Minimum energy combined and separated bounds on elastic constants of transversely-isotropic composites

IF 3.4 3区 工程技术 Q1 MECHANICS
Duc-Chinh Pham
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引用次数: 0

Abstract

The considered linearly-elastic transversely-isotropic composite (TIC) is composed of n isotropic, or more generally, transversely-isotropic components sharing the materials’ common symmetry axis with that of the macroscopic material. Using the basic minimum energy and complementary energy principles with certain free-parameter-dependent mixed-longitudinal-transverse-mode strain and stress trial fields, various combination bounds involving some sets of the macroscopic (effective) mixed-mode elastic constants of the composite, which are inter-connected via the constitutive relations, have been established. Choosing the appropriate parameter values of/or optimizing over the free parameters in those inequalities, the separated bounds on the major effective mixed-transverse-longitudinal-mode elastic constants, including the transverse bulk modulus Keff, the longitudinal Young modulus Eeff, and the longitudinal Poisson’s ratio νeff, are derived, beside the classical arithmetic and harmonic average bounds on the pure-mode ones — the transverse shear (μeff) and longitudinal shear (μ̄eff) moduli. The separated bounds on 4 remaining effective mixed-mode elastic constants are also obtained. The illustrative numerical comparisons of the bounds, in the two component case, with those for the special subclass of unidirectional transversely-isotropic composites (UTIC), having the unidirectional cylindrical boundaries between the component materials parallel to their symmetry axis, and the exact coated-cylinder assemblage and laminate models are presented. The extreme models cover substantial parts between the bounds for TIC; however the laminate models lie outside the bounds for the subclass UTIC.
横向各向异性复合材料弹性常数的最小能量组合约束和分离约束
所考虑的线弹性横向各向同性复合材料(TIC)由 n 个各向同性或更一般的横向各向同性成分组成,这些成分与宏观材料共享共同的对称轴。利用基本的最小能量和互补能量原理以及某些与自由参数相关的纵向-横向混合模式应变和应力试验场,建立了涉及复合材料某些宏观(有效)混合模式弹性常数集的各种组合约束,这些常数集通过构成关系相互连接。选择这些不等式中自由参数的适当参数值或对自由参数进行优化,除了对纯模式弹性常数--横向剪切模量(μeff)和纵向剪切模量(μ̄eff)--的经典算术和谐波平均约束外,还推导出了主要有效横纵混合模式弹性常数的分离约束,包括横向体积模量 Keff、纵向杨氏模量 Eeff 和纵向泊松比 νeff。同时还得到了其余 4 个有效混合模式弹性常数的分离约束。在双组分情况下,对这些边界与单向横向各向同性复合材料(UTIC)特殊子类的边界进行了说明性数值比较,单向横向各向同性复合材料的各组分材料之间的单向圆柱边界平行于其对称轴,而精确的涂覆圆柱装配和层压模型也是如此。极端模型覆盖了 TIC 边界之间的大部分区域,而层压模型则超出了 UTIC 子类的边界。
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来源期刊
CiteScore
6.70
自引率
8.30%
发文量
405
审稿时长
70 days
期刊介绍: The International Journal of Solids and Structures has as its objective the publication and dissemination of original research in Mechanics of Solids and Structures as a field of Applied Science and Engineering. It fosters thus the exchange of ideas among workers in different parts of the world and also among workers who emphasize different aspects of the foundations and applications of the field. Standing as it does at the cross-roads of Materials Science, Life Sciences, Mathematics, Physics and Engineering Design, the Mechanics of Solids and Structures is experiencing considerable growth as a result of recent technological advances. The Journal, by providing an international medium of communication, is encouraging this growth and is encompassing all aspects of the field from the more classical problems of structural analysis to mechanics of solids continually interacting with other media and including fracture, flow, wave propagation, heat transfer, thermal effects in solids, optimum design methods, model analysis, structural topology and numerical techniques. Interest extends to both inorganic and organic solids and structures.
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