The application of complex nonlinear material models of concrete within the numerical simulations is currently the most used way for the purposes of modeling the nonlinear computer response of concrete structures. However, the modeling of nonlinear concrete behavior through the nonlinear material models very often brings with it the major problem. This problem can be specified as a user nescience of a large number of material model parameters which is very common. Nowadays, the solution of this problem is possible with the so called inverse analysis or identification which can be performed via the different methods and approaches. One of the most effective approach for the purposes of the inverse analysis is currently using the combination of sensitivity analysis with optimization algorithms. This mentioned approach is demonstrated within this paper in which the parameters of the material model called the Continuous Surface Cap Model are identified. Material parameter identification is performed on the basis of interaction between nonlinear numerical simulations, statistical and optimization methods and experimental data which are represented by a load-extension curve obtained from the unconfined uniaxial tensile (UUT) test. The final comparison of the experimental data with the numerically-simulated data for optimal parameter values is, of course, also part of this paper.

Steel fibre reinforced concrete (SFRC) is very popular in many branches of civil engineering. Thanks to its increased ductility, it is able to resist various types of loading. When designing a structure, the mechanical behaviour of SFRC can be described by currently available material models (with equivalent material for example) and therefore no problems arise with numerical simulations. But in many scenarios, e.g. high speed loading, it would be a mistake to use such an equivalent material. Physical modelling of the steel fibres used in concrete is usually problematic, though. It is necessary to consider the fact that mesh-based methods are very unsuitable for high-speed simulations with regard to the issues that occur due to the effect of excessive mesh deformation. So-called meshfree methods are much more suitable for this purpose. The Smoothed Particle Hydrodynamics (SPH) method is currently the best choice, thanks to its advantages. However, a numerical defect known as tensile instability may appear when the SPH method is used. It causes the development of numerical (false) cracks, making simulations of ductile types of failure significantly more difficult to perform. The contribution therefore deals with the description of a procedure for avoiding this defect and successfully simulating the behaviour of SFRC with the SPH method. The essence of the problem lies in the choice of coordinates and the description of the integration domain derived from them – spatial (Eulerian kernel) or material coordinates (Lagrangian kernel). The contribution describes the behaviour of both formulations. Conclusions are drawn from the fundamental tasks, and the contribution additionally demonstrates the functionality of SFRC simulations. The random generation of steel fibres and their inclusion in simulations are also discussed. The functionality of the method is supported by the results of pressure test simulations which compare various levels of fibre reinforcement of SFRC specimens.

The paper deals with suitability of use of the explicit and implicit method in heavily nonlinear seismic analysis and also deals with comparison of response of the Drucker-Prager plastic material model and the modified Mazars damage material model to strong seismic loading. Considering typical time of duration of earthquakes from several seconds to approximately twenty seconds, it would seem that use of the implicit method is definitely more suitable. The shape of accelerograms, however, requires quite short time steps. For the explicit method, on the other hand, very short time steps are required in order to obtain a stable solution. Both methods must be compared with respect to a heavily nonlinear response, typical for seismicity. Massive yielding or damage of the material structure is achieved. Behaviour of both models under the seismic loading is fundamentally different and the paper discusses the differences. Conclusions of the paper are made on the basis of detailed numerical study and may be very useful for practice.

The inclusion of material heterogeneities in numerical simulations enables us to come close to the almost perfect description of the behaviour of structures. There are various ways and methods of introducing heterogeneity into a computational model. One of the methods is the creation of areas (fractal fields) in which material properties differ. The shape of such fractals is most frequently based on simple mathematical functions. However, this destroys the ability of the model to represent reality, as the structure of a real material is not based on any mathematical function. Fractals do not have to be based just on one simple mathematical function. On the contrary, they can be based on more complex inputs, such as real images of materials. In the case of images of concrete, fields can be generated which correspond to the presence of an aggregate, a cement binder or an air void. The contribution therefore describes fundamental steps in the creation of fractals, or the creation of fields based on real images of a material. The contribution also deals with the creation of material parameter oscillations and their subsequent inclusion in the numerical code of the Smoothed Particle Hydrodynamics (SPH) method. The conditions necessary for successful simulations if the SPH method is used are described. The whole process is clearly demonstrated using a pressure test conducted on a cylindrical concrete specimens. The presented results show the consequences of the inclusion of material heterogeneity in numerical simulations. These include randomness in the failure type or differences in the stress–strain diagrams of the monitored specimens. The functionality of the proposed process is supported by the results.