arXiv subjects

Olaf Kolditz

Publications and source records attributed to Olaf Kolditz.

3 recordsLinked to original sources

arXiv2026

Freezing of a deformable water-saturated porous medium. Part I: THM formulation, OpenGeoSys-6 implementation and benchmarking

In this contribution, Part I, we present a coupled thermo-hydro-mechanical formulation for modeling and analyzing water-to-ice phase change in a deformable fully-saturated porous medium. It is implemented in the multi-physics computational platform OpenGeoSys-6. We compute a series of carefully designed benchmark problems which critically examine the corresponding formulation components and the overall implementation. Several ingredients that have a qualitative and quantitative impact on the numerical results are identified, particularly dissected and commented on. Simulations also account for soil deformation induced by freezing (as a result of 9% volumetric expansion caused by water-to-ice phase transition). The forthcoming Part II will complete the code verification and validation campaign by considering a real full-scale three-dimensional case study of shallow subsurface ice storage. More specifically, we simulate the ice growth process in a fully saturated soil specimen surrounding a group of borehole heat exchangers (BHEs) that contain subzero temperature coolant fluid. A snapshot of the numerical results of this task is already depicted here in Part I as a teaser.

cond-mat.mtrl-sci↗

arXiv2022

Orthogonal decomposition of anisotropic constitutive models for the phase field approach to fracture

We propose a decomposition of constitutive relations into crack-driving and persistent portions, specifically designed for materials with anisotropic/orthotropic behavior in the phase field approach to fracture to account for the tension-compression asymmetry. This decomposition follows a variational framework, satisfying the orthogonality condition for anisotropic materials. This implies that the present model can be applied to arbitrary anisotropic elastic behavior in a three-dimensional setting. On this basis, we generalize two existing models for tension-compression asymmetry in isotropic materials, namely the volumetric-deviatoric model and the no-tension model, towards materials with anisotropic nature. Two benchmark problems, single notched tensile shear tests, are used to study the performance of the present model. The results can retain the anisotropic constitutive behavior and the tension-compression asymmetry in the crack response, and are qualitatively in accordance with the expected behavior for orthotropic materials. Furthermore, to study the direction of maximum energy dissipation, we modify the surface integral based energy release computation, $G_\theta$, to account only for the crack-driving energy. The computed energies with our proposed modifications predict the fracture propagation direction correctly compared with the standard G-theta method.

math.NA↗

arXiv2016

On Advantages of the Kelvin Mapping in Finite Element Implementations of Deformation Processes

Classical continuum mechanical theories operate on three-dimensional Eu-clidian space using scalar, vector, and tensor-valued quantities usually up to the order of four. For their numerical treatment, it is common practice to transform the relations into a matrix-vector format. This transformation is usually performed using the so-called Voigt mapping. This mapping does not preserve tensor character leaving significant room for error as stress and strain quantities follow from different mappings and thus have to be treated differently in certain mathematical operations. Despite its conceptual and notational difficulties having been pointed out, the Voigt mapping remains the foundation of most current finite element programmes. An alternative is the so-called Kelvin mapping which has recently gained recognition in studies of theoretical mechanics. This article is concerned with benefits of the Kelvin mapping in numerical modelling tools such as finite element software. The decisive difference to the Voigt mapping is that Kelvin's method preserves tensor character, and thus the numerical matrix notation directly corresponds to the original tensor notation. Further benefits in numerical implementations are that tensor norms are calculated identically without distinguishing stress or strain-type quantities and tensor equations can be directly transformed into matrix equations without additional considerations. The only implementational changes are related to a scalar factor in certain finite element matrices and hence, harvesting the mentioned benefits comes at very little cost.

physics.comp-ph↗