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Abstract:
This paper discusses the issue of a lap joint in the form of a thin film attached to a rigid base with the use of a layer of flexible adhesive exhibiting a non-linear constitutive relation between shear stress and distortional strain, which is approximated by the second-order power law. Similarity theory is used to perform a qualitative analysis of the influence of magnitude of non-linearity on the performance of the system. The introduced similarity numbers are proposed to be used in formulation of simple design tools. The analysis is performed by solving the derived governing equations for characteristic cases in a numerical way combining the fourth-order Runge-Kutta algorithm and iterative shooting ruled by a steepest descent method. The results are compared with the results of the plane stress finite element analysis. It can be observed that within considered models the influence of the material non-linearity is of minor importance and in some cases it may be almost entirely surpassed by local effects resulting from boundary conditions. For relatively small load intensity it becomes negligibly small.

Keywords:
flexible adhesives, non-linear elasticity, lap joint, strengthening films

Abstract:
In the paper a new proposition of limit state criteria for anisotropic solids exhibiting different strengths at tension and compression is presented. The proposition is based on the concept of energetically orthogonal decompositions of stress state introduced by Rychlewski. The concept of stress state dependent parameters describing the influence of certain stress modes on the total measure of material effort was firstly presented by Burzynski. The both concepts are reviewed in the paper. General formulation of a new limit criterion as well as its specification for certain elastic symmetries is given. It is compared with some of the other known limit criteria for anisotropic solids. General methodology of acquiring necessary data for the criterion specification is presented. The ideas of energetic and limit state orthogonality are discussed - their application in representation of the quadratic forms of energy and limit state criterion as a sum of square terms is shown

Keywords:
anisotropy, strength hypothesis, material effort, yield condition, plastic potential, strength differential effect, elasticity, plasticity

Abstract:
W artykule przedstawiono propozycję nowego kryterium plastyczności dla blach ortotropowych wykazujących różnicę wytrzymałości przy rozciąganiu i ściskaniu. Nowe kryterium bazuje na energetycznym warunku stanu granicznego dla materiałów anizotropowych zaproponowanym przez Rychlewskiego [2] i łączy się z wprowadzoną przez Burzyńskiego [3] koncepcją zależnych od charakteru stanu naprężenia funkcji określających udział poszczególnych składników rozkładu głównego gęstości energii sprężystej w całkowitej mierze wytężenia materiału. Podano specyfikację kryterium dla wszystkich płaskich symetrii sprężystych. Zaprezentowano ogólną metodę pozyskiwania danych niezbędnych do wyznaczenia parametrów kryterium na podstawie wyników prostych prób wytrzymałościowych - rozciągania, ściskania i ścinania. Wskazano na szczególne konsekwencje w opisie deformacji plastycznej blach w przypadku przyjęcia prawa płynięcia plastycznego stowarzyszonego z zaprezentowanym warunkiem plastyczności.

Keywords:
blachy walcowane, anizotropia, asymetria zakresu sprężystego, kryterium plastyczności, hipotezy wytężenia

Abstract:
In the paper a new proposition of an energy-based hypothesis of material effort is introduced. It is based on the concept of influence functions introduced by Burzyński [3] and on the concept of decomposition of elastic energy density introduced by Rychlewski [18]. A new proposition enables description of a wide class of linearly elastic materials of arbitrary symmetry exhibiting strength differential effect.

Keywords:
linear elasticity, anisotropy, material effort hypotheses, limit state criteria

Abstract:
The aim of the paper is to propose an extension of the Burzyński hypothesis of material effort to account for the influence of the third invariant of stress tensor deviator. In the proposed formulation the contribution of the density of elastic energy of distortion in material effort is controlled by Lode angle. The resulted yield condtion is analyzed and possible applications and comparison with the results known in the literature are discussed.

Keywords:
Burzyński yield condition, strength differential effect, pressure sensitivity, Lode angle, third invariant of stress tensor deviator

Abstract:
In the paper a new proposition of an energy-based hypothesis of material effort is introduced. It is based on the concept of influence functions introduced by Burzyński [3] and on the concept of decomposition of elastic energy density introduced by Rychlewski [18]. A new proposition enables description of a wide class of linearly elastic materials of arbitrary symmetry exhibiting strength differential effect.

Keywords:
linear elasticity, anisotropy, material effort hypotheses, limit state criteria