displacement input is automatically adjusted to reach the target load level. This produces delamination length results that are independent of element size, eliminating the need for mesh refinement strategies.

A series of simulations has been carried out on an Omega-stiffened composite panel subjected to three different compressive peak loads (25.2, 27.1, and 29.1 kN). The numerical results have been compared with experimental data from the literature to enhance the understanding of the unstable delamination growth phenomenon. This provides additional insights into failure mechanisms and complements the experimental observations.

了解分层生长的稳定性对于保证复合材料结构在压缩疲劳载荷作用下的可靠性至关重要。在后屈曲状态下，裂纹扩展可能变得高度不稳定和非线性，即使施加载荷的微小变化也可能极大地改变损伤演变和残余强度。尽管层间裂纹在循环压缩下的扩展具有重要作用，但人们对其稳定性的了解仍然很少，因此需要精确的数值策略来捕捉其复杂行为。这项工作通过研究峰值压缩载荷如何影响复合材料结构中分层的稳定性和进展来解决这一空白。一种专门的数值方法被开发出来研究这些影响。该方法名为SMART LOOP，将虚拟裂纹闭合技术（VCCT）与基于巴黎定律的损伤累积模型相结合。该方法采用自适应时间步长策略，以确保精确的负载控制和网格无关的预测。SMART LOOP将力控制的疲劳模拟转换为一系列位移控制的静态分析，其中位移输入被自动调整以达到目标负载水平。这产生了独立于元素大小的分层长度结果，消除了对网格细化策略的需要。对omega -加筋复合材料板进行了一系列模拟，分别承受三种不同的峰值压缩载荷（25.2、27.1和29.1 kN）。将数值结果与文献中的实验数据进行了比较，以加深对不稳定分层生长现象的认识。这为失效机制提供了额外的见解，并补充了实验观察结果。

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引用次数: 0

Influence of shear stress on ductile failure initiation: a micromechanical analysis of strain localization 剪切应力对延性破坏起始的影响：应变局部化的微观力学分析

IF 4.2 2区工程技术 Q1 MECHANICS

European Journal of Mechanics A-Solids

Pub Date : 2026-05-01 Epub Date: 2026-01-09 DOI: 10.1016/j.euromechsol.2026.106019

J.C. Zhu , M. Ben Bettaieb , F. Abed-Meraim , B. Jia , J. Li

Shear stress is recognized as a critical factor influencing the ductile failure process. In the present work, we investigate ductile failure initiation under shear-dominated loading by identifying the onset of strain localization, which is predicted using a rigorous bifurcation analysis. Micromechanical computations are performed using cubic voided unit cells (UCs) subjected to fully periodic boundary conditions. Proportional stressing is imposed to keep constant stress triaxiality (T) and Lode parameter (L) throughout the deformation history of UCs. In the proportional stressing, two loading configurations are realized to comparatively study the effect of shear stress component for a given pair of T and L: normal stresses (without shear) versus normal stresses combined with one shear stress component. The effects of initial porosity and void configuration (pattern of voids arrangement) are also systematically analyzed. The results show that the influence of shear stress is strongly modulated by the amount of the initial porosity. While shear stress promotes strain localization at low initial porosity, it conversely delays it at high initial porosity within a specific range of Lode parameters. This porosity-dependent trend reversal is rationalized by a transition from a ligament-thinning-dominated failure mode to an intervoid-shearing-dominated failure mode as the stress state varies. Furthermore, for a given overall initial porosity, the void configuration significantly affects the critical strain locus, the extent of which depends on the imposed triaxiality. These findings provide valuable micromechanical insights for refining predictive modeling in engineering applications.

剪切应力被认为是影响延性破坏过程的关键因素。在目前的工作中，我们通过识别应变局部化的开始来研究剪切主导载荷下的韧性破坏启动，这是使用严格的分岔分析来预测的。微力学计算采用立方空胞（UCs）进行全周期边界条件。在整个变形过程中，施加比例应力以保持应力三轴性(T)和Lode参数(L)不变。在比例应力下，实现了两种加载配置，对比研究了给定T和L对剪应力分量的影响：正应力（无剪应力）与正应力加一个剪应力分量。系统地分析了初始孔隙率和孔洞形态（孔洞排列模式）的影响。结果表明，剪切应力的影响受初始孔隙率的强烈调节。在Lode参数的特定范围内，剪切应力在低初始孔隙度条件下促进应变局部化，反之在高初始孔隙度条件下则延迟应变局部化。随着应力状态的变化，这种依赖于孔隙率的趋势逆转是合理的，从韧带变薄为主的破坏模式转变为间隙剪切为主的破坏模式。此外，对于给定的总体初始孔隙率，孔隙形态显著影响临界应变轨迹，其程度取决于所施加的三轴性。这些发现为改进工程应用中的预测建模提供了有价值的微力学见解。

