Ivica Kožar

Microplane model for concrete with relaxed kinematic constraint

Abstract In the paper, the microplane material model for concrete based on the relaxed kinematic constraint is presented. The model is aimed to be used for three-dimensional damage and fracture analysis of concrete and reinforced concrete structures in the framework of smeared crack approach. In the microplane model, the material is characterized by a relation between the stress and strain components on planes of various orientations. These planes may be imagined to represent the damage planes or weak planes in the microstructure, such as contact layers between aggregate pieces in concrete. The tensorial invariance restrictions need not be directly enforced. They are automatically satisfied by superimposing in a suitable manner the responses from all the microplanes. To realistically model concrete under compressive load, for each microplane, the total strain tensor has to be decomposed into the normal (volumetric and deviatoric) and shear strain component. It is shown that for dominant tensile load the decomposition of the normal microplane strain into volumetric and deviatoric part, together with the fact that the tensile strength of concrete is an order of magnitude smaller than its compressive strength, leads to unrealistic model response. To keep the conceptual simplicity, the model is improved in the framework of the kinematic microplane theory, however, the kinematic constraint at the microplane level is relaxed. The proposed approach finds its physical background in the discontinuity of the strain field. It is demonstrated that the improved model correctly predicts the concrete response for dominant tensile load. The implementation of the initial anisotropy and the modeling of concrete for cyclic loading is also discussed. Comparison with a number of test data for different stress–strain histories shows a good agreement. The model has been recently implemented into a two- and three-dimensional finite element code and coupled with the localization limiter of local (crack band) and nonlocal integral type.

Validation of a simplified micromodel for analysis of infilled RC frames exposed to cyclic lateral loads

An RC frame structure with masonry infill walls (“framed-masonry”) exposed to lateral loads acts as a composite structure. Numerical simulation of framed-masonry is difficult and generally unreliable due to many difficulties and uncertainties in its modelling. In this paper, we reviewed the usability of an advanced non-linear FEM computer program to accurately predict the behaviour of framed-masonry elements when exposed to cyclic lateral loading. Numerical results are validated against the test results of framed-masonry specimens, with and without openings. Initial simplified micromodels were calibrated by adjustment of the input parameters within the physically justifiable borders, in order to obtain the best correlation between the experimental and numerical results. It has been shown that the use of simplified micromodels for the investigation of composite masonry-infilled RC frames requires in-depth knowledge and engineering judgement in order to be used with confidence. Modelling problems were identified and explained in detail, which in turn offer an insight to practising engineers on how to deal with them.

Finite element formulation of the finite rotation solid element

Abstract The paper describes the development of an 8-node solid finite element capable of undergoing both large displacements and large rotations. The constitutive law chosen is for an elastic material. The element is developed on a sound variational basis. The incompatible modes are employed to produce a ‘locking’ free performance. The operator split method is employed in solving the equilibrium equations which resulted in minimal secondary storage requirements. The rotation vector is chosen as a parametrization of large rotations and, as a consequence, the stiffness matrix obtained by the consistent linearization is a symmetric one. Also, the rotation vector is expressed in a unique way so that it can be additively composed and the update procedure is the simplest one possible. In order to improve the behavior of the element for rotations exceeding 2π, we have somewhat modified the total Lagrangian formulation to allow for incremental rotations to appear. The correctness of the procedure is proved with a set of numerical examples.

Security aspects of vertical actions on bridge structure: Comparison of earthquake and vehicle induced dynamical forces

Modern vehicles are characterised by great load and speed so that their dynamical influence in bridge analysis should be taken into account. During design those loads are usually considered through static analysis and the only dynamic analysis is the one concerning eartquake loading. This paper deals with dynamic equation suitable for taking moving load effecs into analysis and compares them with the vertical earthquake influence as it is considered during the bridge design. Some comparisons of stresses in various bridges have been performed taking into account dynamic load influence, direct support acceleration from ground motion and EC8 regulations. It has been shown that in some examples dynamical load influence produces the greatest stresses in bridge structure and should be taken into consideration.

