Macroscopic modeling of porous and granular materials --- microstructure, thermodynamics and some boundary-initial value problems
- Wilmanski, Krzysztof
2010 Mathematics Subject Classification
- 35L50 74J15 80A17 74A20 74F10
- Thermodynamics, Biot's model, poroelastic materials, acoustic waves, surface waves
This work contains the material presented in the key lecture during the Congress Cancam 2003 (Calgary, Canada). It contains a review of the recent development of thermodynamic modeling of porous and granular materials. We present briefly main features of the thermodynamic construction of a nonlinear poroelastic model but the emphasis is put on the analysis of a linear two-component model. In particular we indicate similarities and differences of the thermodynamic model with the classical Biot's model of porous materials. We analyze jacketed and ujacketed Gedankenexperiments which provide a micro-macrotransition procedure for compressibilities. This gives rise to Gassmann-like relations which are incorporated in wave analysis. An acoustic waves analysis is presented in some details. In particular we show the construction of bulk monochromatic waves as well as some surface waves and indicate their practical applications in testing of soils.