arXiv subjects

Geert Degrande

Publications and source records attributed to Geert Degrande.

5 recordsLinked to original sources

arXiv2026

Reduced order computation of 2D elastodynamic Green's functions in layered soil using a low-rank tensor approximation

The evaluation of elastodynamic Green's functions across numerous source-receiver locations, frequencies, and material properties, particularly in the context of parametric studies or boundary element computations, is computationally demanding and memory intensive. This paper presents a reduced order modeling strategy based on the Greedy Tucker Approximation (GTA), which incrementally constructs a low-rank representation of the Green's tensor through rank-one enrichments obtained via a Proper Generalized Decomposition (PGD)-type alternating least squares procedure. A Petrov-Galerkin formulation is employed to improve convergence and approximation accuracy. The resulting multi-dimensional tensor, expressed in terms of one-dimensional basis functions and a compact core, achieves substantial reductions in memory requirements. The methodology is demonstrated for two cases: a soil layer on rigid bedrock and a layered halfspace. Different separable dimensions are considered to capture various combinations of source and receiver configurations, frequencies, and material parameters. Results are validated against those obtained with the direct stiffness method and computation times and memory requirements are compared.

math.NA↗

arXiv2026

An efficient finite element formulation for Newtonian noise analysis

The Einstein Telescope is a third-generation underground gravitational wave observatory designed to achieve unprecedented sensitivity down to 3 Hz. Waves propagating in the soil due to anthropogenic or natural vibration sources generate density fluctuations which cause gravitational attraction, resulting in motion of the mirrors of the laser interferometer known as Newtonian noise. The latter is computed by integrating density fluctuations due to seismic wave fields over the soil domain surrounding the test mass. A finite element formulation is presented which evaluates the total Newtonian noise, as well as the bulk and surface contributions, from a seismic wave field defined on a finite element mesh using Gaussian quadrature. Linear and quadratic tetrahedral and brick finite elements are supported. The approach computes the total, bulk, and surface contributions, and expresses the corresponding volume and surface integrals in terms of finite element coupling matrices that depend only on geometry and material properties. This allows efficient evaluation of the Newtonian noise for different seismic wave fields without recomputing the integrals. The formulation is verified for plane P- and S-waves propagating in an elastic homogeneous full space with a mirror suspended in a spherical cavity, assuming the wavelength is much larger than the cavity radius, so that wave scattering can be ignored. Similar agreement is reported for the Newtonian noise on a test mass above the free surface of a homogeneous elastic halfspace in which a Rayleigh wave propagates. The methodology has been implemented in the ANNA Newtonian Noise analysis toolbox in MATLAB and is compatible with GNU Octave; a Python version is also available. The proposed finite element framework provides a physically consistent and computationally efficient approach for computing gravitational-seismic coupling in heterogeneous media.

physics.app-ph↗

arXiv2023

Multi-temporal decomposition for elastoplastic ratcheting solids

This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. We leverage the proper generalized decomposition (PGD) to decompose the displacements into multiple time scales, separating the spatial and intra-cyclic dependence from the inter-cyclic variation. In contrast with the standard incremental approach, which solves the (non-linear and computationally intensive) mechanical balance equations at every time step, the proposed PGD approach allows the mechanical balance equations to be solved exclusively for the small-time intra-cyclic response, while the large-time inter-cyclic response is described by simple scalar algebraic equations. Numerical simulations exhibiting complex cyclic responses, including a 2D problem and an application to a monopile foundation, demonstrate that PGD solutions with a limited number of space-time degrees of freedom may be obtained numerically, only requiring a few modes to accurately capture the reference response.

math.NA↗

arXiv2021

A micromechanics-based variational phase-field model for fracture in geomaterials with brittle-tensile and compressive-ductile behavior

This paper presents a framework for modeling failure in quasi-brittle geomaterials under different loading conditions. A micromechanics-based model is proposed in which the field variables are linked to physical mechanisms at the microcrack level: damage is related to the growth of microcracks, while plasticity is related to the frictional sliding of closed microcracks. Consequently, the hardening/softening functions and parameters entering the free energy follow from the definition of a single degradation function and the elastic material properties. The evolution of opening microcracks in tension leads to brittle behavior and mode I fracture, while the evolution of closed microcracks under frictional sliding in compression/shear leads to ductile behavior and mode II fracture. Frictional sliding is endowed with a non-associative law, a crucial aspect of the model that considers the effect of dilation and allows for realistic material responses with non-vanishing frictional energy dissipation. Despite the non-associative law, a variationally consistent formulation is presented using notions of energy balance and stability, following the energetic formulation for rate-independent systems. The material response of the model is first described, followed by the numerical implementation procedure and several benchmark finite element simulations. The results highlight the ability of the model to describe tensile, shear, and mixed-mode fracture, as well as responses with brittle-to-ductile transition. A key result is that, by virtue of the micromechanical arguments, realistic failure modes can be captured, without resorting to the usual heuristic modifications considered in the phase-field literature. The numerical results are thoroughly discussed with reference to previous numerical studies, experimental evidence, and analytical fracture criteria.

cond-mat.mtrl-sci↗

arXiv2019

Phase-field modeling of fatigue coupled to cyclic plasticity in an energetic formulation

This paper presents a modeling framework to describe the driving mechanisms of cyclic failure in brittle and ductile materials, including cyclic plasticity and fatigue crack growth. A variational model is devised using the energetic formulation for rate-independent systems, coupling a phase-field description of fatigue fracture to a cyclic plasticity model that includes multi-surface kinematic hardening, gradient-enhanced isotropic hardening/softening and ratcheting. The coupled model embeds two distinctive fatigue effects. The first captures the characteristic features of low-cycle fatigue, driven by the accumulation of plastic strains, while the second accounts for high-cycle fatigue, driven by free energy accumulation. The interplay between these mechanisms allows to describe a wide range of cyclic responses under both force loading and displacement loading, as shown in several numerical simulations. Moreover, the phase-field approach to fracture accounts for the initiation and propagation of fatigue-induced cracks.

math.NA↗