zbMATH — the first resource for mathematics

On one mathematical model of creep in superalloys. (English) Zbl 1042.74511
Summary: The paper deals with modelling of creep in superalloys. The modelled area \(\Omega \subset {\mathbb R}^3\) consists of subdomains \(\Omega _1,\dots ,\Omega _n\) representing mutually separated elastic particles and their complement \(\Omega _0\) representing creeping matrix. The model consists of equations of motion, constitutive relations for viscoelastic material, compatibility conditions on the interface of domains and equations for evolution of the dislocation density. In the matrix the creep is active in a finite number of slip systems.
In the paper precise weak formulation of this complicated evolution system of PDE is introduced and existence of the solution is proved by means of the Rothe method.
Reviewer: J. Franců (Brno)

74D05 Linear constitutive equations for materials with memory
74D10 Nonlinear constitutive equations for materials with memory
74H99 Dynamical problems in solid mechanics
Full Text: DOI EuDML
[1] Appell J., Zabrejko P.P.: Nonlinear Superposition Operators. Cambridge University Press, Cambridge, 1990. · Zbl 0701.47041
[2] Denis S., Hazotte A., Wen I.H., Gautieu E.: Micromechanical approach by finite elements to the microstructural evolutions and mechanical behaviour of two-phase metallic alloys. IUTAM’95 symposium on micromechanics of plasticity and damage of multiphase materials in Paris, Pineau A., Zaoui A. (eds.), Kluwer Academic Publishers, Dordrecht, 1995, pp. 289-296.
[3] Gajewski H., Gröger K., Zacharias K.: Nonlinear Operator Equations and Operator Differential Equations (in German). Akademie Verlag, Berlin, 1974.
[4] Greguš M., Švec M., Šeda V.: Ordinary Differential Equations (in Slovak). Alfa, Bratislava, 1985.
[5] Kačur J.: Solution to strongly nonlinear parabolic problem by a linear approximation scheme. Preprint M2-96. Comenius University (Faculty of Mathematics and Physics), Bratislava, 1996.
[6] Kolář V.: Nonlinear mechanics (in Czech). ČSVTS, Ostrava, 1985.
[7] Maz’ya V.G.: Sobolev spaces (in Russian). Leningrad University Press, Leningrad (St. Petersburg), 1985.
[8] Nečas J., Hlaváček I.: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction. Elsevier, Amsterdam, 1981.
[9] Petterman H.E., Böhm H.J., Rammerstorfer F.G.: An elasto-plastic constitutive law for composite materials. Modelling in materials science and processing, Rappaz M., Kedro M. (eds.), European Commission (COST 512 Action Management Committee), Brussels, 1996, pp. 384-392.
[10] Svoboda J., Lukáš P.: Modelling of kinetics of directional coarsening in Ni-superalloys. Acta materialia 44 (1996), 2557-2565. · doi:10.1016/1359-6454(95)00349-5
[11] Svoboda J., Vala J.: Micromodelling of creep in composites with perfect matrix/particle interfaces. Metallic Materials 36 (1998), 109-126.
[12] Vala J., Svoboda J., Kozák V., Čadek J.: Modelling discontinuous metal matrix composite behavior under creep conditions: effect of diffusional matter transport and interface sliding. Scripta metallurgica et materialia 30 (1994), 1201-1206.
[13] Vala J.: Software package CDS for strain and stress analysis of materials consisting of several phases (in Czech). Programs and Algorithms of Numerical Mathematics 8 (1996), Proceedings of the summer school in Janov nad Nisou, pp. 199-206.
[14] Vala J.: Micromechanical considerations in modelling of superalloy creep flow. Numerical Modelling in Continuum Mechanics 3 (1997), Proceedings of the conference in Prague, pp. 483-489.
[15] Valanis K.C.: A gradient theory of finite viscoelasticity. Archives of Mechanics 49 (1997), 589-609. · Zbl 0877.73025
[16] Yosida K.: Functional Analysis (in Russian). Mir, Moscow, 1967. · Zbl 0152.32102
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.