Plasticity based approach for failure modelling of unreinforced masonry Nitin Kumar a , Amirtham Rajagopal a,⇑ , Manoj Pandey b a Department of Civil Engineering, Indian Institute of Technology Hyderabad, Andhra Pradesh, India b Department of Mechanical Engineering, Indian Institute of Technology Madras, Tamil Nadu, India article info Article history: Received 30 May 2013 Revised 7 August 2014 Accepted 12 August 2014 Keywords: Masonry modelling Plasticity Composite interface model Failure criteria abstract In this work, a plasticity based composite interface model is proposed for failure analysis of unreinforced masonry. The hyperbolic composite interface model consists of a single surface yield criterion, which is a direct extension of Mohr-Coulomb criteria with cut in tension region and a cap in compression region. The inelastic behaviour includes potential crack, slip, and crushing of the masonry joints. A micro mechanical based approach is adopted for failure modelling of the masonry. The model is developed by using a fully implicit backward-Euler integration strategy. It is combined with a local/global Newton solver, based on a consistent tangent operator compatible with an adaptive sub stepping strategy. The model is implemented in standard finite element software (ABAQUS) by using user defined subroutine and verification is conducted in all its basic modes. Finally, the model is validated by comparing with experimental results available in the literature. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Masonry is a heterogeneous anisotropic continuum; made up of the brick and mortar arranged in a periodic or non periodic man- ner. In particular, the inhomogeneity is due to the different mechanical properties of its constituents, and the anisotropy is due to the different masonry patterns, that can be obtained by var- iation of geometry, nature and arrangement of mortar and brick. The behaviour of masonry is very complex and highly non-linear due to the behaviour of its constituents, which are quasi-brittle in nature and have a large difference in their stiffness. It represents a very particular mechanical behaviour, which is primarily due to the lack of homogeneity and standardization (see [1,2]). The structural response of such a composite material derives from the complex interaction between its constituents. Under the in- plane loading, masonry is subjected to a biaxial state of stress and thus masonry constituents may fail in individual or combined mechanisms (see [3–6]). These failure mechanism are used in micro modelling of masonry to understand its behaviour. Many computational studies have been carried out at various scales to understand and simulate the behaviour of masonry. The modelling of masonry at different scales depends up on the level of accuracy and simplicity desired. This includes micro- modelling and macro-modelling. In micro-modelling, the unit and mortar are represented by continuum elements and unit-mortar interface is represented by a discontinuous interface element. This detailed micro-modelling procedure leads to very accurate results, but requires an intensive computational effort. This drawback can be partially overcome in simplified micro- modelling, by making an assumption that mortar and two unit-mortar interface is lumped into a joint between expended units. The units are expended in order to keep the geometry of structure unchanged. The computational cost of simplified micro-model can be further reduced, by replacing expanded units by the rigid element. Using rigid elements decreases the number of degrees of freedom, which consequently reduces the computational time. In macro-modelling, masonry is considered as a composite, which does not make any distinction between units and joints. The material is regarded as a fictitious homoge- neous anisotropic continuum. 2. Literature review There has been several experimental studies reported in litera- ture for understanding behaviour of the masonry for instance (see [7–12]). Masonry exhibits a quasi-brittle behaviour due to its con- stituents, thus failure analysis of a masonry structure abides in the realistic modelling of the fractures and associated softening behaviour. Therefore modelling techniques of masonry are analo- gous to that developed in concrete and rock mechanics. Many plasticity based constitutive models have been proposed in the recent years that can simulate initiation and propagation of crack under combined normal and shear stresses [13–18]. http://dx.doi.org/10.1016/j.engstruct.2014.08.021 0141-0296/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: rajagopal@iith.ac.in (R. Amirtham). Engineering Structures 80 (2014) 40–52 Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct