Investigation of the Fatigue Stress of Orthotropic Steel Decks Based on an Arch Bridge with the Application of the Arlequin Method

Orthotropic steel decks are widely used in the construction of steel bridges. Although there are many fatigue-evaluation methods stipulated by codes, unexpected fatigue cracks are still detected in some bridges. To justify whether the local finite element model commonly used in fatigue investigations on orthotropic decks can correctly instruct engineering practices, the Arlequin framework is applied in this paper to determine the full fatigue stress under traffic loads. The convergence on and validity of this application for orthotropic decks are checked. Results show that the Arlequin model for deck-fatigue analysis established in this paper tends to be an efficient method for complete fatigue stress acquisition, whereby the vulnerable sites of orthotropic steel decks under traffic loads are defined. Vehicles near the flexible components, such as hangers or cables, can have adverse effects on the fatigue durability of decks. Additionally, the total number of vehicles and their arrangement concentration also affect fatigue performance. Complex traffic conditions cannot be fully loaded in local models. Regardless of the gross bridge mechanics and deck deformation, the fatigue stress range is underestimated by about 30–40%. Such a difference in fatigue assessment seems to explain the premature cracks observed in orthotropic steel decks.

A multiscale DEM–FEM coupled approach for the investigation of granules as crash-absorber in ship building

This paper covers a numerical analysis of a novel approach to increasing the crashworthiness of double hull ships. As proposed in Schöttelndreyer (Füllstoffe in der Konstruktion: ein Konzept zur Verstärkung vonSchiffsseitenhüllen, Technische Uni-versitt Hamburg, Hamburg, 2015), it involves the usage of granular materials in the cavity of the double hull ship. For the modeling of this problem, the discrete element method (DEM) is used for the granules while the finite element method is used for the ship’s structure. In order to account for the structural damage caused by collision, a gradient-enhanced ductile damage model is implemented. In addition to avoid locking, an enhanced strain-based formulation is used. For large-scale problems such as the one in the current study, modeling of all granules with realistic size can be computationally expensive. A two-scale model based on the work of Wellmann and Wriggers (Comput Methods Appl Mech Eng 205:46–58, 2012) is applied—and the region of significant localization is modeled with the DEM, while a continuum model is used for the other regions. The coupling of both discretization schemes is based on the Arlequin method. Numerical homogenization is used to estimate the material parameters of the continuum region with the granules. This involves the usage of meshless interpolation functions for the projection of particle displacement and stress onto a background mesh. Later, the volume-averaged stress and strain within the representative volume element is used to estimate the material parameters. At the end, the results from the combined numerical model are compared with the results from the experiments given in Woitzik and Düster (Ships Offshore Struct 1–12, 2020). This validates both the accuracy of the numerical model and the proposed idea of increasing the crashworthiness of double hull vessels with the granular materials.

Study of Spurious Wave Reflection at the Interface of Peridynamics and Finite Element Regions

Peridynamics ability to model crack as a material response removes deficiencies associated with using classical continuum-based methods in modeling discontinuities. Due to its nonlocal formulation, however, peridynamics is computationally more expensive than the classical continuum-based numerical methods such as finite element method. To reduce the computational cost, peridynamics can be coupled with finite element method. In this method, peridynamics is used only in critical areas such as the vicinity of crack tip and finite element method is used everywhere else. The main issue associated with such coupling methods is the spurious wave reflections occurring at the interface of peridynamics and finite elements. High frequency waves traveling from peridynamics to finite element spuriously reflect back at the interface and the amplitude of transmitted waves also alter. In this paper, we take an analytical approach to study this phenomenon of spurious reflections. We study the impact of factors such as horizon size of peridynamic formulation, discretization, and change in mesh size on the amplitude of spuriously reflected waves. Finally, we present a method to reduce these spurious reflections by using Arlequin method.

Computing Flatness Defects in Sheet Rolling by Arlequin and Asymptotic Numerical Methods

Rolling of thin sheets generally induces flatness defects due to thermo-elastic deformation of rolls. This leads to heterogeneous plastic deformations throughout the strip width and then to out of plane displacements to relax residual stresses. In this work we present a new numerical technique to model the buckling phenomena under residual stresses induced by rolling process. This technique consists in coupling two finite element models: the first one consists in a three dimensional model based on 8-node tri-linear hexahedron which is used to model the three dimensional behaviour of the sheet in the roll bite; we introduce in this model, residual stresses from a full simulation of rolling (a plane-strain elastoplastic finite element model) or from an analytical profile. The second model is based on a shell formulation well adapted to large displacements and rotations; it will be used to compute buckling of the strip out of the roll bite. We propose to couple these two models by using Arlequin method. The originality of the proposed algorithm is that in the context of Arlequin method, the coupling area varies during the rolling process. Furthermore we use the asymptotic numerical method (ANM) to perform the buckling computations taking into account geometrical nonlinearities in the shell model. This technique allows one to solve nonlinear problems using high order algorithms well adapted to problems in the presence of instabilities. The proposed algorithm is applied to some rolling cases where “edges-waves” and “center-waves” defects of the sheet are observed.