Aneta Ustrzycka, Ph.D. 

Doctoral thesis
20121219  Optymalne kształtowanie elementów konstrukcyjnych z uwagi na czas zniszczenia mieszanego w warunkach pełzania (PK)
 1245 
Recent publications
1.  Ustrzycka A., Szuwalski K.^{♦}, Annular rotating disks optimal with respect to mixed creep rupture, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 14292955, DOI: 10.15632/jtampl.56.1.57, Vol.56, No.1, pp.5769, 2018 Abstract: Optimal shapes in the class of polynomial functions for rotating annular disks with respect to the mixed creep rupture time are found. Two effects leading to damage: diminishing of transversal dimensions and growth of microcracks are simultaneously taken into account. The first of them requires the finite strain analysis, the latter is described by Kachanov’s evolution equation. Behaviour of the material is described by nonlinear Norton’s law, generalized for true stresses and logarithmic strains, and the shape change law in form of similarity of true stresses and logarithmic strains deviators. For optimal shapes of the disk, changes of geometry and a continuity function are presented. The theoretical considerations based on the perception of the structural components as some highlighted objects with defined properties is presented Keywords:annular disk, mixed creep rupture, optimal design Affiliations:
 
2.  Ustrzycka A., Mróz Z., Kowalewski Z.L., Experimental analysis and modelling of fatigue crack initiation mechanisms, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 14292955, DOI: 10.15632/jtampl.55.4.1443, Vol.55, No.4, pp.14431448, 2017 Abstract: The present work is devoted to simulation of fatigue crack initiation for cyclic loading within the nominal elastic regime. It is assumed that damage growth occurs due to action of meanstress and its fluctuations induced by crystalline grain inhomogeneity and the free boundary effect. The macrocrack initiation corresponds to a critical value of accumulated damage. The modelling of damage growth is supported by Electronic Speckle Pattern Interferometry (ESPI) apparatus using coherent laser light. Keywords:fatigue crack initiation, damage evolution, optical methods Affiliations:
 
3.  Skoczeń B.^{♦}, Ustrzycka A.^{♦}, Kinetics of evolution of radiation induced microdamage in ductile materials subjected to timedependent stresses, International Journal of Plasticity, ISSN: 07496419, DOI: 10.1016/j.ijplas.2016.01.006, Vol.80, pp.86110, 2016 Abstract: The present paper aims at predicting evolution of radiation induced damage in the solids subjected to mechanical loads beyond the yield stress. Moreover, the evolution of radiation induced damage is combined with the evolution of mechanically induced damage within the common framework of Continuum Damage Mechanics (CDM). An additive formulation with respect to damage parameters (tensors) has been postulated. Multiscale constitutive model containing strong physical background related to the mechanism of generation of clusters of voids in the irradiated solids has been built. The model is based on the experimental estimation of concentration of lattice defects (interstitials, diinterstitials, interstitial clusters, vacancies, divacancies, vacancy clusters) in Al as a function of dpa (displacement per atom), and comprises the relevant kinetics of evolution of radiation induced damage under mechanical loads. Two kinetic laws of damage evolution were taken into account: the Rice & Tracey model and – for comparison – the Gurson model. As an application, estimation of lifetime of a cylindrical shell (coaxial target embedded in a detector of particles) subjected to combination of irradiation and mechanical loads, has been carried out. It is demonstrated that the number of cycles to failure depends strongly on the accumulation of microdamage due to irradiation. The lifetime of irradiated components has been expressed as a function of two parameters: maximum dpa and axial stress amplitude on cycle. Affiliations:
 
