Thermoinduced plastic flow and shape memory effects

We propose an enhanced form of thermocoupled J2-flow models of finite deformation elastoplasticity with temperature-dependent yielding and hardening behaviour. The thermomechanical constitutive structure of these models is rendered free and explicit in the rigorous sense of thermodynamic consistency. Namely, with a free energy function explicitly introduced in terms of almost any given form of the thermomechanical constitutive functions, the requirements from the second law are identically fulfilled with positive internal dissipation. We study the case when a dependence of yielding and hardening on temperature is given and demonstrate that thermosensitive yielding with anisotropic hardening may give rise to appreciable plastic flow either in a process of heating or in a cyclic process of heating/cooling, thus leading to the findings of one- and two-way thermoinduced plastic flow. We then show that such theoretical findings turn out to be the effects found in shape memory materials, such as one- and two-way memory effects. Thus, shape memory effects may be explained to be thermoinduced plastic flow resulting from thermosensitive yielding and hardening behaviour. These and other relevant facts may suggest that, from a phenomenological standpoint, thermocoupled elastoplastic J2-flow models with thermosensitive yielding and hardening may furnish natural, straightforward descriptions of thermomechanical behaviour of shape memory materials

Advanced mechanics of solids

Mechanics, and in particular, the mechanics of solids, forms the basis of all engi­ neering sciences. It provides the essential foundations for understanding the action of forces on bodies, and the effects of these forces on the straining of the body on the one hand, and on the deformation and motion of the body on the other. Thus, it provides the solutions of many problems with which the would-be engineer is going to be confronted with on a daily basis. In addition, in engineering studies, mechanics has a more vital importance, which many students appreciate only much later. Because of its clear, and analyt­ ical setup, it aids the student to a great extent in acquiring the necessary degree of abstraction ability, and logical thinking, skills without which no engineer in the practice today would succeed. Many graduates have confirmed to me that learning mechanics is generally per­ ceived as difficult. On the other hand, they always also declared that the preoccu­ pation with mechanics made an essential contribution to their successful education. Besides, as far as my experience goes, this success does not depend very much on the inclusion of special chapters, or the knowledge of particular formulae. Rather, it is important that to a sufficient degree, one has learned how to logically describe a given physical phenomenon, starting from the preconditions. And that from this description one can derive rules for related phenomena, and also rules for layout design, for dimensioning, etc. similarly supported structures

ALTERNATIVNI PRISTUP KONAČNIM DEFORMACIJAMA

In elastoplasticity formulation constitutive relations are usually given in rate form, i.e. they represent relations between stress rate and strain rate. The adopted constitutive laws have to stay independent in relation to the change of frame of reference, i.e. to stay objective. While the objectivity requirement in a material description is automatically satisfied, in an Eulerian description, especially in the case of large deformations, the objectivity requirement can be violated even for objective quantities. Thus, instead of a material time derivative in the Eulerian description objective time derivatives have to be implemented. In this work the importance of the objective rate implementation in the constitutive relations of finite elastoplasticity is clarified. Likewise, it shows the overview of the most frequently used objective rates nowadays, their advantages and shortcomings, as well as the distinctive features of the recently introduced logarithmic rate.U savremenoj formulaciji elastoplastičnog ponašanja materijala konstitutivne relacije su uglavnom date u formi izvoda, tj. predstavljaju vezu između izvoda napona i izvoda deformacije kako u formulaciji plastičnog tako i elastičnog dela deformacije. Usvojene konstitutivne relacije moraju ostati nezavisne u odnosu na promenu koordinatnog sistema, tj. da ostanu objektivne. Dok je preduslov objektivnosti u materijalnoj deskripciji automatski zadovoljen, u Ojlerovoj deskripciji, posebno u slučaju velikih deformacija, objektivnost može biti narušena čak i za objektivne promenljive. Stoga, umesto materijalnog izvoda, u konstitutivnim relacijama datim u Ojlerovoj deskripciji moraju se implementirati objektivni izvodi. Ovaj rad doprinosi pojašnjenju važnosti implementacije objektivnih izvoda u konstitutivnim relacijama konačne elastoplastičnosti i daje pregled danas najčešće korišćenih objektivnih izvoda, njihovih prednosti i nedostataka, kao i izuzetnih karakteristika nedavno uvedenog logaritamskog izvoda

