Challenges of porous media models in geo- and biomechanical engineering including electro-chemically active polymers and gels

Self Cite

Originated from a lung tumour, cancer cells can spread via the blood-vessel system, travel to the cerebrum and may pass the blood-brain barrier. The extravasation is followed by migration, and the formation of micrometastases. Further proliferation causes interveined metastases. A pressure-driven infusion of a therapeutic solution counteracts the disturbance by the metastases within the brain. These processes are described with a continuum-mechanical model based on the Theory of Porous Media. Numerical applications demonstrate the feasibility of the model and include multicellular-tumour spheroid experiments in the macroscopic simulation of metastases growth and atrophy.

“…[3]. Therein, the processes on the microstructure are volumetrically homogenised over a representative element volume (REV) yielding a macroscopic multi-component model, cf.…”

Section: Continuum-mechanical Modelling Approachmentioning

confidence: 99%

Multi‐component modelling and simulation of metastases proliferation within brain tissue

Schröder

Wagner

Ehlers

2016

Self Cite

“…Here, the developed constitutive model is based on the well-founded TPM. Therefore, a homogenisation process over a representative elementary volume (REV) is performed, see [2]. The balance relations are derived in analogy to the balance relations of classical, singlephasic continuum mechanics but allow for interactions between the constituents by so-called production terms.…”

Section: Modelling Approachmentioning

confidence: 99%

“…In order to evaluate the overall response of these materials, a macroscopic continuum-mechanical modelling approach is used. Therefore, the complex inner structure is regarded in a multi-phasic and multi-component manner by means of the TPM, see [2]. The mechanical behaviour is solved using the FEM, see [3].…”

Section: Introductionmentioning

confidence: 99%

Application and modification of the POD method and the POD‐DEIM for model reduction in porous‐media simulations

Fink¹,

Ehlers²

2015

Self Cite

Researchers with a continuum-mechanical background typically use a multi-phasic and multi-component modelling approach for materials with a saturated porous microstructure. Therefore, the mechanical behaviour is considered in a continuummechanical manner and solved using the finite-element method (FEM). The developed models need to be complex enough to capture the relevant properties of the considered materials, what often results in expensive simulations with a very large number of degrees of freedom (DOF). The aim of the present contribution is to reduce the computing time of these simulations through model-reduction methods, while the accuracy of the solution needs to be maintained. Therefore, the method of properorthogonal decomposition (POD) for linear problems and the discrete-empirical-interpolation method (DEIM) in combination with the POD method (POD-DEIM) for nonlinear problems are investigated.Using the POD method, a given data set is approximated with a low-dimensional subspace. To generate this data set, the vector of unknowns of the FE simulation is stored in a pre-computation in the full (unreduced) system in each time-step (so-called "snapshots" of the system). Dealing with porous-media problems, the primary variables are the solid displacement, the pore pressure and, depending on the particular problem, other primary variables. Following this, the primary variables have entries with very huge differences in their absolute values. As a result, non-negligible rounding errors may occur when applying the POD method. To overcome this problems, modifications of the classical POD method need to be performed for such problems. The present contribution discusses this issue and presents results for the reduced simulations of porous media.

“…However, a detailed micro-mechanical modelling exhibits the drawback that all geometrical and physical conditions of the individual parts of the complex macroscopic aggregate have to be known. Therefore, we rather proceed from a macroscopic continuum-mechanical modelling approach, which is based on the well-founded Theory of Porous Media (TPM), cf., e. g., [2] and citations therein. The ternary bone-cement-injection model, described in [1], is basically constituted via…”

Section: Multicomponent Modelling Approach For Bone-cement Injectionsmentioning

confidence: 99%

“…In Equation (2) 2 , the overall Cauchy stress T = T S E −p I contains the overall pore pressure p = s C p CR +s M p M R . The solid extra-stress T S E is described by an isotropic finite Neo-Hookean elasticity law, cf., e. g., [2]. Finally, a constitutive equation to specify the pore-liquid volume fractions n C and n M from the porosity n…”

Section: Multicomponent Modelling Approach For Bone-cement Injectionsmentioning

confidence: 99%

Porous‐media simulation of bone‐cement spreading during vertebroplasty

Wagner¹,

Bleiler²,

Stadelmann

et al. 2013

Self Cite

The reinforcement of porous vertebral cancellous bone by the injection of bone cement is a practical procedure for the stabilisation of osteoporotic compression fractures and other weakening lesions. This contribution concerns the reproduction and prediction of the resulting bone-cement distribution during the injection procedure by means of numerical simulation. A detailed micromechanical (locally single-phasic) model exhibits the drawback that all geometrical and physical transition conditions of the individual parts of the complex aggregate have to be known. Therefore, we rather proceed from a macroscopic (and multi-constituent) continuum-mechanical model based on the Theory of Porous Media. In this regard, the homogenisation of the underlying micro-structure results in a model of three constituents: these are the solid bone skeleton, which is saturated by the liquid bone marrow that may be displaced by the injected liquid bone cement. The influence of the microarchitecture of the pore space on the spreading of the bone cement is considered by a spatial diversification of the anisotropic permeability tensors, obtained through image processing techniques applied to medical imaging data (µCT). The numerical investigation of the strongly coupled problem enables the study of vertebroplasty and allows for the comparison between the simulation results and the experimentally determined bone-cement distribution that were imaged during injections.