Contents lists available at ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech Non-proportional loading in sequentially linear solution procedures for quasi-brittle fracture: A comparison and perspective on the mechanism of stress redistribution M. Pari a,⁎ , M.A.N. Hendriks a,b , J.G. Rots a a Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, 2600 GA Delft, the Netherlands b Norwegian University of Science and Technology (NTNU), Rich. Birkelandsvei 1A, 7491 Trondheim, Norway ARTICLE INFO Keywords: Non-proportional loading Quasi-brittle materials Sequentially linear analysis (SLA) Force-release method Stress redistribution ABSTRACT Sequentially linear solution procedures provide a robust alternative to their traditional incre- mental-iterative counterparts for finite element simulation of quasi-brittle materials. Sequentially linear analysis (SLA), one such non-incremental (total) approach, has been extended to non- proportional loading situations in the past few years. Although the process of damage propa- gation and localisation is often dynamic in nature, the simulation being quasi-static poses a fundamental problem. This article gives an overview of the different approaches to address non- proportional loading in SLA and other sequentially linear methods, and their corresponding re- distribution methodologies to address the dynamic phenomenon. Furthermore, the inherent differences between two such methods: SLA (total) and the Force-Release method (incremental), and their suitability to structural continuum models involving non-proportional loading, are il- lustrated using real-life concrete and masonry experimental benchmarks tested up to and beyond brittle collapse. In each illustration, SLA is shown to enforce equilibrium during dynamic failure by load reduction, using the intermittent proportional loading, while allowing for active damage propagation resulting in a relaxed failure mechanism which manifests as snap-back(s). Contrarily, the Force-Release method is shown to describe the collapse through states of dis- equilibrium. 1. Introduction Finite element (FE) models, in use for simulation of materials characterised by brittle failure like concrete and masonry, often encounter problems related to snap back, bifurcation points, divergence or material softening leading to negative tangent stiffness and the consequent ill conditioning of the formulation. Convergence issues, resulting from multiple integration points being pushed simultaneously into strain softening, may lead to inaccurate results due to deviation of the simulation into alternative equilibrium paths. Use of path following procedures like the Arc-length control method help but requires extreme care from the user to steer the analysis (and possibly prior knowledge of crack locations). This gave rise to several alternate solution approaches which can generally be classed into three categories: purely total approaches wherein unloading and reloading is done non-proportionally, purely in- cremental approaches wherein the stress and loading history is explicitly tracked and finally a class of combined incremental-total approaches. The Sequentially Linear Analysis (SLA) is a feature, as a part or whole, of all three aforementioned categories. https://doi.org/10.1016/j.engfracmech.2020.106960 Received 19 November 2019; Received in revised form 21 February 2020; Accepted 23 February 2020 ⁎ Corresponding author. E-mail address: [email protected] (M. Pari). Engineering Fracture Mechanics 230 (2020) 106960 Available online 29 March 2020 0013-7944/ © 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/BY/4.0/). T
Non-proportional loading in sequentially linear solution procedures for quasi-brittle fracture: A comparison and perspective on the mechanism of stress redistribution
Jun 16, 2023
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Related Documents
