arXiv subjects

Andrés A León Baldelli

Publications and source records attributed to Andrés A León Baldelli.

2 recordsLinked to original sources

arXiv2024

Variational Solvers for Irreversible Evolutionary Systems

We study irreversible evolutionary processes with a general energetic notion of stability. We dedicate this contribution to releasing three nonlinear variational solvers as modular components (based on FEniCSx/dolfinx) that address three mathematical optimisation problems. They are general enough to apply, in principle, to evolutionary systems with instabilities, jumps, and emergence of patterns which is commonplace in diverse arenas spanning from quantum to continuum mechanics, economy, social sciences, and ecology. Our motivation proceeds from fracture mechanics, with the ultimate goal of deploying a transparent numerical platform for scientific validation and prediction of large scale natural fracture phenomena. Our solvers are used to compute one solution to a problem encoded in a system of two inequalities: one (pointwise almost-everywhere) constraint of irreversibility and one global energy statement. As part of our commitment to open science, our solvers are released as free software.

math.AP↗

arXiv2014

On the asymptotic derivation of Winkler-type energies from 3D elasticity

We show how bilateral, linear, elastic foundations (i.e. Winkler foundations) often regarded as heuristic, phenomenological models, emerge asymptotically from standard, linear, three-dimensional elasticity. We study the parametric asymptotics of a non-homogeneous linearly elastic bi-layer attached to a rigid substrate as its thickness vanishes, for varying thickness and stiffness ratios. By using rigorous arguments based on energy estimates, we provide a first rational and constructive justification of reduced foundation models. We establish the variational weak convergence of the three-dimensional elasticity problem to a two-dimensional one, of either a "membrane over in-plane elastic foundation", or a "plate over transverse elastic foundation". These two regimes are function of the only two parameters of the system, and a phase diagram synthesizes their domains of validity. Moreover, we derive explicit formulae relating the effective coefficients of the elastic foundation to the elastic and geometric parameters of the original three-dimensional system.

math-ph↗