arXiv subjects

Bruno A. Roccia

Publications and source records attributed to Bruno A. Roccia.

5 recordsLinked to original sources

arXiv2026

A data-driven solving strategy based on a greedy optimization algorithm for the analysis of nonlinear beam structures

In the last decade, data-driven computational mechanics (DDCM) has emerged as a novel paradigm in computational mechanics, enabling the direct use of constitutive data - such as stress-strain pairs obtained from experiments, without relying on ad-hoc material models and thereby avoiding information loss. In this work, we extend our data-driven solving strategy GO-ADM, which combines a greedy optimization algorithm with the alternating direction method (ADM), to the structural analysis of geometrically exact beams formulated using director-based kinematics. We discuss a data initialization strategy for nonlinear systems based on a conventional finite element analysis of the same structure using a prescribed constitutive model. The resulting discrete stress and strain fields, possibly obtained under multiple loading scenarios, may also be employed as artificial datasets for the subsequent data-driven computations. Furthermore, we investigate the thermomechanical consistency of both the dataset and the discrete solution, and propose a weak enforcement of this consistency in the latter via a penalty approach. Numerical examples involving single- and multi-member structures demonstrate that the proposed penalty term leads to thermomechanically consistent discrete stress and strain fields. Moreover, for the studied examples, the solving strategy GO-ADM yields a generally improved approximation of the globally optimal solution compared to the standard ADM-based direct solver.

cs.CE↗

arXiv2026

Solving strategies for data-driven one-dimensional elasticity exhibiting nonlinear strains

In this work, we extend and generalize our solving strategy, first introduced in [1], based on a greedy optimization algorithm and the alternating direction method (ADM) for nonlinear systems computed with multiple load steps. In particular, we combine the greedy optimization algorithm with the direct data-driven solver based on ADM which is firstly introduced in [2] and combined with the Newton-Raphson method for nonlinear elasticity in [3]. We numerically illustrate via one- and two-dimensional bar and truss structures exhibiting nonlinear strain measures and different constitutive datasets that our solving strategy generally achieves a better approximation of the globally optimal solution. This, however, comes at the expense of higher computational cost which is scaled by the number of "greedy" searches. Using this solving strategy, we reproduce the first cycle of the cyclic testing for a nylon rope that was performed at industrial testing facilities for mooring lines manufacturers. We also numerically illustrate for a truss structure that our solving strategy generally improves the accuracy and robustness in cases of an unsymmetrical data distribution and noisy data.

cs.CE↗

arXiv2025

A study on nodal and isogeometric formulations for nonlinear dynamics of shear- and torsion-free rods

In this work, we compare the nodal and isogeometric spatial discretization schemes for the nonlinear formulation of shear- and torsion-free rods introduced in [1]. We investigate the resulting discrete solution space, the accuracy, and the computational cost of these spatial discretization schemes. To fulfill the required C1 continuity of the rod formulation, the nodal scheme discretizes the rod in terms of its nodal positions and directors using cubic Hermite splines. Isogeometric discretizations naturally fulfill this with smooth spline basis functions and discretize the rod only in terms of the positions of the control points [2], which leads to a discrete solution in multiple copies of the Euclidean space R3. They enable the employment of basis functions of one degree lower, i.e. quadratic C1 splines, and possibly reduce the number of degrees of freedom. When using the nodal scheme, since the defined director field is in the unit sphere S2, preserving this for the nodal director variable field requires an additional constraint of unit nodal directors. This leads to a discrete solution in multiple copies of the manifold R3xS2, however, results in zero nodal axial stress values. Allowing arbitrary length for the nodal directors, i.e. a nodal director field in R3 instead of S2 as within discrete rod elements, eliminates the constrained nodal axial stresses and leads to a discrete solution in multiple copies of R3. To enforce the unit nodal director constraint, we discuss two approaches using the Lagrange multiplier and penalty methods. We compare the resulting semi-discrete formulations and the computational cost of these discretization variants. We numerically demonstrate our findings via examples of a planar roll-up, a catenary, and a mooring line.

math.NA↗

arXiv2025

On the use of an advanced Kirchhoff rod model to study mooring lines

In this work, we investigate the application of an advanced nonlinear torsion- and shear-free Kirchhoff rod model, enhanced with a penalty-based barrier function (to simulate the seabed contact), intended for studying the static and dynamic behavior of mooring lines. The formulation incorporates conservative and non-conservative external loads, including those coming from the surrounding flow (added mass, tangential drag, and normal drag). To illustrate the favorable features of this model, we consider some key scenarios such as static configurations, pulsating force applications at the fairlead, and fluid-structure interaction between mooring lines and the surrounding flow. Verification against well-established solutions, including catenary configurations and OpenFAST simulations, shows excellent accuracy in predicting mooring line responses for a floating offshore wind turbine. Among the most important results, we can mention that under normal pulsating loads at the fairlead, the mooring line exhibits a transition from a drag-dominated regime at low frequencies to an added-mass-dominated regime at higher frequencies. Furthermore, tangential forcing at the fairlead reveals a strong coupling between axial and bending dynamics, contrasting with normal forcing scenarios where axial dynamics remain largely unaffected. These findings underscore the potential of the proposed approach for advanced mooring line simulations.

physics.flu-dyn↗

arXiv2024

Nonlinear dynamic analysis of shear- and torsion-free rods using isogeometric discretization and outlier removal

In this paper, we present a discrete formulation of nonlinear shear- and torsion-free rods introduced by Gebhardt and Romero in [20] that uses isogeometric discretization and robust time integration. Omitting the director as an independent variable field, we reduce the number of degrees of freedom and obtain discrete solutions in multiple copies of the Euclidean space (R^3), which is larger than the corresponding multiple copies of the manifold (R^3 x S^2) obtained with standard Hermite finite elements. For implicit time integration, we choose the same integration scheme as Gebhardt and Romero in [20] that is a hybrid form of the midpoint and the trapezoidal rules. In addition, we apply a recently introduced approach for outlier removal by Hiemstra et al. [26] that reduces high-frequency content in the response without affecting the accuracy, ensuring robustness of our nonlinear discrete formulation. We illustrate the efficiency of our nonlinear discrete formulation for static and transient rods under different loading conditions, demonstrating good accuracy in space, time and the frequency domain. Our numerical example coincides with a relevant application case, the simulation of mooring lines.

cs.CE↗