Prace IPPT PAN z roku 2001




1.       BASISTA Michał - Micromechanical and Lattice Modeling of Brittle Damage. - (Praca habilitacyjna). - Warszawa 2001 s.  237. - Prace IPPT    3/2001.

2.       SZEMPLIŃSKA - STUPNICKA Wanda, TYRKIEL Elżbieta - Bifurkacje, chaos i fraktale w dynamice wahadła. - Warszawa 2001 s.  32. - Prace IPPT    2/2001.

3.       ANTUNEZ Horacio J. - Bulk-metal Forming Processes from Computational Modelling via Sensitivity Analysis to Tool Shape Optimization. - (Praca habilitacyjna). - Warszawa 2001 s.  207. - Prace IPPT    1/2001.



Micromechanical and Lattice Modeling of Brittle Damage.

(Praca habilitacyjna).

Warszawa 2001 s.  237.

Prace IPPT    3/2001.


   This thesis is a multi-aspect study concerned with theoretical modeling of damage in brittle solids with special emphasis on rocks and plain concrete. Motivated by the complex and diverse nature of damage processes in these materials, an integrated approach involving micromechanical, phenomenological and lattice modeling is pursued. It is shown that these seemingly disparate classes of models turn to be complementary in their objectives and utility. The bulk of the work is devoted to the local description of damage problems in rock-like materials under quasi-static mechanical loading (tensile or compressive) at isothermal conditions. Slightly off the mainstream but well in tune with the micromechanical damage modeling promoted in this thesis, a type of environmental damage of concrete due to chemically aggressive ambient is also investigated. Application of the methods of physics of critical phenomena to brittle damage and fracture problems constitutes an important part of this study. It is suggested that the percolation and other disorder models be used at large microdefects densities where the traditional methods of micromechanical and continuum damage mechanics cease to be valid. The individual chapters of the thesis can be summarized as follows.

   Chapter 1 presents in a concise way the basic definitions and assumptions of the damage mechanics. Main differences (and similarities, if any) between damage and fracture, damage and plasticity are pointed out. It is stressed that the presently used name of damage mechanics (shortly DM) shall not be identified with early phenomenological damage theories (CDM) which were chronologically the first to deal with the damage problems in the framework of continuum mechanics. The former is much a wider class comprising micromechanical damage models, statistical damage models, statistical damage models, and the CDM models themselves. In Chapter 1, these three classes of models are briefly characterized and critically evaluated in the context of brittle deformation.

   Chapter 2 provides experimental background for the analytical models proposed in this thesis. Mechanisms of tensile and compressive microcracking in rocks inducing inelastic macroscopic stress-strain behavior, microcrack related anisotropy, positive dilatancy, pressure dependence, hysteresis, etc. are discussed in considerable detail. Additionally, some basic facts about the subcritical microcrack growth as well as the acoustic emission application to rock microcracking and fracture are reviewed. It seems that acoustic emission (AE) is gaining a steadily growing reputation as a reliable, non-destructive technique capable of unraveling focal mechanisms and locating, both temporary and spatially, the evolving microcracks within the material volume. The important point is that AE allows for continuous screening of the microcrack nucleation, growth and localization into a dominant fault.

   Chapters 3, 4, 5, 6, 7, 8 constitute the original research part of the thesis. Chapter 3 is concerned with a relatively straightforward case of damage development in brittle materials subjected to displacement-controlled (homogeneous) tensile loading. On the example of plain concrete and using a general internal-variable thermodynamic framework, it is shown in a systematic manner how a workable micromechanical damage model can be constructed starting with the behavior of a single tensile microcrack in the unit cell. A new microcrack growth condition (3.5)-(3.6) is proposed based on an experimentally supported dependence of the fracture toughness on the microcrack length. The model is formulated for the uniaxial tension and then generalized for two-dimensional case. Typical configurations of interacting microcracks having analytical solutions for the K 1 factors are incorporated into the model to illustrate how the stress amplification effects might influence the overall s-e behavior in tension.

   Chapter 4 deals with the compressive damage in rocks. Of several possible micromechanism of inelastic rock deformation in brittle regime, the sliding microcrack model is selected for modeling purposes owing to its remarkable versatility in replicating the macroscopically observed effects of rock response in compression. The original contribution of this chapter includes application of the Rice thermodynamic formalism with microstructural variables to the sliding microcrack deformational mechanism, detailed analysis of all phases of sliding microcrack behavior in loading and unloading, derivation of the ensuing incremental stress-strain equations, their numerical implementation and comparison of the computed results with the available test data on granite to show the model at work.

   Chapter 5 is devoted to estimation of the stress intensity factors for interacting slits endowed with frictional and cohesive resistance and for sliding microcracks with developed tension wings under overall compression. The very effective analytical-numerical method of Kachanov (1987) is extended and modified to account for friction and cohesion on the crack faces. Also, the case of point-force loading on interacting cracks is considered. Using a developed FORTRAN code, a number of test problems of crack interaction is solved and compared with the corresponding „exact” BEM results.