4.  Szuwalski K.^{♦}, Ustrzycka A.^{♦}, Mathematical and numerical modelling of large creep deformations for annular rotating disks, APPLIED MATHEMATICS AND MECHANICSENGLISH EDITION, ISSN: 02534827, DOI: 10.1007/s1048301519947, Vol.36, No.11, pp.14411448, 2015 Abstract: A simulation model is presented for the creep process of the rotating disks under the radial pressure in the presence of body forces. The finite strain theory is applied. The material is described by the NortonBailey law generalized for true stresses and logarithmic strains. A mathematical model is formulated in the form of a set of four partial differential equations with respect to the radial coordinate and time. Necessary initial and boundary conditions are also given. To make the model complete, a numerical procedure is proposed. The given example shows the effectiveness of this procedure. The results show that the classical finite element method cannot be used here because both the geometry and the loading (body forces) change with the time in the creep process, and the finite elements need to be redefined at each time step. Keywords:creep process, rotating disk, finite strain theory, simulation model Affiliations:
 
5.  Szuwalski K.^{♦}, Ustrzycka A.^{♦}, Mathematical and numerical modelling of large axisymmetric creep strains and damage, APPLIED MECHANICS AND MATERIALS, ISSN: 16627482, DOI: 10.4028/www.scientific.net/AMM.784.241, Vol.784, pp.214248, 2015 Abstract: The paper presents a simulation model for the creep process of rotating disks under radial tensional pressure subjected to of body force. The finite strain theory is applied. The material is described by the Norton  Bailey law generalized for true stresses and logarithmic strains. The mathematical model is formulated in form of set of four partial differential equations with respect to radial coordinate and time. Necessary initial and boundary conditions are also given. To make the model complete, the numerical procedure for solving this set is proposed. What is worth noticing the classical F EM is not applicable , because not only geometry, but also loading (body forces) change in time during the creep process. It would demand redefinition of finite elements at each time step. In uniaxial problem similar model was presented in [ 4 ], but now it is developed for complex stress state. Possible different formulations of initial and boundary conditions may be found in [ 5 ]. The procedure may be useful in problems of optimal design of full disks in [ 6 ] Keywords:creep process, rotating disks, finite strain theory, simulation model Affiliations:
 
6.  Baussan E.^{♦}, Bielski J.^{♦}, Bobeth C.^{♦}, Bouquerel E.^{♦}, Caretta O.^{♦}, Cupial P.^{♦}, Davenne T.^{♦}, Densham C.^{♦}, Dracos M.^{♦}, Fitton M.^{♦}, Gaudiot G.^{♦}, Kozien M.^{♦}, Lacny L.^{♦}, Lepers B.^{♦}, Longhin A.^{♦}, Loveridge P.^{♦}, Osswald F.^{♦}, Poussot P.^{♦}, Rooney M.^{♦}, Skoczeń B.^{♦}, Szybinski B.^{♦}, Ustrzycka A.^{♦}, Vassilopoulos N.^{♦}, Wilcox D.^{♦}, Wroblewski A.^{♦}, Wurtz J.^{♦}, Zeter V.^{♦}, Zito M.^{♦}, Neutrino super beam based on a superconducting proton linac, PHYSICAL REVIEW SPECIAL TOPICS  ACCELERATORS AND BEAMS, ISSN: 10984402, DOI: 10.1103/PhysRevSTAB.17.031001, Vol.17, No.3, pp.031001126, 2014 Abstract: We present a new design study of the neutrino Super Beam based on the Superconducting Proton Linac at CERN. This beam is aimed at megaton mass physics, a large water Cherenkov detector, proposed for the Laboratoire Souterrain de Modane in France, with a baseline of 130 km. The aim of this proposed facility is to study CP violation in the neutrino sector. In the study reported here, we have developed the conceptual design of the neutrino beam, especially the target and the magnetic focusing device. Indeed, this beam presents several unprecedented challenges, related to the high primary proton beam power (4 MW), the high repetition rate (50 Hz), and the low kinetic energy of the protons (4.5 GeV). The design is completed by a study of all the main components of the system, starting from the transport system to guide the beam to the target up to the beam dump. This is the first complete study of a neutrino beam based on a pebblebed target capable of standing the large heat deposition of MW class proton beams Affiliations:
 
