Journal: European Journal of Mechanics - A/Solids

Abbreviation

Eur. J. Mech. A. Solids

Publisher

Elsevier

Journal Volumes

ISSN

0997-7538
1873-7285

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Publications 1 - 10 of 10
  • Bifurcation phenomena in non-smooth dynamical systems
    Item type: Conference Paper
    Leine, R. I.; Campen, D. H. van (2006)
    European Journal of Mechanics - A/Solids
  • Physics-Informed Neural Networks for shell structures
    Item type: Journal Article
    Bastek, Jan-Hendrik; Kochmann, Dennis M. (2023)
    European Journal of Mechanics - A/Solids
    The numerical modeling of thin shell structures is a challenge, which has been met by a variety of finite element method (FEM) and other formulations—many of which give rise to new challenges, from complex implementations to artificial locking. As a potential alternative, we use machine learning and present a Physics-Informed Neural Network (PINN) to predict the small-strain response of arbitrarily curved shells. To this end, the shell midsurface is described by a chart, from which the mechanical fields are derived in a curvilinear coordinate frame by adopting Naghdi’s shell theory. Unlike in typical PINN applications, the corresponding strong or weak form must therefore be solved in a non-Euclidean domain. We investigate the performance of the proposed PINN in three distinct scenarios, including the well-known Scordelis–Lo roof setting widely used to test FEM shell elements against locking. Results show that the PINN can accurately identify the solution field in all three benchmarks if the equations are presented in their weak form, while it may fail to do so when using the strong form. In the small-thickness limit, where classical methods are susceptible to locking, training time notably increases as the differences in scaling of the membrane, shear, and bending energies lead to adverse numerical stiffness in the gradient flow dynamics. Nevertheless, the PINN can accurately match the ground truth and performs well in the Scordelis–Lo roof benchmark, highlighting its potential for a drastically simplified alternative to designing locking-free shell FEM formulations.
  • Failure of topologically interlocked structures — a Level-Set-DEM approach
    Item type: Journal Article
    Feldfogel, Shai; Karapiperis, Konstantinos; Andrade, Jose; et al. (2024)
    European Journal of Mechanics - A/Solids
    Topological Interlocking Structures (TIS) are assemblies of interlocking building blocks that hold together solely through contact and friction at the block interfaces and thus do not require any connective elements. This salient feature makes them highly energy-absorbent, resistant to crack propagation, geometrically versatile, and reusable. It also gives rise to failure mechanisms that, differently from ordinary structures, are governed by multiple contact interactions between blocks and frictional slip at their interfaces. Commonly-used modeling tools for structural analysis struggle to capture and quantify these unusual failure mechanisms. Here, we propose a different approach that is well-suited for modeling the complex failure of slab-like TIS. It is based on the Level-Set-Discrete-Element-Method, which was originally developed for granular mechanics applications. After introducing the basic assumptions and theoretical concepts underlying our model, we show that it accurately captures the slip-governed failure of slab-like TIS panels as observed in the literature, that it can closely estimate the force–displacement curves, and that it is can be used to explore important features governing the structural mechanics of TIS. The theoretical foundation, together with the results of this study, provide a proof-of-concept for our new approach and point to its potential to improve our ability to model and understand the behavior of interlocked structural forms.
  • Prediction of shear-dominated ductile fracture in a butterfly specimen using a model of plastic porous solids including void shape effects
    Item type: Journal Article
    Morin, Léo; Leblond, Jean-Baptiste; Mohr, Dirk; et al. (2017)
    European Journal of Mechanics - A/Solids
  • A set-valued force law for spatial Coulomb-Contensoufriction
    Item type: Journal Article
    Leine, R. I.; Glocker, Ch. (2003)
    European Journal of Mechanics - A/Solids
  • Finite Element simulation of dense wire packings
    Item type: Journal Article
    Vetter, Roman; Wittel, Falk K.; Stoop, Norbert; et al. (2013)
    European Journal of Mechanics - A/Solids
  • Damage preserving transformation for materials with microstructure
    Item type: Journal Article
    Müller, Philip P.; Wittel, Falk K.; Kammer, David S. (2023)
    European Journal of Mechanics - A/Solids
    The failure of heterogeneous materials with microstructures is a complex process of damage nucleation, growth and localisation. This process spans multiple length scales and is challenging to simulate numerically due to its high computational cost. One option is to use domain decomposed multi-scale methods with dynamical refinement. If needed, these methods refine coarse regions into a fine-scale representation to explicitly model the damage in the microstructure. However, damage evolution is commonly restricted to fine-scale regions only. Thus, they are unable to capture the full complexity and breath of the degradation process in the material. In this contribution, a generic procedure that allows to account for damage in all representations is proposed. The approach combines a specially designed orthotropic damage law, with a scheme to generate pre-damaged fine-scale microstructures. Results indicate that the damage approximation for the coarse representation works well. Furthermore, the generated fine-scale damage patterns are overall consistent with explicitly simulated damage patterns. Minor discrepancies occur in the generation but subsequently vanish when explicit damage evolution continuous; for instance under increased load. The presented approach provides a methodological basis for adaptive multi-scale simulation schemes with consistent damage evolution.
  • Size effect in true mode II fracturing of rocks: Theory and experiment
    Item type: Journal Article
    Bahrami, Bahador; Ghouli, Saeid; Nejati, Morteza; et al. (2022)
    European Journal of Mechanics - A/Solids
    The influence of specimen size on the measured values of true mode II fracture toughness (KIIc) of rocks have been investigated both experimentally and theoretically. In the experimental study, the double-edge notched Brazilian disk (DNBD) test is utilised to perform fracture toughness experiments with various specimen radii ranging from 27 to 101 mm. Test results demonstrate a significant increase of KIIc with the specimen size. The reason for this trend is explained by a novel mathematical model developed based on the fracture process zone and the energy release rate (ERR) concepts. Comparing the predictions of the theoretical model with the experimental data reveals that the proposed theory can accurately predict the size effect phenomenon in the DNBD test data. To compare the results of KIIc with KIc, similar experimental and theoretical analyses are also performed for mode I fracture toughness tests using the semi-circular bend specimens. Lastly, we present a set of correction factors as functions of specimen size, whereby making it possible to estimate the size independent value of KIIc from the test results obtained from laboratory size DNBD specimens.
  • Bifurcation and stability analysis of static equilibrium configuration of curved pipe conveying fluid
    Item type: Journal Article
    Yan, Hao; Li, Mingwu; Wang, Lin (2023)
    European Journal of Mechanics - A/Solids
    We present bifurcation and stability analysis of static equilibrium configurations of a clamped-clamped curved pipe conveying fluid in this paper. To capture large deformations of the pipe, this pipe is modeled with an absolute nodal coordinate formulation (ANCF). A technique of parameter continuation is used to solve the equilibria of the governing equation of this pipe system. Effects of external force, flow velocity and arc angle on the nonlinear responses of the curved pipe conveying fluid are discussed in detail. In the case of the curved pipe without any external loadings, the system admits two stable equilibria and an unstable equilibrium when the flow velocity exceeds a critical value on which a saddle-node bifurcation occurs. This critical flow velocity that characterizes the onset of the multistability is increased as the arc angle of the pipe increases. In addition, a pitchfork bifurcation occurs along the branch of the unstable equilibria. When the curved pipe is subjected to a concentrated force at its midpoint, the pipe deforms only in symmetrical mode shapes and undergoes a snap-through buckling under variations in the concentrated force. In contrast, when the curved pipe is subject to a gravity and the arc angle of the pipe exceeds a critical value, a pitchfork bifurcation buckling is observed under variations in the gravity. Along the secondary branch of this pitchfork bifurcation, equilibria in asymmetric mode shapes are found. Finally, effects of system parameters on these critical buckling loads are carefully explored.
  • Phase-field modeling of brittle fracture in heterogeneous bars
    Item type: Journal Article
    Vicentini, Francesco; Carrara, Pietro; De Lorenzis, Laura (2023)
    European Journal of Mechanics - A/Solids
    We investigate phase-field modeling of brittle fracture in a one-dimensional bar featuring a continuous variation of elastic and/or fracture properties along its axis. Our main goal is to quantitatively assess how the heterogeneity in elastic and fracture material properties influences the observed behavior of the bar, as obtained from the phase-field modeling approach. The results clarify how the elastic limit stress, the peak stress and the fracture toughness of the heterogeneous bar relate to those of the reference homogeneous bar, and what are the parameters affecting these relationships. Overall, the effect of heterogeneity is shown to be strictly tied to the non-local nature of the phase-field regularization. Finally, we show that this non-locality may amend the ill-posedness of the sharp-crack problem in heterogeneous bars where multiple points compete as fracture locations.
Publications 1 - 10 of 10