The paper focuses on the numerical prediction of the compressive response of masonry by means of detailed micro-modelling techniques. In such a model, the material constituents (mortar and units) and the unit-mortar interfaces are separately described by means of specific constitutive equations.The available modeling choices are evaluated through a literature review of related case studies. A systematic approach is proposed and is corroborated by the numerical simulation of a large number of experimental cases from various sources. A total of fifty experimental results are simulated resulting in an overall good prediction of the compressive strength and elastic modulus of the masonry composite, as well as a realistic depiction of the failure mode.This study focuses on the numerical prediction of the compressive strength of masonry, extending to issues pertaining to global stiffness, failure mode, hardening and softening behavior of masonry and their numerical simulation. The masonry typology considered consists of solid units, primarily brick, and mortar of mostly lower strength and higher deformability. Highlights• The behavior of masonry in compression is investigated using micro-models• A combined smeared cracking-plasticity law is used for the units and mortar• A total of fifty experimental compression tests are simulated• Compressive strength and Young's modulus of masonry is well approximated• Remarks on the behavior and failure mode of masonry in compression are made

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