Multiscale model for the prediction of equation of state for cement paste and mortar

S. Zhutovsky, Y. S. Karinski, D. Z. Yankelevsky, V. R. Feldgun

Research output: Contribution to journalArticlepeer-review


The behavior of cementitious materials under severe loading is of major importance for the security protection of concrete structures. One of the key mechanical properties of materials subjected to extremely high loading is the relationship between hydrostatic pressure and volumetric strain, which is often referred as the equation of state. In porous materials such as cement paste and mortar, this relationship is substantially inelastic due to the closure and collapse of capillary pores. At extremely high pressures, after all pores are closed, the equation of state approaches the elastic properties of the matrix. This paper presents an updated theoretical model of the equation of state of cement paste and mortar using a multi-scale approach. At the micro-scale level, an elastic-plastic spherical domain is considered with a single concetrical spherical cavity. The updated model includes a strain-hardening flow rule to describing the plastic closure of pores. At the macro-scale level, it is assumed that every differential spherical domain has random radial parameters following a realistic distribution function of pore sizes. The equations of state of the fine aggregates are assumed linear elastic and Hirsch phase mix rule is applied to obtain the equation of state of the composite material. All phases are assumed to be subjected to hydrostatic pressure. An extensive experimental study was conducted to calibrate and validate the proposed model. The comparison shows good agreement between the present model and the measured data.

Original languageEnglish
Pages (from-to)324-335
Number of pages12
JournalInternational Journal of Solids and Structures
StatePublished - Nov 2018


  • Cement paste and mortar
  • Equation of state
  • Multi-scale modeling
  • Stochastic pore distribution

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics
  • General Materials Science
  • Modelling and Simulation


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