The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions
The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions
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DOI：
10.1098/rspa.2023.0214
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发表时间：
2023-08
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影响因子：
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通讯作者：
B. Gurrutxaga-Lerma
中科院分区：
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作者：
B. Gurrutxaga-Lerma
本文提供了夹杂物多极场扩展的一般公式。推导了椭圆体包含体的任意阶多极矩，显示了其远场和近场弹性场的已知特征。使用整数点枚举理论，相同的公式扩展到所有多面包裹体，这用于模拟在例如中发现的多面包裹体。火成岩和变质岩、颗粒增强复合材料或合金中的金属间沉淀物。推导了计算任意数量顶点的多面体多极矩的通用算法。给出了四面体、立方体和十二面体夹杂物的许多示例。结果表明，多面夹杂物的轴向力矩函数的宇称反映了夹杂物的对称性。这代表了其弹性场的主要特性，包括长场和近场衰减。如果夹杂物相对于给定轴对称，则场将在远场中以 1/r2 衰减，在近场中以 1/r4 衰减。如果沿该方向的对称性丢失，正如大多数真实包裹体所预期的那样，衰变率将以 1/r2 进展，但近场以 1/r3 进展。
The article offers a general formulation for the multipolar field expansion of an inclusion. The multipolar moments of arbitrary order for the ellipsoidal inclusion are derived, showing known features of their elastic fields in both the far and near field. Using integer point enumeration theory, the same formulation is extended to all polytopal inclusions, which serve to model faceted inclusions found in, e.g. igneous and metamorphic rocks, particle reinforced composite materials, or as intermetallic precipitates in alloys. A general algorithm for the calculation of the multipolar moments of polytopes of any number of vertices is derived. A number of examples for tetrahedral, cuboidal and dodecahedral inclusions are given. It is shown that the parity of the axial moment function of a polytopal inclusion mirrors the symmetry of the inclusion. This represents the main properties of their elastic fields, including the long- and near-field decay. If the inclusion is symmetric with respect to a given axes, the fields will decay with 1/r2 in the far field and 1/r4 in the near field. If symmetry along that direction is lost, as is expected in most real inclusions, the decay rate progresses with 1/r2 but the near field with 1/r3.