New article: Castillón, M., Segurado, J. and Romero, I. (2026). A correction method for crack area overestimation in phase-field fracture, Computational Mechanics. (link).

Phase-field fracture models systematically overestimate the crack area, a consequence of the diffuse crack representation and of numerical artifacts such as strain localization, where the phase-field variable saturates artificially across finite elements. In this article we propose a correction framework built on the principle of energy equipartition: as the length-scale parameter vanishes, the contributions of the phase field and of its gradient to the fracture energy become equal. Since the numerical artifacts affect mainly the phase-field term while leaving the gradient term largely unperturbed, the crack area can be approximated as twice the gradient-dependent energy. The resulting estimate is mesh-independent, applies to the whole domain, and extends naturally to three dimensions. The method is validated against benchmarks with analytical solutions, compared with skeletonization algorithms, and applied to complex geometries with curvilinear crack paths and to a three-dimensional simulation.

Today, Miguel Castillón successfully defended his PhD thesis entitled Numerical Methods and Algorithms for Phase-Field Fracture Modeling, co-advised by J. Segurado and Ignacio Romero. Congratulations!

Ignacio Romero gave a talk entitled A regularized formulation of the Neumann problem in elasticity: theory and finite element approximation (with M. A. Kaleem and C. Gebhardt) at the Congress on Numerical Methods in Engineering (CMN 2026) in Gijón, Spain.

Néstor Rossi gave a talk entitled Addressing Remeshing-Induced Internal Variable Diffusion in Solids Using a Mixed Finite Element Approach (with I. Romero) at the Congress on Numerical Methods in Engineering (CMN 2026) in Gijón, Spain.

Yufei Liu gave a talk entitled Bayesian Calibration of Steel Creep Model with ACBICI (with C. Schenk and I. Romero) at the Congress on Numerical Methods in Engineering (CMN 2026) in Gijón, Spain.

A. Kaleen gave a talk entitled Thermomechanical Simulations of Additive Manufacturing Processes with Temperature-Dependent Material Properties (with N. Rossi and I. Romero) at the Congress on Numerical Methods in Engineering (CMN 2026) in Gijón, Spain.

David Portillo gave a talk entitled A Flexible Coupling Strategy for Incompatible Meshes: A Structural-Arlequin Approach (with N. Rossi) at the Congress on Numerical Methods in Engineering (CMN 2026) in Gijón, Spain.

Jacobo Ayensa-Jiménez gave a talk entitled Rate-Independent Epigenetics: A thermodynamically consistent framework for epigenetic evolution at the International Workshop on Perspectives in Nonlinear Continuum Theories (eds. J. Merodio and R. Ogden), held in Castro Urdiales, Spain, June 29 – July 3, 2026. Co-author: I. Romero.

New article: Romero, I. and Ortiz, M. (2026). Identification of optimal history variables and corresponding hereditary laws in linear viscoelasticity, Computer Methods in Applied Mechanics and Engineering, 461, 119122. (link).

In this article, we develop an operator-theoretic formulation of linear hereditary constitutive models and characterize optimal finite-rank internal-variable approximations in the sense of Kolmogorov 𝑁-widths. The history operator is shown to be compact under natural assumptions on the relaxation kernel, thereby admitting optimal low-rank approximations. The resulting reduced models inherit thermodynamic consistency, stability, and provable approximation bounds. An analysis clarifies the structural relation between hereditary representations and internal-variable theories and provides a rigorous basis for reduced-order modelling in computational mechanics. Selected numerical examples showcase optimal convergence of approximations with respect to rank and sampling.

New article: Schenk, C. and Romero, I. (2026). A Framework for the Bayesian Calibration of Complex and Data-Scarce Models in Applied Sciences, Archives of Computational Methods in Engineering. (link).

In this review article, we present a unified framework for the Bayesian calibration of computational models, with particular emphasis on applications involving computationally expensive simulations and scarce experimental data. The article describes four calibration strategies of increasing complexity — covering simple and expensive models, with and without model discrepancy — and introduces ACBICI, a new open-source Python library that implements all of them. The library supports single- and multi-output calibration with Gaussian process surrogates, MCMC and variational inference, and provides practical guidelines for reliable Bayesian calibration in engineering and applied sciences.