Analytical solutions for the effective viscoelastic properties of composite materials with different shapes of inclusions

IF 0.7 Q4 MECHANICS
Minh‐Quan Thai, Sy-Tuan Nguyen, Thanh-Sang Nguyen, Phu-Son Mai
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引用次数: 0

Abstract

This paper aims to model the effect of different shapes of inclusions on the homogenized viscoelastic properties of composite materials made of a viscoelastic matrix and inclusion particles. The viscoelastic behavior of the matrix phase is modeled by the Generalized Maxwell rheology. The effective properties are firstly derived by combining the homogenization theory of elasticity and the correspondence principle. Then, the effective rheological properties in time space are explicitly derived without using the complex inverse Laplace?Carson transformation (LC). Closed-form solutions for the effective bulk and shear rheological viscoelastic properties, the relaxation and creep moduli as well as the Poisson ratio are obtained for the isotropic case with random orientation distribution and different shapes of inclusions: spherical, oblate and elongate inclusions. The developed approach is validated against the exact solutions obtained by the classical inverse LC method. It is observed that the homogenized viscoelastic moduli are highly sensitive to different shapes of inclusions.
含不同形状夹杂物的复合材料有效粘弹性的解析解
本文旨在模拟不同形状的夹杂物对由粘弹性基体和夹杂物颗粒组成的复合材料均质粘弹性性能的影响。用广义麦克斯韦流变性理论对基体相的粘弹性行为进行了建模。首先将弹性均质理论与对应原理相结合,导出了有效性质。然后,在不使用复拉普拉斯逆变换的情况下,显式地推导出时间空间中的有效流变性能。卡森变换(LC)得到了各向同性随机取向分布和不同包裹体形状(球形、扁圆形和长条形)情况下的有效体积和剪切流变粘弹性、松弛模量和蠕变模量以及泊松比的封闭解。与经典LC逆法得到的精确解进行了对比验证。观察到均匀化的粘弹性模量对不同形状的夹杂物高度敏感。
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
4
审稿时长
32 weeks
期刊介绍: Theoretical and Applied Mechanics (TAM) invites submission of original scholarly work in all fields of theoretical and applied mechanics. TAM features selected high quality research articles that represent the broad spectrum of interest in mechanics.
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