A formulation for an unsaturated porous medium undergoing large inelastic strains

Abstract

This paper presents a formulation for a saturated and partially saturated porous medium undergoing large elastic or elastoplastic strains. The porous material is treated as a multiphase continuum with the pores of the solid skeleton filled by water and air, this last one at constant pressure. This pressure may either be the atmospheric pressure or the cavitation pressure. The governing equations at macroscopic level are derived in a spatial and a material setting. Solid grains and water are assumed to be incompressible at the microscopic level. The isotropic elastoplastic behaviour of the solid skeleton is described by the multiplicative decomposition of the deformation gradient into an elastic and a plastic part. The effective stress state is limited by the Drucker-Prager yield surface, for which a particular "apex formulation" is advocated. The water is assumed to obey Darcy's law. Numerical examples of strain localisation of dense and loose sand conclude the paper

Arbitrary Lagrangian–Eulerian method for large‐strain consolidation problems

“…Equation (12) shows that the stress-integration schemes used for small deformation have to be modified to include the additional terms due to rigid body rotation. Considering the skew-symmetry of i j , it is possible to show that the second integration 1027 in (12) is equivalent to a stress transformation: (13) with…”

Multiphase Modelling of Thermomechanical Behaviour of Early-Age Silicate Composites

“…The terms u ε i,j v ε j and v ε i,j v ε j , can be understood in the sense of scalar products grad u ε · v ε , grad v ε · v ε by (Sanavia, 2001), p. 139 (though the construction of such general grad-operator is not quite trivial). More precisely, the geometry of structured continua is described using fiber bundles and Riemanian manifold in (Yavari & Marsden, 2009) The classical constitutive relation for the solid phase between τ, u s , v s , etc., considers a linearized sufficiently small strain tensor and its additive decomposition into several parts, typically to the linear elastic and the power-law viscoelastic (creep) ones, containing facultative corrections due to microcracking, as in (Gawin et al, 2006a), p. 343, and (in more details) in (Gawin et al, 2006b) Majorana (2010) suggests even M = 9, taking into account i) elastic deformation, ii) plastic deformation, iii) damage, iv) cracking, v) creep, vi) shrinkage, vii) lits, viii) thermal strain, ix) autogenous strain, covering most items a)-e) from Introduction.…”

“…The special (linear) form of these relations, suggested in (Sanavia, 2001), p. 9 (this part of (Sanavia, 2001) contains much more technical details than its later revision (Sanavia et al, 2002)…”

“…Four phases are distinguished: solid skeleton, liquid water, vapour and dry air, whose densities are considered (under the passive air assumption) as constants; the whole hygro-thermo-chemo-mechanical process is then studied as the time evolution of capillary pressure, gas pressure, temperature and displacement of points related to the reference (initial) configuration, driven by balance equations of classical thermodynamics and conditioned by corresponding constitutive laws. The detailed geometrical analysis (Sanavia et al, 2002) (without phase changes) offers the possibility to extend such considerations beyond the assumption of small deformations and involve some elements of fracture mechanics. The development, laboratory testing and computational simulations of new materials, namely those for the application of advanced engineering structures, belong to the research priorities of the Faculty of Civil Engineering of Brno University of Technology.…”

Unsaturated hydro-mechanical–chemical constitutive coupled model based on mixture coupling theory: Hydration swelling and chemical osmosis

“…The Mechanics approach is based on the classical consolidation theories of Terzaghi [12] and Biot [13,14]. Work done in this approach in Geomechanics includes coupled hydro-mechanical models [15][16][17][18][19], and coupled thermo-hydro-mechanical-chemical models [20][21][22]. However, the Mechanics approach lacks systemic self development theory [23].…”