Induced fields in isolated elliptical inhomogeneities due to imposed polynomial fields at infinity
Induced fields in isolated elliptical inhomogeneities due to imposed polynomial fields at infinity
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由于在无穷远处施加多项式场而导致孤立椭圆不均匀性中的感应场
DOI：
10.1080/00207160.2018.1455972
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发表时间：
2018
影响因子：
1.8
通讯作者：
Calvo-Jurado C
中科院分区：
文献类型：
--
作者：
Calvo-Jurado C
Eshelby不均匀性问题在非均匀介质的有效力学行为的微观力学分析中起着至关重要的作用，因为它提供了一种机制来预测与椭球不均匀性相关的内部场。在线性弹性的背景下，Eshelby表明，给定一个孤立的椭圆形（二维）或椭球形（三维）嵌入无限范围的均匀材料中的不均匀性，那么对于任何均匀应变或牵引施加在远场，内部的不均匀性引起的应变也是均匀的。在非均匀远场条件下，Eshelby证明了如果载荷是n阶多项式，则相关的内场由相同阶的多项式表征。这通常被称为“Eshelby多项式守恒定理”。从那时起，这个问题已经被许多人研究，但在大多数情况下，均匀加载的情况下，即当应变或牵引力在远场是均匀的。然而，在许多应用中，例如介电常数、电导率、弹性等，非均匀条件的情况也是令人感兴趣的，此外，需要处理非椭圆和非椭球不均匀性的方法。在这项工作中，对于指定的非均匀多项式远场条件，我们介绍了一种方法来近似内部场孤立的椭圆形的不均匀性。这一子问题与许多复合材料的近似有效性质有关，因为组分不均匀性通常是这种形式或限制形式，例如层状和纤维增强复合材料。我们验证了所得结果符合多项式守恒性质，并与用保形映射或经典的圆包含定理确定的结果一致。最后，我们讨论了该方法如何可以直接扩展到非椭圆不均匀性的情况下。
The Eshelby inhomogeneity problem plays a crucial role in the micromechanical analysis of the effective mechanical behaviour of inhomogeneous media since it provides a mechanism to predict interior fields associated with ellipsoidal inhomogeneities. In the context of linear elasticity, Eshelby showed that given an isolated elliptical (two dimensions) or ellipsoidal (three dimensions) inhomogeneity embedded in a homogeneous material of infinite extent, then for any uniform strain or traction imposed in the far field, the induced strain inside the inhomogeneity is also uniform. In the case of non-uniform far-field conditions, Eshelby showed that if the loading is a polynomial of ordern, the associated interior field is characterized by a polynomial of the same order. This is often called ‘Eshelby's polynomial conservation theorem’. Since then, the problem has been studied by many, but in most cases for the uniform loading scenario, i.e. when strains or tractions in the far field are uniform. However, in many applications, e.g. permittivity, conductivity, elasticity, etc., the case of non-uniform conditions is also of interest and furthermore, methods to deal with non-elliptical and non-ellipsoidal inhomogeneities are required. In this work, for prescribed non-uniform polynomial far-field conditions, we introduce a method to approximate interior fields for isolated inhomogeneities of elliptical shape. This subproblem is relevant for approximating effective properties of numerous composites since constituent inhomogeneities are often of this form, or limiting forms, e.g. layered and fibre reinforced composites. We verify that the obtained results agree with the polynomial conservation property and with results determined using conformal mappings or the classical circle inclusion theorem. We close with a discussion of how the method can be straightforwardly extended to the case of non-elliptical inhomogeneities.
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两点统计对三相复合材料 Hashin-Shtrikman 界限的影响
影响因子：
2.4
作者：
Calvo-Jurado C
通讯作者：
Calvo-Jurado C
含有曲线纤维的长丝复合材料的纵向剪切模量
DOI：
--
发表时间：
1970
期刊：
影响因子：
--
作者：
G. Sendeckyj
通讯作者：
G. Sendeckyj
DOI：
10.1098/rspa.2017.0080
发表时间：
2017-05
期刊：
Proceedings. Mathematical, physical, and engineering sciences
影响因子：
--
作者：
Joyce D;Parnell WJ;Assier RC;Abrahams ID
通讯作者：
Abrahams ID
影响因子：
1.7
作者：
Calvo-Jurado, Carmen;Parnell, William J.
通讯作者：
Parnell, William J.