不相容运动平面线性化弹性的变分公式

IF 1.4 3区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

Journal of Elasticity Pub Date : 2025-08-28 DOI:10.1007/s10659-025-10161-5

Pierluigi Cesana, Edoardo Fabbrini, Marco Morandotti

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引用次数: 0

摘要

我们提出了不相容运动系统在平面应变状态下的力学平衡的变分特征。对于非单连通区域，我们证明了不可提升的应变-应力对的平衡问题可以重新表述为系统的艾里势的适定最小化问题。我们将内部边界上的运动不相容描述为旋转或平移不匹配，与Volterra的斜位和位错建模一致。最后，我们建立了艾里势的最小化问题可以简化为涉及细胞公式的有限维优化问题。

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Variational Formulation of Planar Linearized Elasticity with Incompatible Kinematics

We present a variational characterization of mechanical equilibrium in the planar strain regime for systems with incompatible kinematics. For non-simply connected domains, we show that the equilibrium problem for a non-liftable strain-stress pair can be reformulated as a well-posed minimization problem for the Airy potential of the system. We characterize kinematic incompatibilities on internal boundaries as rotational or translational mismatches, in agreement with Volterra’s modeling of disclinations and dislocations. Finally, we establish that the minimization problem for the Airy potential can be reduced to a finite-dimensional optimization involving cell formulas.

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来源期刊

Journal of Elasticity 工程技术-材料科学：综合

CiteScore

3.70

自引率

15.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Elasticity was founded in 1971 by Marvin Stippes (1922-1979), with its main purpose being to report original and significant discoveries in elasticity. The Journal has broadened in scope over the years to include original contributions in the physical and mathematical science of solids. The areas of rational mechanics, mechanics of materials, including theories of soft materials, biomechanics, and engineering sciences that contribute to fundamental advancements in understanding and predicting the complex behavior of solids are particularly welcomed. The role of elasticity in all such behavior is well recognized and reporting significant discoveries in elasticity remains important to the Journal, as is its relation to thermal and mass transport, electromagnetism, and chemical reactions. Fundamental research that applies the concepts of physics and elements of applied mathematical science is of particular interest. Original research contributions will appear as either full research papers or research notes. Well-documented historical essays and reviews also are welcomed. Materials that will prove effective in teaching will appear as classroom notes. Computational and/or experimental investigations that emphasize relationships to the modeling of the novel physical behavior of solids at all scales are of interest. Guidance principles for content are to be found in the current interests of the Editorial Board.