A method of computational homogenization of a heterogeneous porous medium based on a hyperbolic thermodynamically compatible model Full article
| Journal |
Journal of Computational and Applied Mathematics
ISSN: 0377-0427 |
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| Output data | Year: 2027, Volume: 491, Article number : 118064, Pages count : 21 DOI: 10.1016/j.cam.2026.118064 | ||||
| Tags | Effective elastic moduli, Heterogeneous saturated porous medium, Strain energy-based method, Time marching method for steady-state solution, Diffuse interface, Hyperbolic thermodynamically compatible model | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования РФ | 075-15-2025-348 |
Abstract:
A method for evaluating effective elastic moduli of fluid-saturated deformable porous materials is proposed. The approach is based on calculating the strain energy of a heterogeneous medium and comparing it with the energy of an equivalent homogeneous elastic medium. Heterogeneity is described using a Hyperbolic Thermodynamically Compatible (HTC) system of equations for a porous medium, simplified for small deformations; this formulation permits the use of a diffuse interface representation in the presence of regions occupied by either purely elastic solid or pure fluid.
By comparing the energies of the porous medium and its equivalent elastic counterpart while solving a series of simple stationary stress-strain problems for a sample, all components of the effective compliance tensor, and consequently all components of the effective stiffness tensor,
together with the corresponding effective wave velocities can be determined.
For the numerical solution of the governing equations, a high-order finite difference scheme on a staggered grid is applied. To obtain stationary equilibrium solutions for the sample, a steady state is reached via a time-marching technique incorporating artificial velocity relaxation.
A series of test problems demonstrate the flexibility of the method when applied to various types of saturated porous samples. Comparisons are made with known theoretical predictions of effective moduli for selected media. In particular, it is shown that for a liquid-saturated porous
elastic sample with a simple periodic microstructure, the elastic moduli employed in the HTC model are accurately approximated by the numerically obtained effective moduli.
Cite:
Romenski E.
, Reshetova G.
A method of computational homogenization of a heterogeneous porous medium based on a hyperbolic thermodynamically compatible model
Journal of Computational and Applied Mathematics. 2027. V.491. 118064 :1-21. DOI: 10.1016/j.cam.2026.118064 WOS Scopus OpenAlex
A method of computational homogenization of a heterogeneous porous medium based on a hyperbolic thermodynamically compatible model
Journal of Computational and Applied Mathematics. 2027. V.491. 118064 :1-21. DOI: 10.1016/j.cam.2026.118064 WOS Scopus OpenAlex
Dates:
| Submitted: | Mar 10, 2026 |
| Accepted: | Jul 29, 2026 |
| Published online: | Aug 11, 2026 |
Identifiers:
| ≡ Web of science: | WOS:001851358500001 |
| ≡ Scopus: | 2-s2.0-105047322752 |
| ≡ OpenAlex: | W7202188774 |