ECCOMAS 2024

Analytical-Based Multiscale Modeling of Masonry

  • Rios Silveira, Pedro Henrique (Delft University of Technology)
  • Esposito, Rita (Delft University of Technology)

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Due to its widespread use in both historical heritage and vernacular construction, the structural assessment of unreinforced brick masonry (UBM) is an important and challenging undertaking. To assist in the task, numerical models play a crucial role. However, despite the wide range of simulation strategies available, only a limited amount of models can be effectively applied for the assessment of existing UBM structures in combination with non/minor-invasive testing. Brick-based formulations treat each unit and their interactions explicitly, which leads to prohibitive computational costs for larger structures. Continuum-based models, on the other hand, treat masonry as a homogeneous material. They are computationally cheaper, but often overly simplified and/or too difficult to calibrate. Multiscale models can bridge the gap between these two approaches. Generally, they discretize the analyzed structure at the continuum level, with the constitutive behavior defined from upscaling brick-based models, which are commonly more accurate and easier to calibrate. Nevertheless, multiscale approaches have problems of their own. To cite a few: the number of non-linear parameters still needed for the brick-based model, issues with regularization, the larger computational cost compared to ‘direct’ continuum models, etc. Given such constraints, this work proposes the use of microporomechanics to develop an analytical multiscale model for UBM. In this theory, cracks are treated as penny-shaped inclusions and homogenized against the undamaged composite using mean-field techniques. Crack growth is then defined based on principles from linear elastic fracture mechanics. The use of microporomechanics has a few notable advantages. The softening behavior of the homogenized medium is directly obtained from the tensile strength of the composite and the geometrical and elastic properties of its constituents. This drastically reduces the need for toughness parameters that are challenging to obtain on-site. Cracks are also directional and can be independent. Therefore, the formulation is inherently anisotropic. Lastly, it relies mostly on closed-form solutions, which facilitates implementation. This work presents details about the microporomechanical formulation along with preliminary results considering cracks on an isotropic medium. Key formulation features are demonstrated along with intended next steps to extend the model to orthotropic materials.