   In Chapter 6, a micromechanical model is formulated for the deformation of hardened concrete exposed to chemical corrosion by sulphate ions migrating into the concrete structure from ground water. The model is quite complex involving several coupled physico-chemical processes such as non-steady diffusion, heterogeneous chemical reactions, expansion of reaction products, microcracking of heterogeneous matrix (hardened cement paste with ettringite inclusion), and percolation. These processes are modeled on the microscale and resulting equations are volume-averaged leading to the macroscopic expansions which closely match the test data of Ouyang et al. (1988) on ASTM recommended specimens.

   Chapter 7 suggests a micromechanically-based phenomenological damage model for brittle response of solids. For deformation processes dominated by Mode I microcracking, the inelastic change of the compliance tensor is identified as the flux, and the fourth-order tensor                Q = 1/2 (s Ä s) as the affinity. The conditions under which a damage potential exists are indicated. Illustrative examples are worked out.

   Chapter 8 is devoted to modeling brittle damage and fracture using methods of statistical physics of the critical phenomena - an alternative modeling methodology which is entirely different from the conventional (micromechanical or phenomenological) damage mechanics models. In the search for possible interrelations between damage mechanics and statistical lattice models, two classes of disordered systems are given particular attention: percolation model and central-force model. It is found that the percolation theory can be quite useful when verifying the accuracy of the effective-continua methods in predicting the effective elastic constants of a damaged solid. Furthermore, results of the numerical simulations on central-force triangular in Hansen, et al. (1989) are compared with the corresponding analytical estimates yielded by the parallel bar model (widely used in damage mechanics). To this end, a number of original results is obtained in this chapter including accuracy assessment of the effective-media methods, selection of the secant effective compliance tensor as the damage variable, microcrack interaction in tension, etc.



Bifurkacje, chaos i fraktale w dynamice wahadła.

Warszawa 2001 s.  32.

Prace IPPT    2/2001.


   Opracowanie materiału przedstawionego w tym zeszycie zostało poprzedzone bogatym doświadczeniem dydaktycznym, studiami literatury naukowej na temat zjawisk drgań chaotycznych w układach fizycznych oraz publikacjami serii oryginalnych prac naukowych w międzynarodowych czasopismach naukowych. Dodatkowym, ale bardzo istotnym doświadczeniem były seminaria, referaty lub krótkie serie wykładów, przedstawione zarówno w IPPT PAN, jak i na wyższych uczelniach dla tych środowisk naukowych, których zainteresowanie zjawiskami drgań chaotycznych w prostych deterministycznych układach nie było poprzedzone systematycznymi studiami na ten temat. Ograniczony czas seminarium lub referatu na konferencji naukowej dawał tu bodźce do przemyślenia, jaką wybrać metodę referowania materiału tak, by trafił on do wyobraźni i przekonania słuchaczy w sposób prosty, a zarazem pobudził ich zainteresowanie i zachęcił do głębszego studiowania przedmiotu. Ten kierunek myślenia doprowadził do spostrzeżenia, że w tej nieuchwytnie matematycznie dziedzinie dobrą metodą jest przedstawienie zarówno zagadnień podstawowych, jak i zaawansowanych, przy maksymalnym wykorzystaniu interpretacji geometrycznej. Interpretacja ta posługuje się w dużej mierze rysunkami: zarówno wykresami schematycznymi, jak i graficzną interpretacją wyników obliczeń komputerowych.

   Po wygłoszeniu referatów na temat własnych wyników w dziedzinie drgań chaotycznych na konferencjach krajowych, często padało pytanie o literaturę podstawowa na te tematy. Chodziło oczywiście o książkę dostępną w Polsce, i to książkę nadającą się do wstępnego zapoznania się z przedmiotem. Najczęściej odpowiadam wtedy, że najlepiej zacząć od książki F. Moona pt. Chaotic vibrations, an introduction for applied scientists and engineers [1], aczkolwiek zdawałam sobie sprawę, że książka ta nie jest powszechnie dostępna w Polsce. Poza tym jest ona dość obszerna, a przedstawiony materiał jest tak poszatkowany na dużą liczbę rozdziałów, że przestudiowanie jej wcale nie jest łatwe. Istnieje jednak pierwsza wersja tej książki o mniejszej objętości. Otóż, jak pisze prof. Moon we wstępie, bodźcem do napisania tej książki było zaproszenie IPPT PAN w roku 1984 do wygłoszenia 8 godzin wykładów na temat drgań chaotycznych, i że książka ta jest właśnie rozszerzeniem tematu tych wykładów. Tak więc, pierwszą, krótszą wersję książki F. Moona można znaleźć w zeszycie IPPT 28/1985 pt. Chaos w nieliniowej mechanice [2], zawierającym prace przygotowane na konferencję szkoleniową pod tym samym tytułem, która odbyła się w Jabłonnie w dniach 12-17 sierpnia 1984 r.

