Rate constitutive theory for ordered thermoelastic solids

Karan S. Surana1, Daniel Núñez1, J. N. Reddy2, Albert Romkes1
1Department of Mechanical Engineering, University of Kansas, Lawrence, USA
2Department of Mechanical Engineering, Texas A&M University, College Station, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids, volume 1, fluid mechanics, second edition. Wiley, New York

Spencer AJM (1980) Continuum mechanics. Longman, London

Belytschko T, Liu WK, Moran B (2000) Non-Linear finite elements for continua and structures. Wiley, Chichester

Haupt P (2002) Continuum mechanics and theory of material, 2nd edn. Springer, Berlin

Reddy JN (2008) An introduction to continuum mechanics: with application. Cambridge University Press, Cambridge

Surana KS, Ma Y, Reddy JN, Romkes A (2010) The rate constitutive equations and their validity for progressibely increasing deformation. Mech Adv Mater Struct 17:509–533

Surana KS, Reddy JN (2012) Continuum mechanics (Textbook manuscript in preparation, 2012)

Hill R (1968) On constitutive inequalities for simple materials—i. J Mech Phys Solids 16:229–242

Hill R (1968) On constitutive inequalities for simple materials—ii. J Mech Phys Solids 16:315–322

Hill R (1970) Constitutive inequalities for isotropic elastic solids under finite strain. Proc R Soc Lond A 314:457–472

Jaumann G (1905) Grundlagen der Bewegungslehre. J.A. Barth, Leipzig

Oldroyd JG (1958) Non-Newtonian effects in steady motion of some idealized elastico-viscous liquids. Proc R Soc Lond A 245:278–297

Giesekus H (1962) Die rheologische zustandsgleichung elasto-viskoser flüssigkeiten—insbesondere von weissenberg-flüssigkeiten—für allgemeine und stationäre fließvorgänge. J Appl Math Mech/Zeitschrift für Angewandte Mathematik und Mechanik 42:32–61

Rivlin RS, Ericksen JL (1955) Stress-deformation relations for isotropic materials. J Rational Mech Anal 4:323–425

Giesekus H (1956) Das reibungsgesetz strukturviskosen flüssigkeit. Kolloid Z. 147:29–45

Prud’homme RK, Bird RB (1978) The dilatational properties of suspensions of gas bubbles in incompressible Newtonian and non-Newtonian fluids. J Non-Newtonian Fluid Mech 3:261–279

Murnagham FD (1951) Finite deformation of an elastic solid. Wiley, New York

Truesdell CA, Toupin RA (1963) The classical field theories of mechanics. Handbuch der Physik 3/1:226–793

Truesdell CA, Noll W (1965) The non-linear field theories of mechanics. Handbuch der Physik 3/3:1–602

Gurtin ME (1981) An introduction to continuum mechanics. Academic Press, New York

Malven LE (1969) Introduction to the mechanics of a continuous medium. Prentice-Hall, Englewood

Eringen AC (1967) Mechanics of continua. Wiley, New York

Eringen AC (1962) Nonlinear theory of continuous media. McGraw-Hill, New York

Udaykumar HS, Tran L, Belk DM, Vanden KJ (2003) An Eulerian method for computation of multimaterial impact with ENO shock-capturing and sharp interfaces. J Comput Phys 186:136–177

Tran L, Udaykumar HS (2004) A particle-level set-based sharp interface cartesian grid method for impact, penetration, and void collapse. J Comput Phys 193:469–510

Surana KS, Nunez D, Reddy JN, Romkes A (2012) Rate constitutive theories for ordered thermofluids. Int J Contin Mech Thermodyn (in review)

Wang CC (1969) On representations for isotropic functions, part I. Arch Rational Mech Anal 33:249

Wang CC (1969) On representations for isotropic functions, part II. Arch Rational Mech Anal 33:268

Wang CC (1970) A new representation theorem for isotropic functions, part I and part II. Arch Rational Mech Anal 36:166–223

Wang CC (1971) Corrigendum to “representations for isotropic functions”. Arch Rational Mech Anal 43:392–395

Smith GF (1970) On a fundamental error in two papers of C.C. Wang, on representations for isotropic functions, part I and part II. Arch Rational Mech Anal 36:161–165

Smith GF (1971) On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors. Int J Eng Sci 9:899–916

Spencer AJM, Rivlin RS (1959) The theory of matrix polynomials and its application to the mechanics of isotropic continua. Arch Rational Mech Anal 2:309–336

Spencer AJM, Rivlin RS (1960) Further results in the theory of matrix polynomials. Arch Rational Mech Anal 4:214–230

Spencer AJM (1971) Theory of invariants. In: Eringen AC (ed) Chapter 3 "Treatise on continuum physics, I". Academic Press, New York

Boehler JP (1977) On Irreducible representations for isotropic scalar functions. J Appl Math Mech/Zeitschrift für Angewandte Mathematik und Mechanik 57:323–327

Zheng QS (1993) On transversely isotropic, orthotropic and relatively isotropic functions of symmetric tensors, skew-symmetric tensors, and vectors. Int J Eng Sci 31:1399–1453

White FM (2010) Fluid mechanics, 7th edn. McGraw-Hill, New York

Panton RL (2005) Incompressible flow, 3rd edn. Wiley, New York

Hill R (1978) Aspects of invariance in solid mechanics. Adv Appl Mech 18:1–72

Bazant ZP (1991) Stability of structures: elastic, inelastic, fracture and damage theories. Oxford University Press, Oxford

Surana KS, Ma YT, Romkes A, Reddy JN (2011–2012) Fluid–solid interaction of incompressible media in h, p, k mathematical and computational framework. Comput Methods Eng Mech (under review, 2011–2012)