arXiv subjects

Stijn François

Publications and source records attributed to Stijn François.

8 recordsLinked to original sources

arXiv2026

Phase-field modeling of cyclic behavior in quasi-brittle materials: A micromechanics-based approach

In this paper, we extend a micromechanics-based phase-field framework for fatigue fracture to incorporate cyclic plasticity with ratcheting. This mechanism is particularly relevant for low-cycle fatigue, where the accumulation of inelastic strains plays a critical role in the progression to final failure. An energetic formulation is proposed in which the ratcheting strain is explicitly incorporated into both the free energy and the dissipation potential. Ratcheting is modeled within a pressure-dependent, non-associative plasticity framework through the evolution of a ratcheting strain that progressively accumulates over loading cycles, capturing the characteristic inelastic strain growth of cyclic plasticity in a thermodynamically consistent manner. The plastic potential is formulated such that the deviatoric and volumetric components of ratcheting can be controlled independently. A staggered solution scheme is employed to solve for the internal variables, including the ratcheting strain. The model is validated through numerical simulations under a wide range of loading conditions, including monotonic and cyclic regimes (stress- and strain-controlled, low- and high-cycle fatigue), enabling evaluation of its performance and the influence of ratcheting on the material response, and demonstrating its applicability to realistic engineering scenarios.

physics.app-ph↗

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↗

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↗

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↗

arXiv2021

On the Selection of Random Field Evaluation Points in the p-MLQMC Method

Engineering problems are often characterized by significant uncertainty in their material parameters. A typical example coming from geotechnical engineering is the slope stability problem where the soil's cohesion is modeled as a random field. An efficient manner to account for this uncertainty is the novel sampling method called p-refined Multilevel Quasi-Monte Carlo (p-MLQMC). The p-MLQMC method uses a hierarchy of p-refined Finite Element meshes combined with a deterministic Quasi-Monte Carlo sampling rule. This combination yields a significant computational cost reduction with respect to classic Multilevel Monte Carlo. However, in previous work, not enough consideration was given how to incorporate the uncertainty, modeled as a random field, in the Finite Element model with the p-MLQMC method. In the present work we investigate how this can be adequately achieved by means of the integration point method. We therefore investigate how the evaluation points of the random field are to be selected in order to obtain a variance reduction over the levels. We consider three different approaches. These approaches will be benchmarked on a slope stability problem in terms of computational runtime. We find that for a given tolerance the Local Nested Approach yields a speedup up to a factor five with respect to the Non-Nested approach.

math.NA↗

arXiv2020

Interior-point methods for the phase-field approach to brittle and ductile fracture

The governing equations of the variational approach to brittle and ductile fracture emerge from the minimization of a non-convex energy functional subject to irreversibility constraints. This results in a multifield problem governed by a mechanical balance equation and evolution equations for the internal variables. While the balance equation is subject to kinematic admissibility of the displacement field, the evolution equations for the internal variables are subject to irreversibility conditions, and take the form of variational inequalities, which are typically solved in a relaxed or penalized way that can lead to deviations of the actual solution. This paper presents an interior-point method that allows to rigorously solve the system of variational inequalities. With this method, a sequence of perturbed constraints is considered, which, in the limit, recovers the original constrained problem. As such, no penalty parameters or modifications of the governing equations are involved. The interior-point method is applied in both a staggered and a monolithic scheme for both brittle and ductile fracture models. In order to stabilize the monolithic scheme, a perturbation is applied to the Hessian matrix of the energy functional. The presented algorithms are applied to three benchmark problems and compared to conventional methods, where irreversibility of the crack phase-field is imposed using a history field or an augmented Lagrangian.

math.NA↗

arXiv2020

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↗