Derivation, simulation and validation of poroelastic models in dental biomechanics

Poroelasticity and mechanics of growth are playing an increasingly relevant role in biomechanics. This work is a self- contained and holistic presentation of the modeling and simulation of non-linear poroelasticity with and without growth inhomogeneities. Balance laws of poroelasticity are derived in Cartesian coordinates. These allow to write the governing equations in a form that is general but also readily implementable. Closure relations are formally derived from the study of dissipation. We propose an approximation scheme for the poroelasticity problem based on an implicit Euler method for the time discretization and a finite element method for the spatial discretization. The non-linear system is solved by means of Newton's method. Time integration of the growth tensor is discussed for the specific case in which the rate of inelastic deformations is prescribed. We discuss the stability of the mixed finite element discretization of the arising saddle-point problem. We show that a linear finite element approximation of both the unknowns, that is not LBB compliant for the elasticity problem, is nevertheless stable when applied to the linearized poroelasticity problem. This choice enables a fast assembling phase. The discretization of the poroelastic system may present unphysical oscillations if the spatial and temporal step-sizes are not properly chosen. We study the source of these wiggles by comparing the pressure Schur complement to a reaction- diffusion problem. From our analysis, we define a novel Péclet number for the poroelastic system and we show how it depends on the shear and bulk moduli of the solid phase. This number allows to introduce a stability condition that ensures that the solution is free of unphysical oscillations. If this condition on the Péclet number is not met, we introduce a fluid pressure Laplacian stabilization in order to remove the wiggles. This stabilization technique depends on a numerical parameter, whose optimal value is given by the derived Péclet number. Finally, we propose a coupled elastic-poroelastic model for the simulation of a tooth-periodontal ligament system. Because of the high resolution required by this system, we develop an efficient multigrid Newton's method for the non-linear poroelasticity system. The stability condition has again a significant influence on the performances of this solver. If the condition on the Péclet number is not satisfied on all levels of the multigrid algorithm, poor convergence rates or even divergence of the solver can be observed. The stabilization of the coarse grid operators with the optimal fluid pressure Laplacian method is a simple and efficient method to improve the convergence rate of the multigrid solver applied to this saddle-point system. We validate our coupled model against experimental measurements realized by the group of Prof. Bourauel at the University of Bonn

An Equi-Dimensional Finite Element Approach for Flow Problems in Fractured Porous Media

We propose a novel approach for flow simulations in fractured porous media based on an equi-dimensional representation of the fractures and a standard continuous finite element (FE) method. We employ an adaptive mesh refinement strategy to automatically adjust an initial regular mesh to any fracture distribution with a desired accuracy. The proposed approach is easily implementable in any FE software, does not involve the coupling of different discretizations, and provides symmetric and positive definite stiffness matrices. We provide a systematic validation of our method and we show that it can be used to simulate fluid flow for fracture networks of realistic complexity

Seismic Signatures of Fractured Porous Rocks: The Partially Saturated Case

Seismic attenuation and phase velocity dispersion due to mesoscopic fluid pressure diffusion (FPD) have received increasing attention due to their inherent sensitivity to the hydromechanical properties of monosaturated fractured porous media. While FPD processes are directly affected by key macroscopic properties of fractured rocks, such as fracture density and fracture connectivity, there is, as of yet, a lack of comprehension of the associated characteristics when multiple immiscible phases saturate the probed fractured medium. In this work, we analyze the variations experienced by P and S wave attenuation and phase velocity dispersion when CO2 percolates into an initially brine-saturated fractured porous rock. We study such variations considering a simple model of a porous rock containing intersecting orthogonal fractures as well as a more complex model comprising a fracture network. In the latter, we simulate the flow of a CO2 plume into the medium using an invasion percolation procedure. Representative samples are subjected to numerical upscaling experiments, consisting of compression and shear tests, prior to and after the CO2 invasion process. Results show that fracture-to-background FPD is only sensitive to the presence of CO2, which decreases its effects. However, fracture-to-fracture FPD depends on both the overall CO2 saturation and the fluid distribution within the fracture network. While the former modulates the magnitude of the dissipation, the latter can give rise to a novel FPD process occurring between CO2-saturated and brine-saturated regions of the fracture network.Fil: Solazzi, Santiago Gabriel. Universite de Lausanne; Suiza. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Hunziker, Jürg. Universite de Lausanne; SuizaFil: Caspari, Eva. Universite de Lausanne; Suiza. Montanuniversität Leoben; AustriaFil: Rubino, Jorge German. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Favino, Marco. Universite de Lausanne; SuizaFil: Holliger, Klaus. Universite de Lausanne; Suiza. Zhejiang University; República de Chin

Dalla conoscenza alla conservazione: il territorio della Civita di Tarquinia

Forthcoming