Pablo Antolin

John-Eric Dufour, Pablo Antolin, Giancarlo Sangalli et al.

This paper introduces a cost-effective strategy to simulate the behavior of laminated plates by means of isogeometric 3D solid elements. Exploiting the high continuity of spline functions and their properties, a proper out-of-plane stress state is recovered from a coarse displacement solution using a post-processing step based on the enforcement of equilibrium in strong form. Appealing results are obtained and the method is shown to be particularly Peffective on slender composite stacks with a large number of layers.

Pablo Antolin, Annalisa Buffa, Mathieu Fabre

In this paper, we consider unilateral contact problem without friction between a rigid body and deformable one in the framework of isogeometric analysis. We present the theoretical analysis of the mixed problem using an active-set strategy and for a primal space of NURBS of degree $p$ and $p-2$ for a dual space of B-Spline. A inf-sup stability is proved to ensure a good property of the method. An optimal a priori error estimate is demonstrated without assumption on the unknown contact set. Several numerical examples in two- and three-dimensional and in small and large deformation demonstrate the accuracy of the proposed method.

Gonzalo Bonilla Moreno, Giuliano Guarino, Pablo Antolin

We present a domain decomposition method for the fast simulation of large lattice structures described by level set functions. The method does not rely on homogenization or multiscale techniques, and therefore avoids their underlying assumptions such as scale separation and periodicity. Individual cells are defined through level set functions and mapped into physical space using arbitrary order mappings, allowing the creation of complex graded designs with varying geometries and topologies. The discretization is based on unfitted p-FEM, where each cell is approximated by a single high order element. This choice naturally handles the implicit geometric description and provides high accuracy with a moderate number of degrees of freedom. The solver is built on the Balanced Domain Decomposition by Constraints (BDDC) method, where each cell corresponds to one subdomain. To accelerate the assembly of the cell stiffness matrices, we combine a fast assembly technique that separates the contributions of the geometric mapping from the trimmed domain with a reduced order model (ROM) based on the matrix discrete empirical interpolation method (MDEIM). The ROM surrogate is trained offline and reused for any geometric mapping, restricting the expensive quadrature on cut elements to the training stage. A stabilization term ensures the scalability of the solver when using the ROM approximation, at the cost of a small and controllable error. We validate the method through numerical experiments and demonstrate its performance on a complex 2D problem with more than 17,000 cells of varying geometry, solved in approximately 30 seconds on a standard laptop. The number of solver iterations remains bounded as the number of subdomains grows, provided the ratio between subdomain and mesh sizes is kept constant, in agreement with classical BDDC scalability properties.

Yannis Voet, Matthias Möller, Pablo Antolin et al.

Trimming is a ubiquitous operation in computer-aided-design whereby parts of a geometry are merged, intersected, or simply discarded. While it grants virtually unlimited flexibility in geometric design, it introduces a plethora of other difficulties when such geometries are used within immersed finite element methods. In particular, small cut elements lead to severely ill-conditioned system matrices requiring dedicated penalization, stabilization, or preconditioning techniques. In this work, we highlight the limitations of existing preconditioning strategies by first carefully examining the condition number of the diagonally scaled matrix and later providing realistic counter-examples for some well-established preconditioning strategies. Building on those insights, we propose a robust deflation-based preconditioning technique tailored to immersed finite element methods.

Ignacio G. Tejada, Pablo Antolin

A data-driven framework was used to predict the macroscopic mechanical behavior of dense packings of polydisperse granular materials. The Discrete Element Method, DEM, was used to generate 92,378 sphere packings that covered many different kinds of particle size distributions, PSD, lying within 2 particle sizes. These packings were subjected to triaxial compression and the corresponding stress-strain curves were fitted to Duncan-Chang hyperbolic models. A multivariate statistical analysis was unsuccessful to relate the model parameters with common geotechnical and statistical descriptors derived from the PSD. In contrast, an artificial Neural Network (NN) scheme, trained with a few hundred DEM simulations, was able to anticipate the value of the model parameters for all these PSDs, with considerable accuracy. This was achieved in spite of the presence of noise in the training data. The NN revealed the existence of hidden correlations between PSD of granular materials and their macroscopic mechanical behavior.