NUMERIČKA ANALIZA KONAČNIH HIPOELASTIČNIH CIKLIČNIH DEFORMACIJA SA VELIKIM ROTACIJAMA

Constitutive relations which describe engineering materials behaviour during the finite elastoplastic deformations are usually presented in the form of rates of stresses and strains. One of the possible approaches in the constitutive relations formulation is the additive decomposition of the total deformation rate into its elastic part and its plastic part. The elastic deformation rate contributes to any elastoplastic deformation at any stage. Hence, its exact and well-considered formulation is of particular importance and it has to be properly predicted by the corresponding material law. This is of great importance in particular when deformation cyclic processes are considered, in which case small errors may accumulate, even if the total deformation is small.The implementation of the most frequently used corotational rates, i.e. the Jaumann rate and the Green-Naghdi rate, in the hypo-elastic constitutive relations regarding small and moderate rotations gives accurate results for low number of repeated deformation cycles. With increased number of cycles, however, the implementation of these rates results in different and physically non-admissible material responses. This instability in results is particularly observable during the cyclic deformations with large rotations, which is the main subject of this work. In contrast to the aforementioned objective rates, the results of the logarithmic rate implementation into the hypo-elastic constitutive relations for the case of pure elastic deformation describe a physically stable process.Konstitutivne relacije koje opisuju ponašanje materijala pri konačnim elastoplastičnim deformacijama su najčešće date u formi izvoda napona i deformacija. Jedan od mogućih pristupa u formulaciji ovih konstitutivnih relacija je aditivna dekompozicija ukupnog tenzora brzine deformacije na njegov elastični i plastični deo. Kako je doprinos elastične deformacije prisutan na svakom nivou ukupne elastoplastične  deformacije, tačna i unapred dobro razmotrena formulacija elastičnog dela tenzora brzine deformacije je neophodna. Rešenje ovog problema je primena odgovarajućeg materijalnog zakona u kome glavnu ulogu imaju objektivni izvodi, koji u slučaju konačnih deformacija moraju zameniti materijalni izvod. Izbor odgovarajućeg objektivnog izvoda koji figuriše u konstitutivnoj relaciji ima ključnu ulogu i najvažniji je cilj ovog rada. Ovo može biti od posebne važnosti kada se razmatraju ciklične deformacije, čak i ukoliko su ukupne deformacije male.U slučaju čiste elastične deformacije, implementacijom najčešće korišćenih korotacionih izvoda, t.j. Jaumanovog i Grin-Nagdijevog izvoda, u hipoelastičnim konstitutivnim relacijama pri malim i srednjim rotacijama dobijaju se tačni rezultati, dok je broj ponovljenih deformacionih ciklusa mali. Sa povećanjem broja ciklusa, međutim, implementacija ovih izvoda daje rezultate koji se medjusobno dosta razlikuju, a takođe često opisuju fizički nerealno ponašanje materijala. Ova nestabilnost u rezultatima je posebno uočljiva pri modeliranju cikličnih deformacija pri kojima se javljaju velike rotacije, što je glavni zadatak ovog rada. Suprotno predhodno pomenutim objektivnim izvodima, primena logaritamskog izvoda u hipoelastičnim konstitutivnim relacijama daje rezultate koji u slučaju čiste elastične deformacije opisuju fizički stabilan proces

SYSTEM IDENTIFICATION APPROACH APPLICATION FOR EVALUATION OF SYSTEM PROPERTIES DEGRADATION UDC 624.01:624.042.8(045)=20

Abstract. In respect to the subspace identification method as one of the possible variants of inverse dynamic analyses, behavior of real structural systems with real load and real noise contaminated input/output data was investigated in this work. A useful and non-destructive dynamic parameters evaluation tool- vibration monitoring of the structure- is proposed. The report of original investigation on real models excited by an impulse load in laboratory is also presented. A special contribution is a software program for experiment monitoring and for determination of relevant mechanical characteristics as well as of the location of a possible structural damage. 1

The invention of the Eigenstress calculation in plasticity

Almost one hundred years ago, Heinrich Hencky, in a work published in German and probably for this reason less noticed, laid the essential foundations for today's calculation methods of elastic-plastically deformed structures. In short remarks the importance of this work for several of today's commonly used methods is underlined