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引用次数: 0

Flexural-torsional buckling of circular arches with variable cross-section under uniformly distributed radial loads 均布径向荷载作用下变截面圆拱的弯扭屈曲

IF 4.2 2区工程技术 Q1 MECHANICS

European Journal of Mechanics A-Solids

Pub Date : 2026-05-01 Epub Date: 2025-12-11 DOI: 10.1016/j.euromechsol.2025.105995

Zixiang Zhang , Weile Wang , Yuanyuan Liu , Airong Liu , Sritawat Kitipornchai , Shaoyu Zhao

Variable cross-section design is a common approach in practical engineering to achieve superior structural characteristics and better landscape effects. This strategy, however, produces complex inner forces in the arch axis and affects the structural out-of-plane flexural-torsional behaviors. To explore the buckling mode and reveal their failure mechanism, this paper carries out an in-depth analysis on the out-of-plane elastic buckling of variable cross-section circular arches with a variable in-plane boundary condition under uniformly distributed radial loads. The cross-section is assumed to be linearized tapered, and the in-plane equilibrium equations of the system are built considering an energy principle. By solving the in-plane governing equations via a harmonic differential quadrature (HDQ) algorithm, the pre-buckling cross-sectional inner forces are obtained. Based on the assumption that the out-of-plane flexural-torsional buckling occurs from an adjacent pre-buckling in-plane deformed equilibrium state, the out-of-plane total potential energy is established. The critical buckling load of variable cross-section circular arches is then determined by solving the out-of-plane governing equations corresponding to lateral displacement and twist angle. Effects of in-plane boundary conditions, cross-section shape, included angle, and slenderness ratio on the flexural-torsional behaviors are further explored. It is found that as the cross-section change parameter continues to grow, the out-of-plane critical buckling load of variable cross-section circular arches decreases gradually, the buckling position shifts towards the arch crown.

变截面设计是在实际工程中实现优越的结构特性和较好的景观效果的常用方法。然而，这种策略在拱轴上产生复杂的内力，并影响结构的面外弯扭行为。为探索其屈曲模式，揭示其破坏机理，本文对均布径向载荷作用下变截面面内边界条件圆拱的面外弹性屈曲进行了深入分析。假设横截面为线性化的锥形，根据能量原理建立了系统的面内平衡方程。通过谐波微分正交（HDQ）算法求解平面内控制方程，得到了预屈曲截面内力。基于面外弯扭屈曲是从相邻的预屈曲面内变形平衡状态发生的假设，建立了面外总势能。然后通过求解横向位移和扭转角对应的面外控制方程，确定变截面圆拱的临界屈曲载荷。进一步探讨了面内边界条件、截面形状、夹角和长细比对弯扭性能的影响。研究发现，随着截面变化参数的不断增大，变截面圆拱的面外临界屈曲载荷逐渐减小，屈曲位置向拱冠方向偏移。

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引用次数: 0

Fracture mechanism in SUS304 during small punch tests SUS304的小冲孔断裂机理

IF 4.2 2区工程技术 Q1 MECHANICS

European Journal of Mechanics A-Solids

Pub Date : 2026-05-01 Epub Date: 2025-11-24 DOI: 10.1016/j.euromechsol.2025.105953

Chong Gao , Yihui Huang , Qian Sun , Bo Cao , Takeshi Iwamoto , Tsutomu Umeda , Takayuki Kusaka

