Anisotropic elastoplastic response of double-porosity media

Yang Zhao, Ronaldo I. Borja

Research output: Contribution to journalArticlepeer-review


We present a continuum framework to simulate fluid flow through anisotropic elastoplastic media with double porosity. Two effective stress measures σ and σ′′ emerge from the thermodynamic formulation, which are energy-conjugate to the elastic and plastic components of strain, respectively. Both effective stress measures can be expressed as a combination of the total Cauchy stress σ and the average pore pressure p¯ in the two pore scales. In the effective stress for elasticity, p¯ is scaled with a rank-2 Biot tensor, whereas the effective stress for plasticity follows the Terzaghi form in which p¯ is scaled by the Kronecker delta. The Biot tensor and storage coefficients are derived as functions of elasticity parameters and porosities. A mixed finite element formulation is introduced to discretize the domain and solve initial boundary-value problems. A stabilization scheme is employed on equal-order interpolation for both displacement and pressure fields throughout the entire range of drainage responses. Numerical simulations reproduce the hydromechanical response of Opalinus shale in one-dimensional consolidation tests throughout the range of primary and secondary consolidation under different external loads. Numerical simulations of the consolidation of a rectangular domain subjected to a strip load demonstrate the efficacy of the proposed stabilization scheme, as well as illustrate the impacts of stress history, mass transfer, and different pore systems on the hydromechanical response.

Original languageEnglish (US)
Article number113797
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Jul 1 2021
Externally publishedYes


  • Anisotropy
  • Double porosity
  • Effective stress
  • Poroplasticity
  • Transverse isotropy

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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