7.  Szuwalski K.^{♦}, Ustrzycka A.^{♦}, Optimal design of full disks with respect to mixed creep rupture time, ENGINEERING STRUCTURES, ISSN: 01410296, DOI: 10.1016/j.engstruct.2013.08.001, Vol.56, pp.17281734, 2013 Abstract: The mixed creep rupture theory to the optimization problem for the complex stress state is used. The problem of optimal shape for the rotating full disk with respect to mixed rupture time is investigated. The mathematical model of mixed creep rupture is described by the system of five partial differential equations. Difficulty of the problem results from two types of nonlinearities: geometrical connected with the use of the finite strain theory and physical – the material is described by the Norton’s creep law, here generalized for true stresses and logarithmic strains. Additional time factor leads to subsequent complications. The parametric optimization describing the initial shape of the disk is applied. The obtained results are compared with the optimal disks with respect to ductile creep rupture time Keywords:Mixed creep rupture, Structural optimization, Full disk Affiliations:
 
8.  Szuwalski K.^{♦}, Ustrzycka A.^{♦}, The influence of boundary conditions on optimal shape of annular disk with respect to ductile creep rupture time, EUROPEAN JOURNAL OF MECHANICS ASOLIDS, ISSN: 09977538, DOI: 10.1016/j.euromechsol.2012.05.006, Vol.37, pp.7985, 2013 Abstract: This article deals with the influence of boundary conditions on the optimal shape of a rotating, axisymmetric annular disk of given volume that maximizes the ductile creep rupture time. The finite strain theory and physical law in form of Norton's law generalized for true stresses and logarithmic strains are applied. The optimal shape is found using parametric optimization. The initial shape of the disk is defined by class of polynomial function. Keywords:Boundary conditions, Optimal design, Ductile creep rupture time, Annular disk Affiliations:
 
9.  Edgecock T.R.^{♦}, Caretta O.^{♦}, Davenne T.^{♦}, Densam C.^{♦}, Fitton M.^{♦}, Kelliher D.^{♦}, Loveridge P.^{♦}, Machida S.^{♦}, Prior C.^{♦}, Rogers C.^{♦}, Rooney M.^{♦}, Thomason J.^{♦}, Wilcox D.^{♦}, Wildner E.^{♦}, Efthymiopoulos I.^{♦}, Garoby R.^{♦}, Gilardoni S.^{♦}, Hansen C.^{♦}, Benedetto E.^{♦}, Jensen E.^{♦}, Kosmicki A.^{♦}, Martini M.^{♦}, Osborne J.^{♦}, Prior G.^{♦}, Stora T.^{♦}, Melo Mendonca T.^{♦}, Vlachoudis V.^{♦}, Waaijer C.^{♦}, Cupial P.^{♦}, Chancé A.^{♦}, Longhin A.^{♦}, Payet J.^{♦}, Zito M.^{♦}, Baussan E.^{♦}, Bobeth C.^{♦}, Bouquerel E.^{♦}, Dracos M.^{♦}, Gaudiot G.^{♦}, Lepers B.^{♦}, Osswald F.^{♦}, Poussot P.^{♦}, Vassilopoulos N.^{♦}, Wurtz J.^{♦}, Zeter V.^{♦}, Bielski J.^{♦}, Kozien M.^{♦}, Lacny L.^{♦}, Skoczeń B.^{♦}, Szybinski B.^{♦}, Ustrzycka A.^{♦}, et al.^{♦}, High intensity neutrino oscillation facilities in Europe, PHYSICAL REVIEW SPECIAL TOPICS  ACCELERATORS AND BEAMS, ISSN: 10984402, DOI: 10.1103/PhysRevSTAB.16.021002, Vol.16, No.2, pp.021002118, 2013 Abstract: The EUROnu project has studied three possible options for future, high intensity neutrino oscillation facilities in Europe. The first is a Super Beam, in which the neutrinos come from the decay of pions created by bombarding targets with a 4 MW proton beam from the CERN High Power Superconducting Proton Linac. The far detector for this facility is the 500 kt MEMPHYS water Cherenkov, located in the Fréjus tunnel. The second facility is the Neutrino Factory, in which the neutrinos come from the decay of μ+ and μ− beams in a storage ring. The far detector in this case is a 100 kt magnetized iron neutrino detector at a baseline of 2000 km. The third option is a Beta Beam, in which the neutrinos come from the decay of beta emitting isotopes, in particular He6 and Ne18, also stored in a ring. The far detector is also the MEMPHYS detector in the Fréjus tunnel. EUROnu has undertaken conceptual designs of these facilities and studied the performance of the detectors. Based on this, it has determined the physics reach of each facility, in particular for the measurement of CP violation in the lepton sector, and estimated the cost of construction. These have demonstrated that the best facility to build is the Neutrino Factory. However, if a powerful proton driver is constructed for another purpose or if the MEMPHYS detector is built for astroparticle physics, the Super Beam also becomes very attractive Affiliations:
 