Past experimental result reveals that a region of the fracture initiation in metastable austenitic stainless steel SUS 304 during a small punch test changes from the loading side to free surface with respect to the loading rate. Since a measurement of a time series of the martensite and temperature distribution, which strongly affects the fracture behavior, is difficult to be realized during testing, a precise finite element (FE) analysis is necessary to support further discussions on the mechanism of the loading rate sensitivity. In the current work, the phenomena observed in the tests are precisely reproduced through the FE analyses including the martensitic transformation and the damage evolution modelled by authors. The condition for the onset of crack extension is provided to assist the future works in determining where the initiation occurs. Even though the austenitic phase is dominant for the fracture, a larger damage variable appears in the region where a significant quantity of martensite is distributed. Simultaneously, the work clarifies the influence of reducing the amount of martensite with respect to the loading rate on ductility of the material. In the dynamic loading, it is newly discovered that the thermal softening plays an important role, inducing the fracture from the free surface of the specimen.

以往的实验结果表明，在小冲孔试验中，亚稳奥氏体不锈钢sus304的断裂起始区域随加载速率从加载侧向自由表面变化。由于在试验过程中难以测量对断裂行为有强烈影响的马氏体和温度分布的时间序列，因此有必要进行精确的有限元分析，以支持进一步讨论加载速率敏感性的机制。在本工作中，通过有限元分析，包括马氏体相变和作者模拟的损伤演化，精确地再现了试验中观察到的现象。提供了裂纹扩展开始的条件，以协助今后的工作确定裂纹扩展开始的位置。尽管奥氏体相在断裂中占主导地位，但在大量分布马氏体的区域出现较大的损伤变量。同时，阐明了相对于加载速率减少马氏体含量对材料延展性的影响。在动加载过程中，新发现热软化起着重要的作用，从试件自由表面诱发断裂。

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引用次数: 0

Oncogenic transformation of tubular epithelial ducts: How mechanics affects morphology 管状上皮管的致癌转化：力学如何影响形态

IF 4.2 2区工程技术 Q1 MECHANICS

European Journal of Mechanics A-Solids

Pub Date : 2026-05-01 Epub Date: 2025-12-03 DOI: 10.1016/j.euromechsol.2025.105984

D. Ambrosi , A. Favata , R. Paroni , G. Tomassetti

We derive a continuum mechanical model to capture the morphological changes occurring at the pre-tumoral stage of epithelial tissues. The mathematical model, derived from first principles, accounts for the competition between the bulk elasticity of the epithelium and the surface tension of the apical and basal boundaries. The variation of the energy functional yields the Euler–Lagrange equations to be numerically integrated. The numerical results reproduce a variety of morphological shapes, from invagination to evagination, depending on the ratio between bulk and surface energy at variance of the length of the section. In particular, using parameters independently measured, we are able to reproduce experimental data reported for a ring partially made of transformed cells.

我们推导了一个连续力学模型来捕捉上皮组织肿瘤前阶段发生的形态学变化。从第一性原理推导出的数学模型解释了上皮的体积弹性与根尖和基底边界的表面张力之间的竞争。能量泛函的变化使欧拉-拉格朗日方程得到数值积分。数值结果再现了各种形态形状，从内翻到外翻，取决于体积和表面能量在截面长度变化时的比例。特别是，使用独立测量的参数，我们能够重现部分由转化细胞组成的环的实验数据。

引用次数: 0

Homogenizing elastic lattices with mechanisms 均质弹性晶格与机构

IF 4.2 2区工程技术 Q1 MECHANICS

European Journal of Mechanics A-Solids

Pub Date : 2026-05-01 Epub Date: 2025-11-26 DOI: 10.1016/j.euromechsol.2025.105956

Basile Audoly , Claire Lestringant , Hussein Nassar

We propose an asymptotic method for homogenizing periodic elastic lattices that works in the presence of mechanisms, both of the macroscopic type (strain-producing modes) and of the microscopic type (internal modes). When a microscopic mechanism is present, the unit-cell problem produced by classical homogenization is singular. It can be fixed by including the amplitude

θ (X)

of the mechanism as an additional macroscopic degree of freedom (enrichment variable) contributing to the effective energy via its gradient

\nabla θ (X)

. When a macroscopic mechanism is present, homogenization delivers a degenerate effective energy at leading order, which can be regularized by accounting for the strain gradient. We introduce an asymptotic second-order homogenization scheme that integrates these two features: it delivers an effective energy capturing both the strain-gradient effect

\nabla ɛ (X)

relevant to macroscopic mechanisms, and the

\nabla θ (X)

regularization relevant to microscopic mechanisms, if any is present. The versatility of the approach is illustrated with a selection of lattices displaying a variety of effective behaviors. It follows a unified pattern that leads to a classification of these effective behaviors. Whereas the procedure delivers known effective models for elastic lattices without mechanisms, it can generate novel effective models for lattices possessing mechanisms.

