Nonlinear analysis of masonry panels using a kinematic enriched plane state formulation

Abstract This paper deals with the nonlinear analysis of masonry walls loaded in their plane. The masonry is regarded as a composite material made of bricks joined by mortar. To correctly reproduce the mortar–brick interaction in the direction of the thickness of the wall, an enriched kinematic model is proposed, so that the model is able, in a feasible form, to account for the out-of-plane strains due to the in-plane loading acting on the wall. Nonlocal nonlinear constitutive laws are considered both for the mortar and the bricks. In particular, a damage-friction law is considered for the mortar, while a damage model with two alternative yield functions is proposed for the bricks, both based on a tensile failure mechanism. A 2D finite element (FE) accounting for the three-dimensional kinematic effect is developed. This is implemented in a numerical procedure based on the backward Euler step-by-step time integration of the constitutive evolution laws and on the predictor-corrector algorithm for the solution of the nonlinear problem. Five applications are presented to highlight the effectiveness of the proposed nonlinear model and the implemented FE procedure. The first aims to show the model’s ability to reproduce the failure of the masonry for transversal damage; the others deal with comparisons with classical small scale and structural scale experimental tests.

[1]  S. Brasile,et al.  Multilevel approach for brick masonry walls. Part II On the use of equivalent continua , 2007 .

[2]  Daniela Addessi,et al.  An equilibrated macro-element for nonlinear analysis of masonry structures , 2014 .

[3]  Gabriele Milani,et al.  Compatible model for herringbone bond masonry: Linear elastic homogenization, failure surfaces and structural implementation , 2013 .

[4]  G. Milani,et al.  In-plane failure surfaces for masonry with joints of finite thickness estimated by a Method of Cells-type approach , 2015 .

[5]  E. Sacco,et al.  Cosserat model for periodic masonry deduced by nonlinear homogenization , 2010 .

[6]  Gilles Pijaudier-Cabot,et al.  CONTINUUM DAMAGE THEORY - APPLICATION TO CONCRETE , 1989 .

[7]  Yong Sheng,et al.  Evaluation of different computational modelling strategies for the analysis of low strength masonry structures , 2014 .

[8]  A. Anthoine.  HOMOGENIZATION OF PERIODIC MASONRY: PLANE STRESS, GENERALIZED PLANE STRAIN OR 3D MODELLING? , 1997 .

[9]  L. Gambarotta,et al.  Mechanical response of solid clay brickwork under eccentric loading. Part I: Unreinforced masonry , 2005 .

[10]  K. Sab,et al.  Three dimensional homogenization of masonry structures with building blocks of finite strength: A closed form strength domain , 2015 .

[11]  P. Lourenço,et al.  A micro-mechanical homogenisation model for masonry: Application to shear walls , 2009 .

[12]  Daniela Addessi,et al.  A kinematic enriched plane state formulation for the analysis of masonry panels , 2014 .

[13]  Mohammad Zaman Kabir,et al.  Experimental response of double-wythe masonry panels strengthened with glass fiber reinforced polymers subjected to diagonal compression tests , 2012 .

[14]  Gian Michele Calvi,et al.  In‐plane seismic response of brick masonry walls , 1997 .

[15]  Thierry Massart,et al.  Mesoscopic modeling of failure in brick masonry accounting for three-dimensional effects , 2005 .

[16]  L. Berto,et al.  Failure mechanism of masonry prism loaded in axial compression: computational aspects , 2005 .

[17]  A. Anthoine,et al.  In-plane and out-of-plane homogenisation of masonry , 2007 .

[18]  Milan Jirásek,et al.  Nonlocal integral formulations of plasticity and damage : Survey of progress , 2002 .

[19]  Z. Bažant,et al.  Nonlocal damage theory , 1987 .

[20]  Elio Sacco,et al.  A nonlinear homogenization procedure for periodic masonry , 2009 .

[21]  Amin Mohebkhah,et al.  Distinct Element Modeling of Masonry-Infilled Steel Frames with Openings , 2012 .

[22]  J. Mazars.  A description of micro- and macroscale damage of concrete structures , 1986 .

[23]  Jessica Toti,et al.  Modeling approaches for masonry structures , 2014 .

[24]  Sergio Lagomarsino,et al.  DAMAGE MODELS FOR THE SEISMIC RESPONSE OF BRICK MASONRY SHEAR WALLS. PART II: THE CONTINUUM MODEL AND ITS APPLICATIONS , 1997 .

[25]  Nicola Cavalagli,et al.  Strength domain of non-periodic masonry by homogenization in generalized plane state , 2011 .

[26]  Serena Cattari,et al.  The use of the diagonal compression test to identify the shear mechanical parameters of masonry , 2010 .

[27]  A. Taliercio.  Closed-form expressions for the macroscopic in-plane elastic and creep coefficients of brick masonry , 2014 .

[28]  Manuel Elices,et al.  Micromechanical modeling of brick-masonry fracture , 2000 .

[29]  M. Kabir,et al.  Modeling of unreinforced brick walls under in-plane shear & compression loading , 2010 .

[30]  Gabriele Milani,et al.  Full 3D homogenization approach to investigate the behavior of masonry arch bridges: The Venice trans-lagoon railway bridge , 2014 .

[31]  E. Jacquelin,et al.  Modelling approaches of the in-plane shear behaviour of unreinforced and FRP strengthened masonry panels , 2006 .

[32]  Kiarash M. Dolatshahi,et al.  A three-dimensional cyclic meso-scale numerical procedure for simulation of unreinforced masonry structures , 2013 .

[33]  P. Trovalusci,et al.  Masonry as structured continuum , 1995 .

[34]  Nicola Cavalagli,et al.  Evaluation of a Statistically Equivalent Periodic Unit Cell for a quasi-periodic masonry , 2013 .