Numerical modelling of two-layer shallow water flow in microtidal salt-wedge estuaries : Finite volume solver and field validation

Abstract A finite volume model for two-layer shallow water flow in microtidal salt-wedge estuaries is presented in this work. The governing equations are a coupled system of shallow water equations with source terms accounting for irregular channel geometry and shear stress at the bed and interface between the layers. To solve this system we applied the Q-scheme of Roe with suitable treatment of source terms, coupling terms, and wet-dry fronts. The proposed numerical model is explicit in time, shock-capturing and it satisfies the extended conservation property for water at rest. The model was validated by comparing the steady-state solutions against a known arrested salt-wedge model and by comparing both steady-state and time-dependant solutions against field observations in Rječina Estuary in Croatia. When the interfacial friction factor λi was chosen correctly, the agreement between numerical results and field observations was satisfactory.

Clay block masonry and mortar joint interlocking

Ako se pri izvedbi konstrukcijskog ziđa upotrebljevaju opecni zidni elementi s vertikalnim supljinama i mort opce namjene, tijekom ispunjavanja sAko se pri izvedbi konstrukcijskog ziđa upotrebljevaju opecni zidni elementi s vertikalnim supljinama i mort opce namjene, tijekom ispunjavanja sljubnica nastupa prodiranje morta u supljine zidnog elementa. Otpornost pri posmiku određuje se na jednak nacin za ziđe od punih ili supljih opecnih zidnih elemenata te stoga utjecaj međusobnog spoja zidnih elemenata i sljubnica morta nije uzet u obzir. Pomocu prostornih nelinearnih proracunskih modela i usporedbom s odzivom fizikalnih modela provjeren je utjecaj međusobnog spoja supljih zidnih elemenata i sljubnica morta na posmicnu nosivost.

Similarity of structures based on matrix similarity

Rad prikazuje numericki postupak za uspostavljanje odnosa između ponasanja dvije razlicite konstrukcije, odnosno određivanje mjerila (faktora skaliranja) između dvije konstrukcije. Ovo novo rjesenje zasnovano je na ideji slicnosti matrica i linearnim transformacijama, uz ogranicenja da se mjerilo između konstrukcija određuje tek nakon provođenja diskretizacije te da obje konstrukcije moraju biti u elasticnom podrucju. Mjerilo konstrukcije može se odrediti u polju opterecenja ili pomaka (ovisno o tome dovode li se u vezu sile ili pomaci konstrukcije) gdje se skaliranje statickog modela konstrukcije zasniva na principu ekvivalentnosti matrica, dok je skaliranje dinamickog modela konstrukcije bazirano na Smith normalnoj formi. Skaliranje konstrukcije u operatorskom prostoru (matrice krutosti ili fleksije stavljaju se u međuodnos) trebalo bi biti bazirano na Sylvester matricnoj jednadžbi. Međutim, takav pristup nije praktican te je zamijenjen Levenberg-Marquardt metodom za dobivanje približno ekvivalentnih matrica krutosti. Numericki primjeri ilustriraju predloženi drugaciji pristup.

Flux determination using finite elements: global vs. local calculation

Original scientific paper Finite difference procedures for flux determination are not well suited for application to field results obtained from finite element calculations. A novel method for flux calculation has been derived. This method is based on the weak formulation and is suitable for use with finite elements. A matrix formulation for local and global application to finite element formulations is presented. An additional benefit of the method is that Neumann boundary conditions can be easily incorporated in the finite element formulation of the nonlinear field problem. A comparison between the finite difference, Pade derivative and novel finite element procedures is demonstrated through oneand two-dimensional examples.

Relating Structure and Model

In order to gain additional insight into large structure a model is usually built which leaves us with a problem of transfer of parameters between the model and the structure. Problem is addressed on the general level but after discretization and is formulated as a relationship between relevant parameters of the structure and its model. Scaling matrices in parameter and in measurement space are determined.

Three-dimensional micromodel of clay block masonry wall

In designing and implementing earthquake resistance for clay block masonry infill integrated into a structural frame, with or without openings, the infill wall should be taken into account. Presumably, simplified models, acceptable for practical use, could be applied for that purpose. However, the anisotropy of clay block masonry units, masonry mortar joints, and unit contact properties as well as the high variance of material properties limit their ability to describe the actual earthquake resistance of clay block masonry. In this work, we consider a three-dimensional micromodel of a clay block masonry wall, with the inclusion of masonry unit anisotropy and masonry mortar joint and unit contact properties. To avoid the excessive calibration procedure of the wall micromodel, the wall constituents were calibrated separately beforehand, which resulted in a high correlation of computational and experimental results without further need for calibration. Using a calibrated micromodel, the influence of variance in material properties on the walls resistance was investigated. The influence was showed not to be negligible, which may significantly affect the presumed behaviour of the whole structure.