   W latach późniejszych ukazały się polskie tłumaczenia niektórych książek opartych na materiale pełnych cykli wykładów, przeważnie na studiach doktoranckich. Wymienię tu przede wszystkim książkę H.G. Schustera pt. Chaos deterministyczny [3] oraz E. Otta pt. Chaos w układach dynamicznych [4], obie ukierunkowane na studia fizyczne. Warta uwagi jest książka J. Kudrewicza pt. Fraktale i chaos [5]. Z powszechnym zainteresowaniem spotkała się książka popularno-naukowa I. Stewarta pod intrygującym tytułem Czy Bóg gra w kości? [6].

   Przedstawione rozważania na temat książek dostępnych w Polsce zarówno na rynkach księgarskich jak i w bibliotekach naukowych, jak również własne doświadczenia dydaktyczne doprowadziły do wniosku, że warto pokusić się o upowszechnienie wiedzy na temat drgań chaotycznych w deterministycznych prostych oscylatorach przez opracowanie publikacji ujmującej tematykę w zupełnie inny sposób niż klasyczne ujęcie podręcznikowe. Ten inny sposób polega m. in. na:

   · skierowanie uwagi czytelnika na jeden, a w dalszej kolejności na następne, dobrze znany deterministyczny model dysypatywnego układu drgającego o jednym stopniu swobody; model, który można sprowadzić do modelu fizycznego kulki poruszającej się po wyznaczonym torze pod działaniem znanych i ciągłych w opisie matematycznym sił. A ponieważ trudno o bardziej znany układ drgający zbadany doświadczalnie niż wahadło matematyczne poddane działaniu zewnętrznego periodycznego wymuszenia, przedstawiony zeszyt dotyczy właśnie tego układu;

   · przypomnieniu najpierw własności układu liniowego, a dalej słabo nieliniowego, przez pryzmat wyników badań doświadczalnych i komputerowych, bez stosowania wzorów i przekształceń matematycznych. Następnie, w miarę zwiększania amplitudy wymuszenia i zbliżania się do zjawisk o charakterze chaotycznym, wyjaśnieniu i interpretowaniu pojawienia się takich zjawisk jak bifurkacje lokalne, granice obszarów przyciągania itd., również w interpretacji geometrycznej. Nie odrywamy tu uwagi czytelnika pokazując np. pełną klasyfikację różnych typów stateczności i niestateczności punktów równowagi (osobliwych), czy pełnej listy różnorodnych typów bifurkacji. Czytelnik obserwuje tylko te zjawiska, które się pojawiają w rozważanej dynamice wahadła;

   · oddzielenie od tekstu podstawowego tych fragmentów, które można ominąć przy pierwszym czytaniu. Fragmenty te (pisane mniejszą czcionką) zawierają rozszerzenie materiału, przedstawiając zarówno uwagi na temat tych problemów, które występują w dynamice wahadła, jak i pewne dodatkowe uwagi teoretyczne, odsyłając czytelnika do odnośnej literatury;

   · ujęciu w ten prosty sposób również zaawansowanych problemów i najnowszych wyników dotyczących związku między teoretycznym pojęciem globalnej bifurkacji a fraktalną strukturą granic obszarów przyciągania, zjawiskiem chaosu przejściowego i wrażliwością na warunki początkowe;

   · połączeniu w jedną całość koncepcji drgań chaotycznych i fraktali, poprzez pokazanie fraktalnej struktury dziwnego (chaotycznego) atraktora.

   Część przedstawionych wyników została opublikowana w czasopismach International Journal of Bifurcation and Chaos, Nonlinear Dynamics oraz Computer Assisted Mechanics and Engineering Science w latach 1997-2001, a część została wykonana dla potrzeb niniejszego opracowania. Wszystkie obliczenia komputerowe i graficzne opracowanie wyników wykonane zostały przez dr Elżbietę Tyrkiel, współautorkę niniejszej publikacji.


ANTUNEZ Horacio J.

Bulk-metal Forming Processes from Computational Modelling via Sensitivity Analysis to Tool Shape Optimization.

(Praca habilitacyjna).

Warszawa 2001 s.  207.

Prace IPPT    1/2001.


   Towards the end of the sixties and the beginning of the seventies, electronic computers started to be developed in a larger scale than up to then, and thus became available to researches. And quite quickly a number of already available methods to solve engineering problems began to be applied.

   Until then such methods has required, even to obtain at least a roughly meaningful result, a prohibitively heavy calculation works as they had to be applied by hand. Basically this involved the solution of relatively large systems of equations or the repetitive solution of rather simple problems.

