Radovan Slavković

A general beam finite element with deformable cross-section

A general beam finite element is proposed in the paper. The formulation of the element relies on the assumption that the beam-type structural response can be described by using the usual beam and 3D continuum theories. The beam behaviour is represented through the beam degrees of freedom of the global nodes on reference axis, and local effects are taken into account through the relative displacements of the cross-sectional nodes defining the in-plane and out-of-plane deformations of the cross-section. Consistent derivations for small and large displacements within incremental analysis are presented. The cross-section is modeled by segments (cross-sectional elements) and can be of arbitrary shape, including thick- and thin-walled types. The element is formulated as a superelement consisting of the isoparametric subelements (3D, shell, beam) with the relative displacements as the internal degrees of freedom of the element group, which is considered as a substructure. The relative displacements can be translations and rotations, depending on the type of the subelements. Continuity of the relative displacements is ensured within the element group, and connection of the beam elements with other finite element (FE) groups is realized through global (beam) degrees of freedom. Incompatible generalized displacements are implemented to subelements to improve their behavior. External loading of the element can correspond to global and cross-sectional nodes. The proposed beam superelement (BS) is easy for application within FE general purpose package (as our program PAK) in the preparation of input and in the postprocessing. A number of typical examples illustrate accuracy of results obtained by use of the beam superelement in linear and geometrically nonlinear analysis.

A General Orthotropic von Mises Plasticity Material Model With Mixed Hardening: Model Definition and Implicit Stress Integration Procedure

A general orthotropic von Mises plasticity model, with an extension of the Hill’s yield criterion to include mixed hardening, is introduced in the paper. Material constants and equivalent stress-equivalent plastic strain curves are defined in a way to suggest their experimental determination. The model represents a special case of a general anisotropic metal plasticity model proposed by the authors. An implicit stress integration procedure, representing an application of the governing parameter method (GPM) introduced by the first author, is presented. The GPM is briefly described, and the computational procedure, together with calculation of the consistent tangent moduli, are given in some detail for a general three-dimensional deformation, with direction of application to plane stress/shell conditions. Numerical examples illustrate applicability of the model and effectiveness of the computational algorithm.

Experimental and numerical thermo-mechanical analysis of shape memory alloy subjected to tension with various stress and strain rates

TiNi shape memory alloy (SMA) is experimentally and numerically investigated in tension tests under different loading rates. The thermomechanical behaviour of the SMA, related to the stress-induced martensitic transformation (SIMT) noticed during the experimental tests, is analysed and the observations are considered for numerical analysis. Initiation, development and saturation of the SIMT are monitored by a fast and sensitive infrared camera. The estimated temperature changes of the SMA sample, related to the exothermic martensitic forward and endothermic reverse transformation, have been analysed with the focus on the rate-dependent response and on the influence of the heat transfer on the mechanical behaviour. The effectively modified constitutive model, proposed by Lagoudas, is implemented in structural PAK finite element method (FEM) software and is thermomechanically coupled with the heat transfer FEM software in a partitioned approach. The experimental results are quantitatively and qualitatively reproduced by the numerical FEM model, which verifies the efficiency and accuracy of the proposed investigation method.

Development of Stress-Induced Martensitic Transformation in TiNi Shape Memory Alloy

TiNi shape memory alloy (SMA) was subjected to tension at strain-controlled test on quasistatic testing machine. The nucleation, development, and saturation of the stress-induced martensitic transformation were investigated, taking into account the obtained dependency of mechanical parameters and the specimen temperature changes measured by an infrared camera (IR). Three kinds of data obtained by the IR system were analyzed: the temperature distribution on the SMA sample surface, the temperature changes derived as average from the chosen sample area, and the temperature profiles obtained along the sample length. The temperature distribution shows nucleation of the transformation process and a creation of the transformation bands. The average temperature reflects the effects of thermomechanical coupling, accompanying exothermic martensitic forward and endothermic reverse transformation. The temperature profiles revealed the temperature difference between the band and the rest of the sample. The experimental results were supported with finite element method numerical analysis (FEM). The FEM software components for structural and heat transfer problems, coupled in partitioned approach, were used for thermomechanical analysis.

