Tomasz Strek

Analytical approximations of the shape factors for conductive heat flow in circular and regular polygonal cross-sections

The heat flux in steady heat conduction through cylinders whose cross-section has an inner or an outer contour in the form of a regular polygon or a circle is considered. To calculate the shape factor the temperature field is determined. Three cases are considered: (a) temperature field for hollow prismatic cylinders bounded by isothermal inner circles and outer regular polygons, (b) temperature field for hollow prismatic cylinders bounded by isothermal inner regular polygons and outer circles, (c) temperature field for hollow prismatic cylinders bounded by isothermal inner and outer regular polygons. The boundary collocation method in the least squares sense for solving appropriate boundary value problems is used. By means of nonlinear approximation (Marquardt method), for the three considered geometry cases, the simple analytical formulas for the shape factors are proposed.

The influence of large deformations on mechanical properties of sinusoidal ligament structures

Studies of mechanical properties of materials, both theoretical and experimental, usually deal with linear characteristics assuming a small range of deformations. In particular, not much research has been published devoted to large deformations of auxetic structures – i.e. structures exhibiting negative Poissons ratio. This paper is focused on mechanical properties of selected structures that are subject to large deformations. Four examples of structure built of sinusoidal ligaments are studied and for each geometry the impact of deformation size and geometrical parameters on the effective mechanical properties of these structures are investigated. It is shown that some of them are auxetic when compressed and non-auxetic when stretched. Geometrical parameters describing sinusoidal shape of ligaments strongly affect effective mechanical properties of the structure. In some cases of deformation, the increase of the value of amplitude of the sinusoidal shape decreases the effective Poissons ratio by 0.7. Therefore the influence of geometry, as well as the arrangement of ligaments allows for smart control of mechanical properties of the sinusoidal ligament structure being considered. Given the large deformation of the structure, both a linear elastic material model, and a hyperelastic Neo-Hookean material model are used.

Computational Modelling of Structures with Non-Intuitive Behaviour

This paper presents a finite-element analysis of honeycomb and re-entrant honeycomb structures made of a two-phase composite material which is optimized with respect to selected parameters. It is shown that some distributions of each phase in the composite material result in the counter-intuitive mechanical behaviour of the structures. In particular, negative values of effective Poisson’s ratio, i.e., effective auxeticity, can be obtained for a hexagonal honeycomb, whereas re-entrant geometry can be characterized by positive values. Topology optimization by means of the method of moving asymptotes (MMA) and solid isotropic material with penalization (SIMP) was used to determine the materials’ distributions.

Estimation of Coupled Thermo-Physical and Thermo-Mechanical Properties of Porous Thermolabile Ceramic Material Using Hot Distortion Plus® Test

In the paper the thermo-mechanical phenomena which occur in thermal shocked thermolabile porous ceramic material were described. Such materials are applied in foundry industry for mould making and they are characterized the low thermal stability losing its strength above 400°C. In [3] the usefulness of Hot Distortion Plus® to estimate the thermo-physical parameters (apparent thermal conductivity, heat capacity) was discussed. These parameters are necessary in data base of simulation codes which permit to simulate the phenomena in casting-mould system. The aim of these tests is to predict the mould material phenomena influence on castings quality. Parameters applied in these thermo-mechanical models (Youngs modulus, Poissons ratio, Yield stress) and their variations with temperature are not really known for thermal unstable mould material. There is no adapted method in literature and description of such total investigations of both parameters groups: thermo-physical and thermo-mechanical. The authors method called Hot Distortion Plus® consists in acquisition of temperature curves of heated sample of material and correlation with curves of their dilatation. Following the simulation using inverse solution method to reproduce the measured parameters with experiment was applied. The tests were carried out for the new quartz sand bonded by resin (approx. 1%). The specimens (dimensions 114 × 25 × 6mm) from binder-sand mixture were made using special core-box.

Computational Modelling of Auxetics

Modern technologies require new materials of special properties. One of the reasons for interest in materials of unusual mechanical properties comes from the fact that they can be used (either as inclusions or as matrices) to form composites of required properties. There is a number of physical properties that we implicitly assume to be positive. However, one may be surprised to discover that they can also be negative. Negative materials include, amongst other ones, those having negative stiffness (Lakes et al., 2001), negative thermal expansion (Hartwig, 1995), negative refractive index (Sang & Li, 2005), negative permittivity (Ruppin, 2000) and/or negative permeability (Ruppin, 2000). It is worth to add that in presence of some constrains even the compressibility can be negative (Lakes & Wojciechowski, 2008). A new field of challenge are studies of materials exhibiting negative Poisson’s ratio. The latter is a negative ratio of relative transverse dimension change to relative longitudinal dimension change of a body when an infinitesimal change of a stress acting along the longitudinal direction occurs whereas the other stress components remain unchanged. Such materials, first manufactured by Lakes (Lakes, 1987) and coined auxetics by Evans (Evans, 1991), are a subject of intensive studies both in the context of fundamental research and applications (Remillat et al., 2009). The aim of this chapter is to demonstrate recently discovered anomalous deformation of an auxetic plate, constrained by fixing two opposite sides, which is loaded by uniform tension (or compression) applied perpendicularly to two other opposite sides of the plate. The problem was studied both in three dimensions (3D) by Strek et al. (Strek et al., 2008) and in two dimensions (2D) by Pozniak et al. (Pozniak et al., 2010) by finite element methods. In all the cases studied it has been assumed that the material was isotropic. 12