10.  Szuwalski K.^{♦}, Ustrzycka A.^{♦}, Optimal design of bars under nonuniform tension with respect to mixed creep rupture time, INTERNATIONAL JOURNAL OF NONLINEAR MECHANICS, ISSN: 00207462, DOI: 10.1016/j.ijnonlinmec.2012.03.002, Vol.47, pp.5560, 2012 Abstract: The first attempt of finding of optimal shape for bars in presence of body forces with respect to mixed creep rupture is made. For given volume of the bar, distribution of initial crosssection, ensuring the longest lifetime to mixed rupture is sought. The finite strain theory and physical law in form of Norton's law generalized for true stresses and logarithmic strains are applied. Using the method of parametric optimization, the best of linear and quadratic functions describing the initial shape of the bar are found. The shape of initial strength is corrected in a way leading to longer lifetime. Results of both approaches are compared Keywords:Mixed rupture, Structural optimization, Nonhomogeneity Affiliations:
 
11.  Ustrzycka A.^{♦}, Optimal design of parabolic disk with respect to ductile creep rupture time, Czasopismo Techniczne. Mechanika, ISSN: 00114561, Vol.108, No.15, pp.123134, 2011 Abstract: Axisymmetric rotating disks optimal with respect to ductile creep rupture time are considered. Finite strain theory is applied. The material is describe d by the NortonBailey law generalized for true stresses and logarithmic strains. The set of four partial differential equations describes the creep conditions of parabolic disk. The optimal shape of the disk is found using parametric optimisation with two free parameters. The results are compared with disks of conical shape. Keywords:finite strain theory, annular disk, ductile creep rupture time, biparametric optimization Affiliations:
 
12.  Szuwalski K.^{♦}, Ustrzycka A.^{♦}, Optimal Design of Conical Disk with Respect to Ductile Creep Rupture Time, Czasopismo Techniczne. Mechanika, ISSN: 00114561, Vol.106, No.12, pp.8595, 2009 Abstract: This paper presents the problem of optimal design with respect to ductile creep rupture time for rotating disk. The material is described by the Norton–Bailey nonlinear creep law, here generalized for true stresses and logarithmic strains. For complex stress states, the law of similarity of deviators, combined with the Huber–Mises–Hencky hypothesis is applied. The set of four partial differential equations describes the creep conditions of annular disk. The optimal shape of the disk is found using parametric optimisation with one free parameter. The results are compared with disks of uniform thickness. Keywords:optimal design, annular disk, ductile creep rupture time Affiliations:
 