我们提出了均匀化周期弹性晶格的渐近方法，该方法在宏观型（应变产生模式）和微观型（内部模式）存在的机制下工作。当存在微观机制时，由经典均匀化产生的单位胞问题是奇异的。它可以通过将机构的振幅θ(X)作为通过其梯度∇θ(X)贡献有效能量的附加宏观自由度（富集变量）来固定。当宏观机制存在时，均质提供了一阶简并有效能，该有效能可以通过考虑应变梯度而正则化。我们引入了一种集成了这两个特征的渐近二阶均匀化方案：它提供了一种有效的能量捕获与宏观机制相关的应变梯度效应∇θ(X)和与微观机制相关的正则化（如果存在的话）。通过选择显示各种有效行为的格来说明该方法的多功能性。它遵循一个统一的模式，将这些有效的行为分类。虽然该过程提供了已知的无机制弹性晶格的有效模型，但它可以为具有机制的晶格生成新的有效模型。

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引用次数: 0

Mechanical properties, microstructure evolution, and strengthening mechanism of Al-Mg-Si alloy welded joints using double-sided friction stir welding 双面搅拌摩擦焊Al-Mg-Si合金焊接接头力学性能、组织演变及强化机制

IF 4.2 2区工程技术 Q1 MECHANICS

European Journal of Mechanics A-Solids

Pub Date : 2026-05-01 Epub Date: 2025-12-07 DOI: 10.1016/j.euromechsol.2025.105987

Yuanpeng Liu , Meixin Ge , Guang Zeng , Kun Chen , Shunxin Liu , Wenjian Tang , Longxin Zhu

As the demand for lightweight materials grows, aluminum alloys are increasingly utilized across various industries. However, conventional fusion welding of medium-thick aluminum plates often results in defects. Friction stir welding (FSW), a solid-state joining process, effectively mitigates these issues. This study investigates double-sided FSW (DS-FSW) and single-sided FSW (SS-FSW) of 6061-T6 aluminum alloy through combined experiments and numerical simulations. The thermal cycles, stress distribution, material flow, microstructure evolution, and mechanical properties of the joints are systematically examined. Results demonstrate that DS-FSW joints exhibit a 31 % higher yield strength (228 MPa) compared to SS-FSW joints (174 MPa), along with superior tensile strength. However, both joint types show lower elongation than the base material, with DS-FSW slightly lower (4.43 %) than SS-FSW (4.87 %). Microhardness distribution is more heterogeneous in DS-FSW, with higher hardness in the heat-affected zone but lower in the nugget zone. Microstructural analysis reveals finer grains, higher dislocation density, and a greater proportion of high-angle grain boundaries in DS-FSW. The study innovatively proposes the hetero-deformation induced (HDI) strengthening mechanism in DS-FSW joints, offering valuable insights for optimizing welding processes for medium-thick aluminum plates in aerospace, automotive, and energy applications.

随着对轻质材料需求的增长，铝合金越来越多地应用于各个行业。然而，传统的中厚铝板熔焊往往会产生缺陷。搅拌摩擦焊（FSW），一种固态连接工艺，有效地缓解了这些问题。采用实验与数值模拟相结合的方法，对6061-T6铝合金的双面FSW （DS-FSW）和单面FSW （SS-FSW）进行了研究。系统地研究了接头的热循环、应力分布、材料流动、微观组织演变和力学性能。结果表明，与SS-FSW接头（174 MPa）相比，DS-FSW接头的屈服强度（228 MPa）提高了31%，抗拉强度也更高。但两种接头的伸长率均低于母材，其中DS-FSW略低于SS-FSW（4.43%）。DS-FSW的显微硬度分布较为不均匀，热影响区硬度较高，而熔核区硬度较低。显微组织分析表明，DS-FSW的晶粒更细，位错密度更高，高角度晶界比例更高。该研究创新性地提出了DS-FSW接头的异质变形诱导（HDI）强化机制，为航空航天、汽车和能源应用中厚铝板的焊接工艺优化提供了有价值的见解。

