arXiv subjects

Hussein Rappel

Publications and source records attributed to Hussein Rappel.

5 recordsLinked to original sources

arXiv2026

A 2.5D NURBS-Trace Infinite-Element Method for Moving-Load Wave Propagation and Soil--Structure Interaction in Semi-Infinite Ground

For moving-load problems whose geometry and material properties are approximately invariant along the traveling direction, 2.5D analysis retains three displacement components at lower cost than full three-dimensional discretization. We present a 2.5D Non-Uniform Rational B-spline (NURBS)-trace infinite-element method (NBIEM), formulated as a coupled finite/infinite-element scheme, for wave propagation in linear viscoelastic semi-infinite geotechnical media. The bounded near field is discretized by isogeometric analysis, while the exterior is represented by tensor products of the boundary NURBS basis and admissible outgoing or evanescent exponential radial functions. Both subdomains share the same NURBS trace space and control-point degrees of freedom, enforcing displacement continuity without projection or mortar variables. For the selected radial functions, far-field stiffness and mass contributions are evaluated through closed-form radial moments, eliminating finite radial cutoff and radial quadrature. Closed-form half-space solutions verify displacement and stress frequency-response functions in sub-Rayleigh, super-shear but sub-compressional, and super-compressional moving-load regimes. Low-frequency studies assess sensitivity to radial parameters and artificial-boundary placement. Additional tests examine complex-valued response accuracy, phase fidelity, computational cost, and the frequency-dependent working range of the default S-wave-informed exterior realization. Applications to layered media, track--subgrade systems, and buried structures demonstrate the ability to handle heterogeneous materials, multi-patch configurations, curved interfaces, and cover-depth-dependent geotechnical responses. The framework provides a geometrically consistent and computationally efficient treatment of moving-load wave propagation and soil--structure interaction in semi-infinite domains.

cs.CE↗

arXiv2024

Gaussian process regression + deep neural network autoencoder for probabilistic surrogate modeling in nonlinear mechanics of solids

Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-investigated problem, especially when input-output relationships are non-linear. To handle this problem, the present work introduces an innovative approach that combines autoencoder deep neural networks with the probabilistic regression capabilities of Gaussian processes. The autoencoder provides a low-dimensional representation of the solution space, while the Gaussian process is a Bayesian method that provides a probabilistic mapping between the low-dimensional inputs and outputs. We validate the proposed framework for its application to surrogate modeling of non-linear finite element simulations. Our findings highlight that the proposed framework is computationally efficient as well as accurate in predicting non-linear deformations of solid bodies subjected to external forces, all the while providing insightful uncertainty assessments.

cs.CE↗

arXiv2023

A probabilistic peridynamic framework with an application to the study of the statistical size effect

Mathematical models are essential for understanding and making predictions about systems arising in nature and engineering. Yet, mathematical models are a simplification of true phenomena, thus making predictions subject to uncertainty. Hence, the ability to quantify uncertainties is essential to any modelling framework, enabling the user to assess the importance of certain parameters on quantities of interest and have control over the quality of the model output by providing a rigorous understanding of uncertainty. Peridynamic models are a particular class of mathematical models that have proven to be remarkably accurate and robust for a large class of material failure problems. However, the high computational expense of peridynamic models remains a major limitation, hindering outer-loop applications that require a large number of simulations, for example, uncertainty quantification. This contribution provides a framework to make such computations feasible. By employing a Multilevel Monte Carlo (MLMC) framework, where the majority of simulations are performed using a coarse mesh, and performing relatively few simulations using a fine mesh, a significant reduction in computational cost can be realised, and statistics of structural failure can be estimated. The results show a speed-up factor of 16x over a standard Monte Carlo estimator, enabling the forward propagation of uncertain parameters in a computationally expensive peridynamic model. Furthermore, the multilevel method provides an estimate of both the discretisation error and sampling error, thus improving the confidence in numerical predictions. The performance of the approach is demonstrated through an examination of the statistical size effect in quasi-brittle materials.

math.NA↗

arXiv2021

Model selection and sensitivity analysis in the biomechanics of soft tissues: a case study on the human knee meniscus

Soft tissues - such as ligaments and tendons - primarily consist of solid (collagen, predominantly) and liquid phases. Understanding the interaction between such components and how they change under physiological loading sets the basis for elucidating the essential link between their internal structure and mechanical behaviour. In fact, the internal heterogeneous structure of this kind of tissues leads to a wide range of mechanical behaviours, which then determine their own function(s). Characterising these behaviours implies an important experimental effort in terms of tissue harvesting, samples preparation and implementation of testing protocols - which, often, are not standardised. These issues lead to several difficulties in both collecting and providing comparable and reliable information. In order to model the behaviours of heterogeneous tissues and identify material parameters, a large volume of reproducible experimental data is required; unfortunately, such an amount of information is often not available. In reality, most of the studies that are focused on the identification of material parameters, are largely based on small sets of experimental data, which present a large variability. Such a large variability opens on to uncertainties in the estimation of material parameters, as reported in the literature. Hence, the use of a rigorous probabilistic framework, that is able to address uncertainties due to paucity of data, is of paramount importance in the field of biomechanics; in this perspective, Bayesian inference represents a promising approach. This study was focused on the analysis of the knee meniscus as a paradigmatic example of human soft tissue.

physics.med-ph↗

arXiv2017

Bayesian inference for the stochastic identification of elastoplastic material parameters: Introduction, misconceptions and insights

We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material parameters. For this purpose a single spring is considered, for which the stress-strain curves are artificially created. Besides offering a didactic introduction to BI, this paper proposes an approach to incorporate statistical errors both in the measured stresses, and in the measured strains. It is assumed that the uncertainty is only due to measurement errors and the material is homogeneous. Furthermore, a number of possible misconceptions on BI are highlighted based on the purely elastic case.

cs.CE↗