   By that time a good amount of theoretical knowledge, which allowed the successful solution of many linear problems, was available. Mechanics, material science, algebra and numerical analysis provided the necessary background for these methods to be applied.

   The first applications of numerical methods concerned those linear problems. Among them, static problems of civil engineering were on top of the list. And this to the extent that many concepts and names taken from this field have remained in the new developing computer methods even when applied to other problems. Typical examples of problems solved in this period are linear elasticity and heat conduction.

   Shortly afterwards, it became clear that nonlinear problems should also be addressed, and this to satisfy countless practical requirements. Hence, the development of a number of disciplines started. In material science, an outstanding step was performed by including more complex constitutive equations, which involved more state and history variables. On the other hand, more powerful mathematical tools were developed to describe large displacement and deformations. Boundary conditions of ongoing processes were more precisely described including, among others, contact conditions and friction.

   It would be hard to summarize all the developments of computational mechanics in the recent decades. Just to mention the subjects they concerned, effort was concentrated in material modelling, geometry and boundary conditions description, numerical methods for discretization and for efficient solution of the equation systems, and operations involving the mesh of finite elements including optimization of the bandwidth, remeshing, mesh refinement and coarsening, all aiming at minimizing an appropriate error norm. Practically all the engineering problems of interest have been addressed, many of them involving coupled problems.

   Still further elaborations included the use of the solved system of equations to perform sensitivity analysis by the so-called analytical methods. These resulted to provide the sensitivity coefficients, and did that at a residual cost as compared to the cost of solving the overall problem. The inclusion of sensitivity analysis with respect to shape parameters finally prepared the way to shape optimization since not only a given design functional, but also its gradient in the design space were available to be used by an optimization algorithm.

   In this historical context, one of the fields which has attracted more interest is that of metal forming simulations, probably for its interest for industrial applications. Practically all the subjects quoted above for computational mechanics in general are dealt with in this field.

   A series of options are available for building a computational model for metal forming simulation. Most frequently, each choice implies to reject other possibilities, and some goals are obtained but some drawbacks arise. Hints about the proper choice may be given by the type of process being simulated. This, confirmed by the experience of many researches, supports the position that it is more convenient to have several specialized programs, each of which effectively analyzes a given class of problems, than to have a complex, much larger general purpose program which, to given extent, is adapted to the characteristic features of (almost?) every practical problem.

   Within the preceding framework, the present work is a collection of developments performed at the Institute of Fundamental Technological Research of PAS. All of them are concerning one specific way of modelling metal forming processes; this is especially suited for hot forming conditions, and has been conceived for steady-state processes, although it can be applied in transient ones as well.

   The naturally suited application of this model is extrusion; however, it can be used also in free forging, cutting and rolling (including seamless tube rolling) for which results are shown as well.

   Stationary and transient processes are separately presented here; not only for the sake of clarity of the exposition and the for historical reasons, but to show the analysis problem, sensitivity analysis and shape optimization as successive steps within a logical line of thinking. Essentially this process was followed in the computer simulation of metal forming, feeding into each step all the results obtained in the preceding ones.

   In this work, the steady state is presented first, starting by the flow approach. Following, the discretization by finite elements is given. Here the different features accounted for in the model are explained. Once the analysis model is complete, the sensitivity is ready to be introduced. First, parametric sensitivity is discussed, what is incidentally useful to show the available methods for sensitivity analysis. Shape sensitivity is considered next, followed by the optimization algorithm which finds, according to given criteria and design restrictions, the optimum design.

   Afterwards transient processes are considered. A full transient formulation is considered and used to obtain an incremental method that makes of linear elements due to a proper time-step splitting. Attention is focused on the full explicit version. Further, sensitivity analysis within such model and discretization is shown. In addition, the pseudo-concentration method is briefly revisited and used in connection to Fourier series expansion of the problem of seamless tube rolling.

   Some additional -but significant- topics are discussed in the course of the main presentation. The simulation of the almost perfect plasticity poses the problem of uniqueness (or its lack), and this is discussed in the context of cutting simulation. Pressure stabilization necessary to apply a friction model based on a Coulomb-type law. In this context a bilinear interpolation is introduced, which takes advantage of a method for similar pressure stabilization used in fluid mechanics. Sensitivity analysis suggests that its results can have an additional application in evaluating the effect on the solution of numerical parameters needed in some models. This is the case of the upwind parameters in coupled thermo-mechanical problems and the step in time integration of transient processes. The introduction of shape sensitivity analysis of forming processes gives the occasion to consider the extension to large displacements of the two available methods. In the shape optimization part, the problem of shape parameterization requires special attention. Two different techniques of interpolating points in the discretized domain in terms of the design parameters are proposed.