Fredrik Larsson

The classical theory of porous media is based on assumed micro‐homogeneity of the solid phase (skeleton). Based on the drained macroscale elastic stiffness, it is possible to analytically compute auxiliary properties such as the Biot‐Willis and Skempton parameters. The more general case of a micro‐heterogeneous solid phase, which is addressed in this paper, requires computational homogenization of the fluid‐solid interaction. Linearized kinematics is adopted, which is a necessary (but not sufficient) assumption for direct upscaling. Linear elasticity with arbitrary anisotropy is then assigned to the solid skeleton, while the fluid motion is modeled as compressible Stokes' flow. The RVE problem is established based on assumed periodicity for the fluctuation parts of solid displacement, pore pressure and fluid velocity. Although the macroscale problem is transient (quasi‐static), we approximate the RVE‐problem as (micro‐)stationary. The macroscale problem reveals the classical structure with displacements and pore pressure as the unknown fields. It is then possible to rigorously show the particular symmetry that the same Biot‐Willis coefficient appears in the “effective stress principle” as well as in the fluid storage function, thereby generalizing the classical model feature. In the numerical examples, we first verify the classical results for a micro‐isotropic and micro‐homogeneous solid phase. We thereby consider a simplified periodic micro‐architecture, which lends itself to an expected orthotropic macroscale response. Next, we consider a micro‐heterogeneous solid skeleton with inclusions, in which case the classical analysis does not apply.

In this study, long-term rail wear is simulated for a given traffic scenario, and the results are validated using field data. The field data captures the material removal due to wear and grinding. The simulations combine dynamic multibody simulations with a semi-Hertzian contact model and Archard-based wear modeling. To improve the prediction accuracy, a model sensitivity study is combined with the calibration ofcoefficients in an adopted wear map. In the calibration, the computational efficiency is improved by using surrogate models for evaluation of selected objective functions to optimize the wear coefficients of each regime. The resulting simulated profile changes agree well with the field measurements, for those used in the calibration and for traffic levels beyond those.

In this paper, we develop a Numerical Model Reduction (NMR) framework for multi‐scale modeling of electro‐chemically coupled ion transport. Upon introducing the governing equations and employing Variationally Consistent Homogenization, a two‐scale model, consisting of a macro‐scale and a sub‐scale part, is obtained. Instead of solving for the computationally expensive FE ² simulation, where the macro‐scale and sub‐scale problems are solved in a nested fashion, we exploit NMR by training a surrogate model that replaces the sub‐scale finite element simulations. The surrogate model is trained by performing Proper Orthogonal Decomposition on snapshots of the primary fields. Each macro‐scale quadrature point is no longer occupied by a Representative Volume Element simulation; instead, it is replaced by a surrogate model that consists of a system of Ordinary Differential Equations. In this way, a computationally efficient solution scheme for solving two‐scale problems is obtained.

In this article, the influence of large deformations on the effective permeability of a bicontinuous porous material is investigated. On the fine‐scale, Neo–Hooke hyperelasticity is considered for the solid skeleton. In a third medium approach, we model the pore space as filled with a softer material of the same type. Fluid flow through the deformed pores is expressed in terms of a Stokes' flow model. The influence of the pore pressure on the deformation is neglected, resulting in a one‐way coupling which allows for a sequential solution of the two physical problems. The framework of Variationally Consistent Homogenization is used to derive a two‐scale formulation based on a Representative Volume Element (RVE) characterizing the microstructure. Finally, a two‐step procedure to compute the deformation dependent permeability is established: Firstly, the deformation of the RVE for a given macroscale deformation gradient is computed. Secondly, sensitivities for the fluid flow through the deformed RVE are computed and used to determine the effective permeability tensor. A numerical study is conducted for sets of RVEs with the same material parameters and different porosity. For the case of uniaxial compression, a significant influence of the deformation on the effective permeability is observed: For a macroscale compression of , the effective permeability orthogonal to the compression direction is reduced by almost .