A hybrid micromechanical-based symbolic regression model for transverse effective conductivity of high-contrast component composites

IF 2.5 3区 工程技术 Q2 MECHANICS
Viet-Hung Vu, Ba-Anh Le, Bao-Viet Tran, Thi-Loan Bui, Van-Hao Nguyen
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Abstract

In the context of combining analytical models with data driven, this paper aims to establish an appropriate computational process for constructing hybrid formulas to predict the transverse effective conductivity of uniaxial composites. Specifically, the paper predicts the geometric parameter r, which represents the size of a pattern shape in the generalized self-consistent approximation model and could characterize the complexity of the material structure. For the case of a random suspension of fibers, the parameter \(r\) can be represented by a ReLU function that allows variation from 1 to 0 as the structure transitions from sparse (central symmetry) to dense (hexagonal structure). For ordered structured configurations, database are constructed for two cases: square and hexagonal arrays. Then, a calculation strategy is proposed based on the genetic programming model to find the most suitable analytical formula for each structure. The resulting models show excellent agreement with both numerical and analytical results, even in cases where the volume fraction approaches the theoretical maximum of 99.9% and the conductivity of the inclusions tends toward infinity. The method is also validated with available experimental data in the most extreme case and further extended to the polydisperse scenario, producing stable and accurate results. The computational process thus holds great potential for extension to various models and different types of composite materials.

Abstract Image

高对比组分复合材料横向有效电导率的混合微力学符号回归模型
在分析模型与数据驱动相结合的背景下,本文旨在建立一个合适的计算过程,用于构建预测单轴复合材料横向有效电导率的混合公式。具体来说,本文预测了几何参数r,它代表了广义自洽近似模型中图案形状的大小,可以表征材料结构的复杂性。对于纤维的随机悬架,参数\(r\)可以用一个ReLU函数表示,当结构从稀疏(中心对称)转变为密集(六边形结构)时,该函数允许从1到0的变化。对于有序的结构化配置,数据库分为两种构造:正方形数组和六边形数组。然后,提出了一种基于遗传规划模型的计算策略,为每种结构寻找最合适的解析公式。即使在体积分数接近理论最大值99.9的情况下,所得到的模型也与数值和分析结果非常吻合% and the conductivity of the inclusions tends toward infinity. The method is also validated with available experimental data in the most extreme case and further extended to the polydisperse scenario, producing stable and accurate results. The computational process thus holds great potential for extension to various models and different types of composite materials.
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来源期刊
CiteScore
4.40
自引率
10.70%
发文量
234
审稿时长
4-8 weeks
期刊介绍: Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.
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