PSI - Issue 73

Roman Vodička et al. / Procedia Structural Integrity 73 (2025) 163 –169 Author name / Structural Integrity Procedia 00 (2025) 000 – 000

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of existing bridges, is a key area of development (Siwowski, T. et al. (2018), Sonnenschein, R. et al. (2016)). The incorporation of FRP composites allows for lightweight, durable, and corrosion-resistant materials, which are highly beneficial in the demanding environments of bridge construction and maintenance (Naser, M. Z. et al. (2021), Ataei, H. and Mamaghani, M. (2017)). In composite FRP-concrete structures, structural elements made of FRP composites are combined with concrete slabs in a compression zone. Such hybrid structures are suitable for short and medium-span bridges (Naser, M. Z. et al. (2021), Kormaníková, E. et al. (2022)) . Their advantages include reduced weight, leading to lower foundation costs, and resistance to corrosion, resulting in decreased maintenance expenses and prolonged service life. Mechanical analysis of the multi-component elements of civil engineering constructions is often accompanied by damage of the material and subsequent formation of cracks which appear either inside the components of the elements, or between them, at the interface. It is very useful and up to date to develop computational models for identification and analysis of stages of development and interaction of cracks. The original idea of (Griffith (1920)) was to relate amount of energy release to the area of crack. Anyhow, (Barenblatt (1962)) followed that microscopically the energy depends also on the displacement jump along the crack which was the way how cohesive zone models were developed (Park (2011)). Inside such crack modelling techniques, one group of approaches introduces an internal variable (Maugin, G. A (2015)) characterising a process of degradation, like that used in the damage theory, which provides the cohesiveness between surfaces that finally separate and form a crack. To represent the state of the system, it is practical especially for numerical solutions based on finite element schemes, to adopt an energy-based formulation. Such a formulation includes the energy balance of the damage process, which accounts for energy stored in the body, energy associated with newly formed defects, or other form of dissipated energy (Bourdin, B. (2008)). In many cases, those processes can be considered as quasi-static, simplifying mathematical analysis and calculations. However, in general, the damage and crack growth processes tend to occur rapidly, and the inertial effects may also be considered ( Roubíček, T. (2019)). The interface cracks involve the contact between the components of the structural element. In this case, the interface is modelled as an extremely thin adhesive layer, and this type of contact is referred to as adhesive contact, see (Raous et al. (1999), Roub í ček et al. (2023)), which considers an internal variable. The rule for the internal variable then affects the dependence of energy release on the displacement gap along the interface. Several computational models have been developed for this type of contact using cohesive zone models, like those in references ( Vodička, R. (2016), Vodička, R. and Mantič, V. (2017)). To solve problems in a variational manner using energy principles, a various types of numerical algorithm are required to optimise the corresponding energy functionals. In the case of damage and crack problems, it is necessary to apply general algorithms of nonlinear programming ( Kormaníková, E. et al. (2024), Vodička, R . et al. (2018)) due to non-convexity of the functionals. The present research topic is studying slab bridges of short to medium spans with several different types of continuous shear connectors. In particular, the paper introduces a computational cohesive model used for the study. Inside its procedures, it discusses influence of modifications in a shape parameter of a jigsaw-puzzle formed shear connector.

Nomenclature E

stored energy

u C φ p

displacement field

internal interface damage variable

stiffness matrix

k n , k s , k z

normal, tangential and transversal stiffness

interface degradation function interface fracture energy

G c

c I ,

I ,

c I

c II

dissipation functional

I critical value of fracture energy in mode I, II and III, respectively

vertical pressure