Elastic-Plastic Orthotropic Multilayered Pipe Deformation Under External Load and Internal Pressure

Elastic-plastic deformation of a thin-walled pipe, composed of layers with material orthotropic in the elastic and plastic domains, is analyzed. The first material direction for each layer is inclined for an angle (+a and -a successively) with respect to the pipe axis. The yield condition of the material represents a generalization of Hills criterion to include material hardening. The pipe is loaded by internal pressure and other external loads, and it is supposed that the pipe cross section is free to expand or contract. The derived incremental relations for stress integration, which take into account the stress-strain conditions in the pipe wall, are based on the governing parameter method, developed by the first author, where the problem of implicit integration of inelastic constitutive relations within a tune (load) step is reduced to solution of one governing nonlinear equation. Also, the expressions for the tangent elastic-plastic constitutive matrix are derived. One solved simple numerical example demonstrates the main characteristics of the developed algorithm, especially suited for a general elastic-plastic analysis of composite pipes (within the displacement-based finite element method). B, N C e, ein p S Nomenclature = material constants = tangent constitutive matrix = total and inelastic strains = governing parameter = deviatoric stress = internal variable = increment of plastic strain = stress

Properties and Behavior of Shape Memory Alloys in the Scope of Biomedical and Engineering Applications

Shape memory alloys (SMA) are widely and frequently applied in cases when it is useful to employ their advantages through specific behavior (pseudoelasticity or shape memory effect) in various conditions. Effects of shape memory and pseudoelasticity can be employed in innovative ways as actuating or sensing elements in many nowadays applications. There are various alloying elements which can form a SMA such as Ni, Ti, Cr, Cu, etc., but the most frequently used and known alloy is NiTi. By addition of other alloying elements the properties of the SMA can be changed to fit demands of the consumers. The investigation of such materials is very important for successful application, so the researchers investigate procedures and algorithms for comparison of experimental and numerical results to provide the best performance of SMA devices. Strong thermomechanical coupling is observed during the SMA loading, so SMA are known as highly thermosensitive materials what can be used as advantage, but also it can be a problem during the alloy production process. The strong thermomechanical coupling and the related high thermosensitivity increase the need for simulation of complex thermomechanical response in realistic problems. The complex stress states and deformation range impose the requirements for accurate analysis of large strain problems. Application of SMA started several decades ago with an engineering application in pipe couplings, while today one of the most commonly known are biomedical applications (i.e. cardiovascular stents and orthodontic braces). The main reasons for wide range of biomedical applications of NiTi alloys are the specific behavior, good biocompatibility and good fatigue performance what is important factor under the high cyclic external loading.

Thermo-mechanical numerical analysis of stent unit cell

This paper aims to highlight importance of coupled thermo-mechanical analysis of structures and devices made of shape memory alloys (SMA). Ti-Ni alloys are recognized as very biocompatible SMA, so theirs usage is very often in medical purpose. Stent implants made of SMA are the best known application of such materials, so the unit cell of some typical stent model is used to demonstrate the necessity of coupled finite element based numerical analysis of such structures. The thermo-mechanical coupling is realized in partitioned approach, whereas software components for structural analysis (PAKS) and heat transfer (PAKT) have been used as suitable solutions. The SMA constitutive model is implemented into PAKS with the capability to solve large strain problems by using multiplicative decomposition of deformation gradient.

Analitička, numerička i eksperimentalna procjena naprezanja kuglastog spremnika velikog obujma

Original scientific paper This paper presents designing of spherical tank using combination of analytical procedure with FEM analysis and experimental testing in order to minimize design time and verify design strength. Analytical procedure for calculation of the tank strength in the initial stages of design process is briefly presented. Based on analytical results, tank is dimensioned and FEM model is created. FEM analysis is used to identify areas with high concentration of stresses. FEM results showed that equivalent value of stress at the points of spherical tank support exceeds the values of yield stress, but this exceedance is not significant and in very small area, so overall design was deemed worthy. Experimental measurements verified FEM results that it is not necessary to reinforce the spherical tank at the points of support. After 8 months experiments were repeated giving the same results as the original measurements, thus justifying decision not to reinforce tank supports.

EMBANKMENT DAM STABILITY ANALYSIS USING FEM

This paper presents stability analysis of embankment dam with the surrounding heterogeneous rock mass using finite element method. In order to perform stability analysis of the dam and surrounding rock mass, several elastic-plastic material models for soil are customized and implemented in program package PAK. A 3D FE model of the embankment dam and the surrounding rock mass containing various material distributions according to their real distribution was made. The model includes a wider area around the dam in order to minimize the influence of the boundary conditions. The initial material parameters were determined using the identification of material parameters on the basis of the material from the dam body. Analysed dam is equipped with dam crest displacement transducers, as well as with transducers for the total and pore pressure in the clay core. Certain deviations have been noticed while comparing the measured values of these quantities with the results of the simulation. Since the analysed dam has been in operation for a long time, these deviations from the initial values of the parameters are caused due to the changes of the mechanical properties of materials during the dam operation. These changes are caused by several factors: the settlement of the dam and foundation, flushing of the material in the body of the dam and foundation, load changes, etc. In order to take into account the change of mechanical properties in materials and achieve the results of numerical simulation to describe the behaviour of the dam as close to the real behaviour, the calibration of the material parameters is carried out. Calibration of material parameters was performed using the measured displacements of the dam crest, as well as pore and total pressures in the clay core. Using the calibration we obtain new material parameters which give results of the numerical simulation that are closer to the behaviour of the real dam. In this manner we manage the dam safety and we can predict its future behaviour.