Micro-mechanical finite element modeling for in-plane behavior of historical masonry

Seismic assessment of unreinforced masonry structures remains a challenge. This dissertation investigates the in-plane behavior of historical masonry elements and proposes an advanced simulation method based on the cohesive zone model (CZM) in a finite element framework.

Cohesive elements are often used to simulate dynamic fracture. To consider contact and friction, a new node-to-node algorithm is implemented in the open-source code Akantu, which offers a parallel computing model. Based on the proposed framework, two types of tests are investigated: the shear test, which is a basic material test to determine parameters such as cohesion and friction coefficient, and the diagonal compression test, which is a standard masonry material test to determine the nominal diagonal tensile strength and shear modulus of masonry. The simulation results correspond well with experimental results.

One potential advantage of the detailed micro-modeling method is the ability to represent and study the influence of the micro-structure of the stone masonry on the force-displacement behavior. However, previous studies focused only on one specific block layout. This constraint was caused by the absence of a stone masonry typology generator. Based on related research in computer vision and geology, a versatile typology generator is developed. To quantify the micro-structure of a stone masonry typology, the line of minimum trace (LMT) is often used. Determining the LMT manually is time consuming and subjective. To facilitate the calculation process, an algorithm to calculate LMT automatically from pictures of masonry patterns is developed.

Based on the proposed typology generator, the influence of the masonry typology on the masonry shear strength under shear-compression boundary condition is then systematically investigated. Starting with regular brick masonry patterns, the roundness and the arrangement of the units are altered gradually. The commonly used shear failure criterion by Mann-Müller is investigated in detail and it is shown that the assumed stress distributions are good approximations of the stress state in the linear elastic range but deviate significantly from the stress distribution at peak shear strength. The numerical results also highlight that the effect of the interlocking between stones on the shear strength is overestimated by the Mann-Müller model. For irregular stone masonry, the correlation between LMT and shear resistance is studied.

While CZM has been widely used to simulate tensile damage dominated fracture and inter-facial failure, continuum modeling method, i.e., concrete damage plasticity (CDP), is more commonly used for simulating the compressive behavior of quasi-brittle materials, e.g., mortar in masonry and concrete. While existing studies already established the equivalence between the continuum modeling method and the CZM under tension dominated fracture process, the behavior of CZM under compression has not been investigated. To consider a wider range of loading conditions, a new traction-separation law based on the plasticity theory was proposed and therefore expanded the usage of CZM.