13.  Ustrzycka A.^{♦}, Próba interpretacji niskich chmur rodzaju Stratus na sodarogramie, PRZEGLĄD GEOFIZYCZNY, ISSN: 00332135, Vol.34, pp.227236, 2006  
14.  Walczewski J.^{♦}, Ustrzycka A.^{♦}, Biometeorologiczne aspekty wysokich temperatur powietrza lata 2003 w Krakowie, WIADOMOŚCI IMGW, ISSN: 18975143, Vol.28, pp.7379, 2005 
List of chapters in recent monographs
1. 553  Ustrzycka A., Szuwalski K.^{♦}, Kowalewski Z.L., Advances in Mechanics of Materials and Structural Analysis, rozdział: Optimal Design of Disks Under Large Creep Deformation, Springer International Publishing, 80, pp.387418, 2018  
2. 433  Skoczeń B.^{♦}, Ustrzycka A.^{♦}, From Creep Damage Mechanics to Homogenization Methods, rozdział: Radiation Damage Evolution in Ductile Materials, Springer International Publishing, 64 of the series Advanced Structured Materials, pp.391406, 2015  
3. 434  Ustrzycka A.^{♦}, Szuwalski K.^{♦}, Computer Aided Optimum Design in Engineering XII, rozdział: Optimal design of full disks with respect to mixed creep rupture time, WIT Transactions on The Built Environment, 125, pp.8394, 2012  
4. 432  Godłowska J.^{♦}, Walczewski J.^{♦}, Tomaszewska A.M.^{♦}, Ustrzycka A.^{♦}, Metody kontroli jakości dla polskiej Państwowej Służby HydrologicznoMeteorologicznej, rozdział: Metoda uzupełniania braków danych dla stacji klimatycznych (temperatura) oparta na analizie ciągów czasowych, Wydawnictwo Instytutu Meteorologii i Gospodarki Wodnej, cz. 1, pp.125137, 2005 
Conference papers
1.  Kowalewski Z.L., Ustrzycka A., Szymczak T.^{♦}, Fatigue Damage Analysis of Power Engineering Materials Using ESPI Method, ACAM9, 9TH Australasian Congress on Applied Mechanics, 20171127/1129, Sydney (AU), pp.18, 2017 Abstract: In most cases, fatigue damage has a local character and it is based on damage development leading to generation of cracks appearing around structural defects or geometrical notches. An identification of these areas and their subsequent monitoring requires a fullfield displacement measurements performed on the objects surfaces. This paper presents an attempt to use the Electronic Speckle Pattern Interferometry (ESPI) method for fatigue damage evaluation and its monitoring on specimens made of the P91 steel and aluminide coated nickel superalloys. In this work, also a development of fatigue damage was investigated using destructive and nondestructive methods in materials commonly applied in power engineering or automotive industry. The fatigue tests for a range of different materials were interrupted for selected number of cycles in order to assess a damage degree. As destructive methods the standard tensile tests were carried out after prestraining due to fatigue. Subsequently, an evolution of the selected tensile parameters was taken into account for damage identification. The ultrasonic or magnetic techniques were used as the nondestructive methods for damage evaluation. In the final step of the experimental programme microscopic observations were performed. The results show that ultrasonic and magnetic parameters can be correlated with those coming from destructive tests. It is shown that good correlation of mechanical and selected nondestructive parameters identifying damage can be achieved for the materials tested Keywords:Fatigue, damage, optical methods, nondestructive techniques Affiliations:

Conference abstracts
1.  Ustrzycka A., Mróz Z., Kowalewski Z.L., Characterization of Damage Evolution Supported by ESPI Analysis, ICEM 2018, 18TH INTERNATIONAL CONFERENCE ON EXPERIMENTAL MECHANICS, 20180701/0705, BRUKSELA (BE), No.082, pp.1, 2018  
2.  Ustrzycka A., Irradiation creep damage in nuclear reactor components, SolMech 2018, 41st SOLID MECHANICS CONFERENCE, 20180827/0831, Warszawa (PL), pp.116117, 2018  
3.  Ustrzycka A., Mróz Z., Kucharski S., Kowalewski Z.L., Analysis of fatigue crack initiation caused by cyclic microplasticity, SolMech 2018, 41st SOLID MECHANICS CONFERENCE, 20180827/0831, Warszawa (PL), pp.272273, 2018  
4.  Ustrzycka A., Kowalewski Z.L., Modelling of fatigue damage mechanisms supported by fullfield optical methods, PLASTICITY 2017, INTERNATIONAL CONFERENCE ON PLASTICITY, DAMAGE, AND FRACTURE 2017, 20170103/0109, Puerto Vallarta (MX), pp.9193, 2017 Abstract: The aim of this work consists a development of the GursonTvergaardNeedleman model (GNT) of damage evolution in elasticplastic materials. This model is supported by optical method of stress and strain monitoring (ESPI) for early detection, localization and monitoring of damage in materials under fatigue loading. Affiliations:
 
