Print Email Facebook Twitter Non-proportional loading in sequentially linear analysis for 3D stress states Title Non-proportional loading in sequentially linear analysis for 3D stress states Author Pari, M. (TU Delft Applied Mechanics) Hendriks, M.A.N. (TU Delft Applied Mechanics; Norwegian University of Science and Technology (NTNU)) Rots, J.G. (TU Delft Applied Mechanics) Date 2019 Abstract Sequentially linear analysis (SLA), a non-incremental-iterative approach towards finite element simulation of quasi-brittle materials, is based on sequentially identifying a critical integration point in the model, to reduce its strength and stiffness, and the associated critical load multiplier (λ crit ), to scale the linear analysis results. In this article, two novel methods are presented to enable SLA simulations for non-proportional loading situations in a three-dimensional fixed smeared crack framework. In the first approach, the cubic function in the load multiplier is analytically solved for real roots using trigonometric solutions or the Cardano method. In the second approach, the load multiplier is expressed as a function of the inclination of a potential damage plane and is deduced using a constrained optimization approach. The first method is preferred over the second for the validation studies due to computational efficiency and accuracy reasons. A three-point bending beam test, with and without prestress, and an RC slab tested in shear, with and without axial loads, are used as benchmarks. The proposed solution method shows good agreement with the experiments in terms of force-displacement curves and damage evolution. Subject 3D stress statesfixed smeared crack modelnon-proportional loadingquasi-brittle materialssequentially linear analysis (SLA) To reference this document use: http://resolver.tudelft.nl/uuid:f2952d8d-8108-4eaf-a445-c26498d0c8e5 DOI https://doi.org/10.1002/nme.6060 Embargo date 2019-09-12 ISSN 0029-5981 Source International Journal for Numerical Methods in Engineering, 119 (6), 506-531 Bibliographical note Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. Part of collection Institutional Repository Document type journal article Rights © 2019 M. Pari, M.A.N. Hendriks, J.G. Rots Files PDF Numerical_Meth_Engineerin ... states.pdf 13.79 MB Close viewer /islandora/object/uuid:f2952d8d-8108-4eaf-a445-c26498d0c8e5/datastream/OBJ/view