A multi-surface interface model for sequentially linear methods to analyse masonry structures

M Pari,A.V Van De Graaf,M.A.N Hendriks,J.G Rots

doi:10.1016/j.engstruct.2021.112123

M Pari, A.V Van De Graaf + Show 2 more

Open Access

https://doi.org/10.1016/j.engstruct.2021.112123

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Abstract

In the finite element modelling of masonry structures, the micro-modelling technique of differentiating the continuum into a linear elastic bulk, and interfaces representing non-linear joints is common. However, this approach of simulating cracking-crushing-shearing failure possibilities in interfaces, typical of damage in masonry, also poses numerical stability issues due to the quasi-brittle nature of the failure. In this regard, the article proposes the use of numerically robust sequentially linear procedures and a suitable discretised tension-shear-compression failure model for interfaces. Sequentially linear solution procedures describe the nonlinear response of a specimen/structure through a sequence of scaled linear analyses, each of which represents locally applied damage increments, using secant-stiffness based discretised constitutive relations called saw-tooth laws. The constitutive formulation proposed herein includes a tension cut-off criterion combined with a uniaxial discretised softening law, a Coulomb friction criterion with a discretised cohesion softening law, and a compression cut-off criterion combined with a uniaxial discretised hardening–softening law. It is presented for both two-dimensional (2D) line interfaces and three-dimensional (3D) planar interfaces. The applicability of these formulations are illustrated using 2D and 3D models of a pushover analysis on a squat unreinforced masonry wall. The simulations are made using Sequentially Linear Analysis (SLA) and the Force-Release method, which are total (load-unload) and incremental sequentially linear methods respectively. The clear global softening in the force–displacement evolution and the localised brittle shear failure observed in the experiment are reproduced well and in a stable manner.

Highlights

Zero-thickness interface elements are used in standard Finite Element (FE) analysis to represent displacement discontinuities, for e.g. in plain and reinforced concrete applications to simulate cracking and bond slip failures
Global failure mechanisms generally comprise rocking, shear sliding and diagonal shear failures, or combinations thereof, which in turn involve a wide range of local mechanisms including cracking and slipping of joints, cracking under direct or diagonal tension of brick units, and masonry crushing at the toe of a rocking pier
Since the 2D formulation has been shown to work well with both Sequentially Linear Analysis (SLA) and Force-Release methods, 3D formulation is shown here only with SLA the Force-Release simulation should be possible in principle

Summary

Introduction

Zero-thickness interface elements are used in standard Finite Element (FE) analysis to represent displacement discontinuities, for e.g. in plain and reinforced concrete applications to simulate cracking and bond slip failures. Linear Analysis (SLA) is a non-incremental (total) [13,14,15], secant stiffness-based event-by-event approach, wherein one linear analysis is performed at a time to identify and damage the critical integration point in the FE model. The strength and stiffness of this integration point are reduced in a step-wise manner based on a discretised constitutive relation, with successively reducing secant stiffnesses and allowable strengths, called the saw-tooth law (Fig. 1) This process of identifying critical events and load scaling is repeated until a user-defined stop criteria is reached or when the FE model is completely damaged. The Coulomb friction criterion which involves multiple stress and/or deformation components requires a more sophisticated approach for use in sequentially linear methods such as the SLA In this regard, step-wise secant Coulomb friction laws proposed by Van de Graaf [8] for SLA are used . In the 2D interface formulation, at the linear elastic stage, the interface tractions tn and tt are related to the corresponding normal and shear relative displacements un and ut by means of the uncoupled constitutive secant matrix Dsec (with an undamaged normal stiffness kn,0 and shear stiffness kt,0) in the following way

Critical load multiplier

Stiffness update

Illustration

Results & Discussion

Concluding remarks