Analysis of the volume averaging relations in continuum mechanics

Summary, in English

In this paper volume average relations related to the multilevel modeling process in continuum mechanics are analyzed and the concept of average consistency is investigated both analytically and numerically. These volume averages are used in the computational homogenization technique, where a transition of the mechanical properties from the local, microscopic, to the global, macroscopic, length scale is obtained. The Representative Volume Element (RVE) is used as a reference placement and the solution, in terms of volume averaged stress, will depend on which boundary conditions are chosen for the RVE. Three types of boundary conditions - periodic, affine and anti-periodic boundary condition are analyzed with respect to the average consistence for the kinematical and stress relations used in continuum mechanics. The inconsistence is quantified by introducing the inconsistence ratio. It is shown analytically, that some average stress relations are fulfilled, assuming periodic boundary condition and anti-periodic traction vector, whereas the average relations connected to the deformation, are in general not average consistent. The inconsistence is investigated in a plane model using finite element technique. The numerical investigation has shown that the inconsistence ratios related to the deformation are also average consistent in the examples considered.

• Författare: Aylin Ahadi; Per Lidström
• Avdelning/ar: Mekanik
• Publiceringsår: 2012
• Språk: Engelska
• Sidor: 476-505
• Publikation/Tidskrift/Serie: Mathematics and Mechanics of Solids
• Volym: 18
• Issue: 5
• Länkar: https://journals.sagepub.com/doi/pdf/10.1177/1081286512442513
• Dokumenttyp: Artikel i tidskrift
• Förlag: SAGE Publications
• Ämne: Applied Mechanics
• Nyckelord: volume average relations; computational homogenization; continuum mechanics; periodic boundary conditions; representative volume element
• Status: Published
• ISBN/ISSN/Övrigt: ISSN: 1741-3028