3,205 research outputs found
Multi-compartment poroelastic models of perfused biological soft tissues: implementation in FEniCSx
Soft biological tissues demonstrate strong time-dependent and strain-rate
mechanical behavior, arising from their intrinsic visco-elasticity and
fluid-solid interactions (especially at sufficiently large time scales). The
time-dependent mechanical properties of soft tissues influence their
physiological functions and are linked to several pathological processes.
Poro-elastic modeling represents a promising approach because it allows the
integration of multiscale/multiphysics data to probe biologically relevant
phenomena at a smaller scale and embeds the relevant mechanisms at the larger
scale. The implementation of multi-phasic flow poro-elastic models however is a
complex undertaking, requiring extensive knowledge. The open-source software
FEniCSx Project provides a novel tool for the automated solution of partial
differential equations by the finite element method. This paper aims to provide
the required tools to model the mixed formulation of poro-elasticity, from the
theory to the implementation, within FEniCSx. Several benchmark cases are
studied. A column under confined compression conditions is compared to the
Terzaghi analytical solution, using the L2-norm. An implementation of
poro-hyper-elasticity is proposed. A bi-compartment column is compared to
previously published results (Cast3m implementation). For all cases, accurate
results are obtained in terms of a normalized Root Mean Square Error (RMSE).
Furthermore, the FEniCSx computation is found three times faster than the
legacy FEniCS one. The benefits of parallel computation are also highlighted.Comment: https://github.com/Th0masLavigne/Dolfinx_Porous_Media.gi
Love Wave Propagation in Poro elasticity
It is observed that on similar reasons as in classical theory of elasticity, SH wave propagation in a semi infinite poroelastic body is not possible and is possible when there is a layer of another poro elastic medium over it i.e., Love waves. Two particular cases are considered in one of which phase velocity can be determined for a given wave length. In the same case, equation for phase velocity is of the same form as that of the classical theory of Elasticity
Coupling of flow, contact mechanics and friction, generating waves in a fractured porous medium
We present a mixed dimensional model for a fractured poro-elasic medium
including contact mechanics. The fracture is a lower dimensional surface
embedded in a bulk poro-elastic matrix. The flow equation on the fracture is a
Darcy type model that follows the cubic law for permeability. The bulk
poro-elasticity is governed by fully dynamic Biot equations. The resulting
model is a mixed dimensional type where the fracture flow on a surface is
coupled to a bulk flow and geomechanics model. The particularity of the work
here is in considering fully dynamic Biot equation, that is, including an
inertia term, and the contact mechanics including friction for the fracture
surface. We prove the well-posedness of the continuous model
Finite-strain poro-visco-elasticity with degenerate mobility
A quasistatic nonlinear model for poro-visco-elastic solids at finite strains is considered in the Lagrangian frame using the concept of second-order nonsimple materials. The elastic stresses satisfy static frame-indifference, while the viscous stresses satisfy dynamic frame-indifference. The mechanical equation is coupled to a diffusion equation for a solvent or fluid content. The latter is pulled-back to the reference configuration. To treat the nonlinear dependence of the mobility tensor on the deformation gradient, the result by Healey & Krömer is used to show that the determinant of the deformation gradient is bounded away from zero. Moreover, the focus is on the physically relevant case of degenerate mobilities. The existence of weak solutions is shown using a staggered time-incremental scheme and suitable energy-dissipation inequalities
The role of structural viscoelasticity in deformable porous media with incompressible constituents: applications in biomechanics
The main goal of this work is to clarify and quantify, by means of
mathematical analysis, the role of structural viscoelasticity in the
biomechanical response of deformable porous media with incompressible
constituents to sudden changes in external applied loads. Models of deformable
porous media with incompressible constituents are often utilized to describe
the behavior of biological tissues, such as cartilages, bones and engineered
tissue scaffolds, where viscoelastic properties may change with age, disease or
by design. Here, for the first time, we show that the fluid velocity within the
medium could increase tremendously, even up to infinity, should the external
applied load experience sudden changes in time and the structural
viscoelasticity be too small. In particular, we consider a one-dimensional
poro-visco-elastic model for which we derive explicit solutions in the cases
where the external applied load is characterized by a step pulse or a
trapezoidal pulse in time. By means of dimensional analysis, we identify some
dimensionless parameters that can aid the design of structural properties
and/or experimental conditions as to ensure that the fluid velocity within the
medium remains bounded below a certain given threshold, thereby preventing
potential tissue damage. The application to confined compression tests for
biological tissues is discussed in detail. Interestingly, the loss of
viscoelastic tissue properties has been associated with various disease
conditions, such as atherosclerosis, Alzheimer's disease and glaucoma. Thus,
the findings of this work may be relevant to many applications in biology and
medicine
Temperature induced pore fluid pressurization in geomaterials
The theoretical basis of the thermal response of the fluid-saturated porous
materials in undrained condition is presented. It has been demonstrated that
the thermal pressurization phenomenon is controlled by the discrepancy between
the thermal expansion of the pore fluid and of the solid phase, the
stress-dependency of the compressibility and the non-elastic volume changes of
the porous material. For evaluation of the undrained thermo-poro-elastic
properties of saturated porous materials in conventional triaxial cells, it is
important to take into account the effect of the dead volume of the drainage
system. A simple correction method is presented to correct the measured pore
pressure change and also the measured volumetric strain during an undrained
heating test. It is shown that the porosity of the tested material, its drained
compressibility and the ratio of the volume of the drainage system to the one
of the tested sample, are the key parameters which influence the most the error
induced on the measurements by the drainage system. An example of the
experimental evaluation of undrained thermoelastic parameters is presented for
an undrained heating test performed on a fluid-saturated granular rock
Stress dependent thermal pressurization of a fluid-saturated rock
Temperature increase in saturated porous materials under undrained conditions
leads to thermal pressurization of the pore fluid due to the discrepancy
between the thermal expansion coefficients of the pore fluid and of the solid
matrix. This increase in the pore fluid pressure induces a reduction of the
effective mean stress and can lead to shear failure or hydraulic fracturing.
The equations governing the phenomenon of thermal pressurization are presented
and this phenomenon is studied experimentally for a saturated granular rock in
an undrained heating test under constant isotropic stress. Careful analysis of
the effect of mechanical and thermal deformation of the drainage and pressure
measurement system is performed and a correction of the measured pore pressure
is introduced. The test results are modelled using a non-linear
thermo-poro-elastic constitutive model of the granular rock with emphasis on
the stress-dependent character of the rock compressibility. The effects of
stress and temperature on thermal pressurization observed in the tests are
correctly reproduced by the model
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