Optimization of the Effective Thermal Conductivity of a Composite

Composite materials by definition are a combination of two or more materials. Although the idea of combining two or more components to produce materials with controlled properties has been known and used from time immemorial, modern composites were developed only several decades ago and have found by now intensive application in different fields of engineering (Vasiliev&Morozov, 2001). These materials are used in various design to improve the characteristic of various construction and reduce their weight. The properties of these materials and the problems of obtaining structural elements based upon them have been studied by researchers and engineers all over the world. The fields of composite applications are diversified (Freger et al., 2004). They include structural elements of flying vehicles, their casinos, wings, fuselages, tails and nose cones, jet engine stators, panels form various purposes, main rotors of helicopters, heat – proofing components, construction elements such as panels, racks, shields, banking elements, etc. Any property of a composite which is made of two (or more) materials has the value which is the resultant of a few factors. Obviously, the most important are the values of a certain property of each constituent material. However, one of the factor that also influences the resultant value of a property of a composite as a whole is its geometrical structure. Such resultant properties are commonly called effective properties of a composite. Temperature is the most important of all environmental factors affecting the behaviour of composite materials, mainly because composites are rather sensitive to temperature and have relatively low effective thermal conductivity. For instance, advanced composites for engineering applications are characterized with low density providing high specific strength and stiffness, low thermal conductivity resulting in high heat insulation, and negative thermal expansion coefficient allowing us to construct hybrid composite elements that do not change their dimensions under heating (Vasiliev & Morozov, 2001). Because experimental evaluation of effective properties (e.g. thermal conductivity) of composites is expensive and time consuming, computational methods have been found to provide efficient alternatives for predicting the best parameters of composites, especially those having complex geometries. To achieve a reliable prediction, one needs to work on two aspects: a good description of the structural details of fibrous materials, and an efficient numerical method for the solution of energy equations through the fibrous structures (Wang et al. 2009). The need to determine the thermal conductivity of fibres for design purposes has been the motivation of work (Al-Sulaiman et al., 2006). Authors developed four

Thermoauxetic Behavior of Composite Structures

This paper presents a study of new two-dimensional composite structures with respect to their thermomechanical properties. The investigated structures are based on very well-known auxetic geometries—i.e., the anti-tetrachiral and re-entrant honeycomb—modified by additional linking elements, material which is highly sensitive to changes of temperature. The study shows that temperature can be used as a control parameter to tune the value of the effective Poisson’s ratio, which allows, in turn, changing its value from positive to negative, according to the temperature applied. The study shows that such thermoauxetic behavior applies both to composites with voids and those completely filled with material.

Vibration Transmission Loss of Auxetic Lattices

The auxetic lattices are structures, which have the negative Poisson’s ratio. When material has negative Poisson’s ratio, has also auxetic properties - during process of stretching, are made wider and during compressing are made narrower. This structures are cellular and negative Poisson’s ratio is depending on the geometry of single auxetic cell. When geometry of the cell is slightly changed also Poisson’s ratio is different. Auxetics have attracted attention of researchers because of their superior dynamic properties. The lattice auxetic structures at one of their natural frequencies exhibit the deformed geometry. It’s can be exploit as resonance to optimization of the power required for the occurrence localized deformations. The dynamic behavior of auxetic and their transmission of the vibration, which is circumscribed by the parameter VTL (Vibration Transmission Loss) will be analyzed in this article.

Identification of Thermal Conductivity of Modern Materials Using the Finite Element Method and Nelder-Mead's Optimization Algorithm

Due to the fact that modern materials are widely used in aerospace industry, automotive industry, medicine and many others it is very important to find out a way to meet all its needful parameters. There is a lot of composites, which arise from a combination of at least two different components on the macroscopic level and whose parameters are unknown. Therefore, it is difficult to get to know their possibilities and functionality. A kind of composite materials are Functionally Graded Materials (FGM). They are characterized by the fact that its composition and structure gradually change over the volume, which follows from changes in properties of material (Miyamoto et al., 1999). There are many works on this topic.