3D meso- and macro-scale models for nonlinear analysis of masonry systems

Abstract

Unreinforced masonry (URM) is a heterogeneous material with complex strongly nonlinear behaviour which depends on the arrangement of its constituents and their individual properties. This work is motivated by the need for more accurate numerical strategies for the simulation of URM structural components and systems. To this end, meso- and macro-scale modelling approaches are proposed, to tackle different challenges in the field. In all the developments, focus is placed on two points: (i) 3D descriptions that predict both the in-plane and out-of-plane behaviour of masonry, (ii) efficiency and robustness, so that the models can be applied in the study of real structures.

Starting from a detailed approach, a 3D mesoscale model which represents the brick units with 3D solid elements and the potential cracking surfaces with zero thickness cohesive interface elements is employed. A nonlinear constitutive law based on plasticity and damage is proposed to describe the cyclic behaviour of the cohesive interfaces. The model can reproduce decohesion and frictional sliding in the interfaces, as well as the crushing of masonry under compression. Increased robustness is achieved by means of a two-step solution procedure that decouples the evolution of plasticity and damage. Subsequently, the issue of coupling of the mesoscale model with meshes of other material components to simulate heterogeneous structures is examined. Within this scope, a coupling finite element for the tying of non-conforming 3D meshes is developed. Using the mesh tying method, a modelling strategy for heterogeneous URM structures is proposed, in which the URM components are described in mesoscale and other material components are modelled independently with continuum meshes. The individual non-conforming domains are then tied together with the use of the coupling element, while their physical interaction is accounted for by cohesive elements arranged along the interface.

Identifying the potentially restraining computational cost of the detailed mesoscale representation of full-scale URM structures, the final part of this work proceeds with the development of a masonry macroelement, which represents a plane URM assembly as an homogeneous block interacting with adjacent elements through cohesive interfaces. Flexural and shear sliding damage within the URM assembly are concentrated in the surrounding interfaces, while additional deformation modes of the inner block represent in and out-of-plane diagonal cracking. As a result, the macroelement captures all the principle in- and out-of-plane failure modes of URM walls under cyclic loading conditions, including mixed-mode damage. In parallel, it ensures computational efficiency and is therefore appropriate for the analysis of large scale URM buildings under complex loading conditions.