5.  Ustrzycka A., Kowalewski Z.L., Grzywna P., Characterization of damage evolution supported by ESPI experimental analysis, XII Konferencja „Nowe Kierunki Rozwoju Mechaniki”, 20170322/0325, Białystok  Supraśl (PL), pp.12, 2017 Abstract: The problem investigated in the present work concerns the damage evolution in elasticplastic materials subjected to cyclic loading. The modeling of damage mechanisms is supported by Electronic Speckle Pattern Interferometry (ESPI) apparatus using coherent laser light. Such a study can help better understanding of the damage and failure mechanism of modern structural materials for practical engineering problems. Keywords:damage mechanisms, void growth, optical methods Affiliations:
 
6.  Pęcherski R.B., Nalepka K.T., Nalepka P.^{♦}, Sztwiertnia K.^{♦}, Kret S.^{♦}, Ustrzycka A., Assessment of the strength of nanocomposites based on interface bonding analysis, ICTAM XXIV, 24th International Congress of Theoretical and Applied Mechanics, 20160821/0826, Montréal (CA), pp.23842385, 2016 Abstract: Recent investigations reveal that interface bonding strength is dependent on the relative orientation of crystallites of the both phases [2]. The experimental, theoretical and computational investigations confirm this observation in the case of Cu/Al2O3 system, [3], [4]. It is shown that the statistical distribution of the values of interface strength for different relative orientations of bonded phases should be included in the phenomenological model of the damage initiation in nanocomposites. The novelty of the presented study is the combination of different experimental techniques: HRTEM, EBSD and molecular dynamics simulations with phenomenological theory of damage development in nanocomposites due to debonding at the interphase boundary [5], [6], [7]. A class of new models with the yield condition determined by one of quadric surfaces, in particular paraboloid or ellipsoid one is considered and the comparison with popular Gurson approach is discussed, [8]. Keywords:nanocompistes, strength, interface, bonding, HRTEM, EBSD, molecular dynamics Affiliations:
 
