Homogenization of discrete mesoscale model of concrete for coupled mass transport and mechanics by asymptotic expansion

Jan Eliáš*, Gianluca Cusatis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Mass transport phenomenon in concrete structures is strongly coupled with their mechanical behavior. The first coupling fabric is the Biot's theory according to which fluid pressure interacts with solid stress state and volumetric deformation rate of the solid induces changes in fluid pressure. Another coupling mechanism emerges with cracks which serve as channels for the fluid to flow through them and provide volume for fluid storage. Especially the second coupling mechanism presents a challenge for numerical modeling as it requires detailed knowledge about cracking process. Discrete mesoscale mechanical models coupled with mass transport offer simple and robust way to solve the problem. On the other hand, however, they are computationally demanding. In order to reduce this computational burden, the present paper applies the asymptotic expansion homogenization technique to the coupled problem to deliver (i) continuous and homogeneous description of the macroscopic problem which can be easily solved by the finite element method, (ii) discrete and heterogeneous mesoscale problem in the periodic setup attached to each integration point of the macroscale along with (iii) equations providing communication between these two scales. The transient terms appear at the macroscale only, as well as the Biot's coupling terms. The coupling through cracking is treated at the mesoscale by changing conductivity of the conduit elements according to the mechanical solution, otherwise the two mesoscale steady state problems are decoupled and can be therefore solved in a sequence. This paper presents verification studies showing performance of the homogenized solution. Further improvement is achieved by pre-computing the initial linear mesoscale solution and adaptively replacing it by the full nonlinear one only at integration points that fulfill Ottosen's stress-based criterion indicating deviation from linearity.

Original languageEnglish (US)
Article number105010
JournalJournal of the Mechanics and Physics of Solids
StatePublished - Oct 2022


  • Biot's theory
  • Discrete model
  • Fracture
  • Homogenization
  • Mass transport
  • Mechanics
  • Multiphysics
  • Multiscale

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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