The paper presents the procedure of implicit stress integration for constitutive models for soil and rock. The theoretical basis of Mohr-Coulomb, Matsuoka-Nakai, Hoek-Brown and Hyperbolic soil constitutive models are presented. Stress integration was performed using the theory of incremental plasticity. The general procedure of implicit stress inte...

By Dragan Rakić, Miroslav Živković

Degradation of structural integrity and fatigue life estimation remain critical challenges in engineering, including biomedical applications. Fracture mechanics and crack propagation prediction are highly sensitive to material parameters, with the Stress Intensity Factor being the most significant physical parameter for the estimation of crack stre...

By Gordana Jovičić, Vladimir Milovanović, Aleksandra Vulović, Miroslav Živković, Nenad Đorđevič, Nenad Filipović

Dynamic analysis of engineering structures is essential in the design process, providing insights into their behavior under various loading conditions. This paper focuses on the comparative study of implicit and explicit dynamic analysis methods using the PAK software and FEMAP with the Nastran software. Both methods have distinct advantages and di...

By Vladimir Dunić, Miloš Pešić, Miroslav Živković, Radovan Slavković

This paper presents a method for improving the numerical analysis of contact problems using a penalty formulation. Since contact phenomena are inherently nonlinear, particularly in the case of large deformations, an incremental solution strategy is required. Conventional Newton-Raphson algorithms often face convergence problems when many nodes make...

By Snežana Vulović, Miroslav Živković, Nenad Grujović, Marko Topalović

The concrete damaged plasticity (CDP) model is one of the most popular constitutive models implemented into various Finite Element Method software. The application to the real structures is documented in the literature, but still there are some doubts about the response in combination with the various finite elements. Simple benchmark examples simu...

By Vladimir Dunić, Nenad Grujović, Aleksandar Bodić, Dragan Rakić, Miroslav Živković

The interaction between the Finite Element Method (FEM) and Smoothed Particle Hydrodynamics (SPH) is crucial in multiphysics simulations of granular–structure systems, impacts, and material behavior. This paper presents a penalty-based contact algorithm with Coulomb friction for FEM–SPH coupling. The method accounts for static and dynam...

By Marko Topalović, Miloš Ivanović, Snežana Vulović, Aleksandar Nikolić, Miroslav Živković

The paper presents various examples of the application of the PAK software and its modules for thermal, filtration, and stress–strain analysis of different complex engineering structures such as gravity dams, arch dams, embankment dams, tunnels, and mines. Examples of research, studies, and projects in which PAK has been applied to assess the...

By Dejan Divac, Slobodan Radovanović, Maja Pavić, Nikola Milivojević, Vladimir Milivojević, Miroslav Živković, Dragan Rakić, Snežana Vulović

Two-equation turbulent models are widely used in finite element analysis of fluid flow. The PAK program package was upgraded from the classical laminar flow to the turbulent k-omega model. The turbulence model was validated using the case of fluid flow in a backward-facing step channel. The analysis results show good agreement with experimental dat...

By Aleksandar Nikolić, Miroslav Živković, Nenad Filipović, Marko Topalović

Efficient memory handling is one of the key issues that engineers and programmers face in developing software for numerical analysis such as the Finite Element Method. This method operates on huge matrices that have a large number of zero coefficients which waste memory, so it is necessary to save it and to work only with non-zero coefficients usin...

By Dragoljub Stevanović, Marko Topalović, Miroslav Živković

A stress-strain history in the material of real concrete structures is usually unknown. An effect of concrete degradation is analyzed to describe how the initial degradation parameter can describe the stress-strain history. The idea is to introduce the initial damage of the structure by the degradation parameter to calculate the internal variables ...

By Dragan Rakić, Vladimir Dunić, Miroslav Živković, Nenad Grujović, Dejan Divac