7.  Skoczeń B.^{♦}, Ustrzycka A.^{♦}, Radiation induced damage in ductile materials subjected to timedependent stresses, ICDM2, 2nd International Conference on Damage Mechanics, 20150708/0711, Troyes (FR), pp.1, 2015  
8.  Ustrzycka A.^{♦}, Szuwalski K.^{♦}, Mathematical and numerical modelling of large axisymmetric creep strains and damage, ICDM2, 2nd International Conference on Damage Mechanics, 20150708/0711, Troyes (FR), pp.1, 2015  
9.  Ustrzycka A.^{♦}, Skoczeń B.^{♦}, Kinetics of evolution of radiation induced damage, PCMCMM 2015, 3rd Polish Congress of Mechanics and 21st Computer Methods in Mechanics, 20150908/0911, Gdańsk (PL), pp.693694, 2015  
10.  Skoczeń B.^{♦}, Ustrzycka A.^{♦}, Radiation damage evolution in ductile materials, Plasticity 2015, 21st International Symposium on Plasticity and its Current Applications, 20150104/0109, Montego Bay (JM), pp.1, 2015  
11.  Ustrzycka A.^{♦}, Skoczeń B.^{♦}, Kinetics of evolution of radiation induced microdamage in ductile materials subjected to timedependent stresses, EMMC14, European Mechanics of Materials Conference, 20140827/0829, Gothenburg (SE), pp.1, 2014  
12.  Ustrzycka A.^{♦}, Skoczeń B.^{♦}, Degradation of material properties due to evolution of radiation induced damage, SolMech 2014, 39th Solid Mechanics Conference, 20140901/0905, Zakopane (PL), pp.12, 2014  
13.  Ustrzycka A.^{♦}, Skoczeń B.^{♦}, Kinetics of evolution of radiation induced microdamage in ductile materials subjected to timedependent stresses, ICMM3, 3rd International Conference on Material Modelling incorporating 13th European Mechanics of Materials Conference, 20130908/0911, Warszawa (PL), pp.162, 2013  
14.  Szuwalski K.^{♦}, Ustrzycka A.^{♦}, Optimal design of full disks with respect to mixed creep rupture time, 12th International Conference on Optimum Design of Structures and Materials in Engineering, 20120620/0622, New Forest (GB), pp.1, 2012 Abstract: Structural elements working under creep conditions belong to the relatively new branches of structural optimization. Among many new possibilities of optimization criteria, which offers optimization of structures in creep conditions, the most important seems to be time to rupture. Most papers on optimal structural design are based on the brittle creep rupture theory proposed by Kachanov (small strain theory). Application of the ductile rupture theory proposed by Hoff in optimization problems are rather scare as it requires finite strain theory. For the first time it was used by Szuwalski [ 1], [2] and Szuwalski, Ustrzycka [4]. The first attempt of application the mixed theory to shape optimization was made by Ustrzycka and Szuwalski [3] for bars under nonuniform tension. Here, for the first time, the optimization problem with respect mixed rupture time, is solved for the complex stress state. Application of mixed rupture theory proposed by Kachanov takes into account: geometrical changes  diminishing of transversal dimensions resulting from large strains (as in ductile rupture) and growth of microcracks (as in brittle rupture). In present paper the problem of optimal shape with respect to mixed creep rupture time for the rotating full disk is investigated. Difficulty of the problem results from two types of nonlinearities: geometrical connected with the use of the finite strain theory and physical  the material is described by the Norton’s creep law, here generalized for true stresses and logarithmic strains. The mathematical model of mixed creep rupture is described by the system of five partial differential equations in dimensionless form. The system must be integrated with respect to material coordinate (Runge – Kutta fourth order method) and to time with variable step (Euler’s method). The parametric optimization with one, or two free parameters describing the initial shape of the disk is applied. The obtained results are compared with the disks with respect to ductile creep rupture time [2] Affiliations:
 
15.  Ustrzycka A.^{♦}, Szuwalski K.^{♦}, Optimal Design of Annular Disks With Respect to Mixed Creep Rupture Time, 8th European Mechanics Conference, 20120709/0713, Graz (AT), pp.1, 2012 Abstract: The problem of optimal design with respect to mixed creep rupture time is a new one. The first attempt of solution for rotation bar was made in 2010 by Szuwalski and Ustrzycka [5]. Difficulties of the problem result from physical an d geometrical nonlinearities, and were observed earlier in solution for ductile creep rupture [4], [6]. Some problems of optimal design for annular rotating disks were discussed by Farshi and Bidabadi [2]. Analytical solution for the elasticplastic stress distribution in rotating annular disks were obtained by Ç ğ allio ğ lu et al. [1] and Gun [3]. Because of those difficulties the parametric optimization was adopted. In certain class of function describing the initial shape of the disk we are looking for optimal parameters leading to the longest time to mixed rupture under assumption of constant volume. The axially symmetric annular disk rotating with constant angular velocity is loaded by centrifugal forces resulting from the own mass of the disk and additional mass uniformly distributed at the outer edge (Figure 1). The mathematical model of mixed creep rupture is described by the system of five partial differential equations in dimensionless form. n the last equation the continuity function Ψ describing damage of material was introduced. The criterion of rupture is fulfilled when Ψ takes values 0. The optimal shape among linear functions (uniparametric optimization) and quadratic functions (biparametric optimization) was found by checking some disks in earlier predicted domain of admissible solutions. The better results were obtained using biparametric optimization. The obtained results are compared with the disks with respect to ductile creep rupture time [6]. Affiliations:
