Spatial and temporal averaging in the homogenisation of the elastodynamic response of periodic laminates

Yağmuroğlu İ., Ozdemir Z., Askes H.

European Journal of Mechanics, A/Solids, vol.100, 2023 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 100
  • Publication Date: 2023
  • Doi Number: 10.1016/j.euromechsol.2023.104973
  • Journal Name: European Journal of Mechanics, A/Solids
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Hill–Mandel Principle, Homogenisation, Multi-scale modelling, Representative Volume Element, Space–time averaging, Wave propagation
  • Istanbul University-Cerrahpasa Affiliated: No

Abstract

This paper suggests a methodology to obtain homogenised material properties from a transient dynamic numerical model. The standard Hill–Mandel Principle, based on spatial averages, is extended with time averaging. Thus, in addition to a sufficiently large Representative Volume Element (RVE) to carry out the averaging in space, a sufficiently large time window is required to carry out the time averaging. The space–time averaging procedure is validated for a periodic laminate bar subjected to a variety of boundary conditions, impedance contrasts and loading conditions. The homogenised results converge to the analytical solutions and confirm that having a higher impedance contrast between laminate components requires not only larger RVE sizes but also longer time averaging windows. The most efficient macroscopic approximation is obtained by a balanced increase in RVE size and time averaging window.