Purpose -The main aim of this paper is to present a three-dimensional numerical material model for concrete which combines plasticity with a classical orthotropic smeared crack formulation. A further aim is to raise a discussion leading to the creation of a comprehensive computer programme for the analyses of reinforced and prestressed concrete structures. Design/methodology/approach -A new numerical material model for concrete is developed and main theoretical explanations are given to aid in understanding the algorithm. The model is based on Mohr-Coulomb criterion for dominant compression and Rankine criterion for dominant tension influences. A multi-surface presentation of the model is implemented which permits the rapid convergence of the mathematical procedure. The model includes associated and non-associated flow rules, strain hardening and softening where the development of the plastic strain was described by the function of cohesion. Findings -Provides information about developing a new numerical material model for concrete. Practical implications -The model is implemented into the computer programme PRECON3D for the three-dimensional nonlinear analysis of the reinforced and prestressed concrete structures. Originality/value -In this model, the very complex behaviour of concrete is defined by elementary material parameters which can be obtained by a standard uniaxial test. The presented model enables a very detailed and precise analysis of reinforced and prestressed concrete structures until crushing with a high accuracy, so that the expensive experimental tests can be reduced. The paper could be very valuable to researchers in this field as a benchmark for their analyses.

This paper describes performed numerical parametric analyses of constant-moment zone length in four point bending of reinforced concrete structures by a developed three-dimensional numerical material model for analyzing reinforced concrete structures. The model is defined by elementary material parameters which can be obtained by a standard uniaxial test so that the very complex behaviour of reinforced concrete structures can be described simply and effectively but with a sufficiently accurate model.

Purpose -To provide an insight in one relatively simple and efficient numerical model for analysing reinforced and prestressed concrete structures, and to raise a discussion leading to the creation of one universal and robust 3D algorithm. Design/methodology/approach -A new numerical model for analysing reinforced and prestressed concrete structures is developed and main theoretical details are described to aid the understandings. The approach is clear, easily readable and the body of the text is divided into logical sections starting from theoretical explanations ending in the large number of different practical examples. Findings -Provides information about developing new and relatively simple numerical model for analysing reinforced and prestressed concrete structures, indicating what can be improved. Recognises the lack of knowing real behaviour of 3D concrete and starts a discussion on it.Research limitations/implications -The knowledge of the 2D and especially 3D concrete behaviour is still poor and the concrete model developers use many simplifications. So, many new experiments should be performed and better numerical models should be developed. There is large area for researchers but having in mind that experiments are very expensive. Practical implications -Obtained results of the 3D analysis of reinforced and prestressed concrete structures can stand as a benchmark for future researches in this field especially to the young researchers and concrete model developers. Originality/value -This paper presents new and very simple numerical model for analysing reinforced and prestressed concrete structures. Paper could be very valuable to the researchers in this field as a benchmark for their analyses.

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This paper demonstrates some computational aspects of two previously developed numerical models for a static and dynamic analysis of shells based on the combined finite‐discrete element method. The dynamic and static response of shells under various boundary conditions, mesh pattern and mesh refinement was analysed and compared with other numerical and analytical results in order to illustrate the accuracy and applicability of the proposed numerical models.