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引用次数: 0

The isotropic relaxed micromorphic model in polar coordinates and its application to an elastostatic axisymmetric extension problem 极坐标下各向同性松弛微态模型及其在轴对称弹静力扩展问题中的应用

IF 4.2 2区工程技术 Q1 MECHANICS

European Journal of Mechanics A-Solids

Pub Date : 2026-05-01 Epub Date: 2025-11-29 DOI: 10.1016/j.euromechsol.2025.105964

Esmaeal Ghavanloo , Patrizio Neff

In this paper, we consider the isotropic relaxed micromorphic model in polar coordinates and use this representation to solve explicitly an elastostatic axisymmetric extension problem involving a linear system of ordinary differential equations. To obtain an analytical solution, modified Bessel functions are utilized and closed-form solutions for the displacement and micro-distortion are obtained. We show how certain limit cases (classical linear elasticity), which are naturally included in the relaxed micromorphic model, can be efficiently achieved. Furthermore, numerical results are calculated and the effects of various parameters are examined. The results can be used to calibrate and check corresponding finite element codes.

本文考虑极坐标系下的各向同性松弛微态模型，并利用该模型显式地求解了一个涉及线性常微分方程组的弹性静力轴对称扩展问题。为了得到解析解，利用修正贝塞尔函数，得到了位移和微畸变的封闭解。我们展示了如何有效地实现松弛微态模型中自然包含的某些极限情况（经典线性弹性）。此外，还对数值结果进行了计算，并对各参数的影响进行了检验。计算结果可用于标定和校核相应的有限元规范。

引用次数: 0

Accounting for plasticity: An extension of inelastic constitutive artificial neural networks 计算塑性：非弹性本构人工神经网络的扩展

IF 4.2 2区工程技术 Q1 MECHANICS

European Journal of Mechanics A-Solids

Pub Date : 2026-05-01 Epub Date: 2025-12-18 DOI: 10.1016/j.euromechsol.2025.105998

Birte Boes , Jaan-Willem Simon , Hagen Holthusen

In this work, we extend the framework of inelastic constitutive artificial neural networks (iCANNs) by incorporating plasticity. Thereby, we increase their applicability to capture more complex material behavior by solving the underlying inequality constraints associated with plasticity, aiming to automatically discover the formulation that matches the experimental data most accurately. Learning on stress–strain data, our approach enables the automatic discovery of the constitutive equations for elasto-plastic materials – including the identification of the material parameters and the underlying functional forms of the Helmholtz free energy, yield function and evolution equations for the inelastic deformations including linear and nonlinear kinematic hardening. These are captured using feed-forward neural networks. The proposed methodology ensures objectivity, material symmetry, and thermodynamic consistency, providing a robust and interpretable basis for automatic model discovery at finite strains. Investigation of our model’s prediction showed that the extended iCANNs successfully predict both linear and nonlinear kinematic hardening behavior based on experimental and artificially generated datasets, showcasing promising capabilities of this framework. Nonetheless, challenges remain in fully capturing complex yield criteria – such as those exhibiting tension–compression asymmetry – and predicting complex nonlinear hardening.

在这项工作中，我们通过纳入可塑性扩展了非弹性本构人工神经网络（icann）的框架。因此，我们通过解决与塑性相关的潜在不等式约束来提高它们的适用性，以捕获更复杂的材料行为，旨在自动发现最准确地匹配实验数据的公式。通过学习应力应变数据，我们的方法能够自动发现弹塑性材料的本构方程，包括材料参数的识别和亥姆霍兹自由能的基本函数形式，屈服函数和非弹性变形的演化方程，包括线性和非线性运动硬化。这些都是用前馈神经网络捕获的。所提出的方法确保了客观性、材料对称性和热力学一致性，为有限应变下的自动模型发现提供了可靠和可解释的基础。对我们模型预测的研究表明，扩展的icann成功地预测了基于实验和人工生成的数据集的线性和非线性运动学硬化行为，展示了该框架的良好能力。尽管如此，在充分捕捉复杂的屈服标准（例如那些表现出拉压不对称的屈服标准）和预测复杂的非线性硬化方面仍然存在挑战。

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引用次数: 0