Modeling of large elastoviscoplastic deformations with thermophysical effects taken into account
Tóm tắt
We propose a mathematical model of large elastoviscoplastic deformations where intensive deformation results in temperature increasing and heat transfer processes. As an example of applying the model relations, we present a solution of the boundary-value problem on rectilinear motion and heating of a medium located in the gap between coaxial rigid cylindrical surfaces.
Tài liệu tham khảo
E. H. Lee, “Elastic-Plastic Deformation at Finite Strains,” Trans. ASME Ser. E. J. Appl.Mech. 36(1), 1–6 (1969).
R. J. Clifton, “On the Equivalence of F e · F p and F p · F e,” Trans. ASME Ser. E. J. Appl. Mech. 39(1), 287–289 (1972).
V. I. Kondaurov, “Equations of ElastoviscoplasticMediumwith Finite Deformations,” Zh. Prikl.Mekh. Tekh. Fiz. 23(4), 133–139 (1982) [J. Appl.Mech. Tech. Phys. (Engl. Transl.) 23 (4), 584–591 (1982)].
S. Nemat-Nasser, “On Finite Deformation Elasto-Plasticity,” Int. J. Solids Struct. 18(10), 857–872 (1982).
V. I. Levitas, Large Elastoplastic Deformations of Materials under High Pressure (Naukova Dumka, Kiev, 1987) [in Russian].
A. V. Shitikov and G. I. Bykovtsev, “Finite Deformations in an Elastoplastic Medium,” Dokl. Akad. Nauk SSSR 311(1), 59–62 (1990) [Sov. Phys. Dokl. (Engl. Transl.) 35, 297 (1980)].
Z. Xia and F. Ellyin, “A Finite Elastoplastic Constitutive Formulation with New Co-Rotational Stress-Rate and Strain-Hardening Rule,” Trans.ASME. J. Appl.Mech. 62(3), 733–739 (1995).
V. P. Myasnikov, “Equations of Motion of Elastoplastic Materials under Large Deformations,” Vestnik DVO RAN, No. 4, 8–14 (1996).
A. A. Rogovoi, “Constitutive Relations for Finite Elastic-Inelastic Strains,” Zh. Prikl. Mekh. Tekh. Fiz. 46(5), 138–149 (2005) [J. Appl.Mech. Tech. Phys. (Engl. Transl.) 46 (5), 730–739 (2005)].
A. D. Chernyshov, “Constitutive Equations for an Elastoplastic Body at Finite Strains,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 120–128 (2000) [Mech. Solids (Engl. Transl.) 35 (1), 102–108 (2000)].
A. A. Burenin, G. I. Bykovtsev, and L. V. Kovtanyuk, “A Simple Model of Finite Strain in an Elastoplastic Medium,” Dokl. Ross. Akad. Nauk 347(2), 199–201 (1996) [Dokl. Phys. (Engl. Transl.) 41 (3), 127–129 (1996)].
L. V. Kovtanyuk and A. V. Shitikov, “On the Theory of Large Elastoplastic Deformations of Materials with Temperature and Rheological Effects Taken into Account,” Vestnik DVO RAN, No. 4, 87–93 (2006).
A. I. Lurie, “Differentiation with Respect to Tensor Argument,” in Problems of Mathematical Physics (Nauka, Leningrad, 1976) [in Russian], pp. 48–57.
G. I. Bykovtsev and T. D. Semykina, “On Viscoplastic Flow of Circular Plates and Shells of Revolution,” Izv. Akad. Nauk SSSR.Mekh. Mashinostr., No. 4, 68–76 (1964).