{"title":"Computational Homogenization in Peristatics of Periodic Structure Composites","authors":"V. Buryachenko","doi":"10.1115/IMECE2018-86517","DOIUrl":null,"url":null,"abstract":"A composite material (CM) of periodic structure with the peristatic properties of constituents (see Silling, J. Mech. Phys. Solids 2000; 48:175–209) is analyzed by a generalization of the classical locally elastic computational homogenization to its peristatic counterpart. One introduces new volumetric periodic boundary conditions (PBC) at the interaction boundary of a representative unit cell (UC). A generalization of the Hill’s equality to peristatic composites is proved. The general results establishing the links between the effective moduli and the corresponding mechanical influence functions are obtained. The discretization of the equilibrium equation acts as a macro-to-micro transition of the deformation-driven type, where the overall deformation is controlled. Determination of the microstructural displacements allows one to estimate the peristatic traction at the geometrical UC’s boundary which is exploited for estimation of the macroscopic stresses and the effective moduli. One demonstrates computationally, through one-dimensional examples, the approach proposed.","PeriodicalId":119220,"journal":{"name":"Volume 1: Advances in Aerospace Technology","volume":"508 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Volume 1: Advances in Aerospace Technology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1115/IMECE2018-86517","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A composite material (CM) of periodic structure with the peristatic properties of constituents (see Silling, J. Mech. Phys. Solids 2000; 48:175–209) is analyzed by a generalization of the classical locally elastic computational homogenization to its peristatic counterpart. One introduces new volumetric periodic boundary conditions (PBC) at the interaction boundary of a representative unit cell (UC). A generalization of the Hill’s equality to peristatic composites is proved. The general results establishing the links between the effective moduli and the corresponding mechanical influence functions are obtained. The discretization of the equilibrium equation acts as a macro-to-micro transition of the deformation-driven type, where the overall deformation is controlled. Determination of the microstructural displacements allows one to estimate the peristatic traction at the geometrical UC’s boundary which is exploited for estimation of the macroscopic stresses and the effective moduli. One demonstrates computationally, through one-dimensional examples, the approach proposed.
一种具有周期性结构的复合材料(CM),具有组分的蠕动特性(参见Silling, J. Mech。理论物理。固体2000;48:175-209)通过将经典的局部弹性计算均匀化推广到它的蠕动对应物来分析。在典型单元胞(UC)的相互作用边界上引入了新的体积周期边界条件(PBC)。证明了希尔方程在蠕动复合材料中的推广。得到了建立有效模量与相应力学影响函数之间联系的一般结果。平衡方程的离散化作为变形驱动型的宏观到微观转变,其中整体变形受到控制。微观结构位移的确定使人们能够估计几何UC边界的蠕动牵引力,该牵引力用于估计宏观应力和有效模量。通过一维的例子,对所提出的方法进行了计算论证。