论文标题
通过谐波分解对微观材料的微态本质关系解释
Interpretation of micromorphic constitutive relations for porous materials at the microscale via harmonic decomposition
论文作者
论文摘要
微态理论成为模拟材料，例如分散，定位现象或（显然）尺寸依赖性特性等材料的尺寸效应的既定工具。然而，足够的构造关系与其大量的本构关系和各自的参数的表述阻碍了整个微态理论的使用，该理论的使用情况下，该理论在各向同性线性弹性案例中已有18个本构参数。尽管显然这些参数与预测的尺寸效应有关，但单个参数的个体含义尚不清楚。目前的工作试图阐明构成关系及其参数的解释。为此，将谐波分解应用于微态理论的管理方程。谐波模式在微观尺度上使用均匀化方法来解释带有球形孔的简单体积元件。使用球形谐波在分析线性弹性情况下通过球形谐波分析求解所得的边界值问题，从而对所有弹性18参数产生封闭形式的表达式。这些值用于预测细长泡沫样品扭转的尺寸效应。将预测与文献相应的实验结果进行了比较。
Micromorphic theories became an established tool to model size effects in materials like dispersion, localization phenomena or (apparently) size dependent properties. However, the formulation of adequate constitutive relations with its large number of constitutive relations and respective parameters hinders the usage of the full micromorphic theory, which has 18 constitutive parameters already in the isotropic linear elastic case. Although it is clear that these parameters are related to predicted size effects, the individual meaning of single parameters has been rather unclear. The present work tries to elucidate the interpretation of the constitutive relations and their parameters. For this purpose, a harmonic decomposition is applied to the governing equations of micromorphic theory. The harmonic modes are interpreted at the microscale using a homogenization method for a simple volume element with spherical pore. The resulting boundary-value problem at the microscale is solved analytically for the linear-elastic case using spherical harmonics resulting in closed-form expressions for all of the elastic 18 parameters. These values are used to predict the size effect in torsion of slender foam specimens. The predictions are compared with respective experimental results from literature.
