The Minimum Energy Principle in Description of Nonlinear Properties of Orthotropic Material
ABSTRACT
In this paper the conception of theoretical determine the relations between material experimental characteristics is presented. On the base of stress-strain relations for nonlinear elastic anisotropic material and geometrical interpretation of deformation state, the general form of strain energy density function was introduced. Using this function and variational methods the relations between material characteristics were achieved. All considerations are illustrated by a short theoretical example.
In this paper the conception of theoretical determine the relations between material experimental characteristics is presented. On the base of stress-strain relations for nonlinear elastic anisotropic material and geometrical interpretation of deformation state, the general form of strain energy density function was introduced. Using this function and variational methods the relations between material characteristics were achieved. All considerations are illustrated by a short theoretical example.
Cite this paper
T. WEGNER and D. KURPISZ, "The Minimum Energy Principle in Description of Nonlinear Properties of Orthotropic Material," Advances in Materials Physics and Chemistry, Vol. 2 No. 4, 2012, pp. 53-55. doi: 10.4236/ampc.2012.24B015.
T. WEGNER and D. KURPISZ, "The Minimum Energy Principle in Description of Nonlinear Properties of Orthotropic Material," Advances in Materials Physics and Chemistry, Vol. 2 No. 4, 2012, pp. 53-55. doi: 10.4236/ampc.2012.24B015.
References
[1] R.W. Ogden, “Non-linear elastic deformations” Dover Publications, Mineola, New York 1997. [2] P. Perzyna, “Coupling of dissipative mechanisms of viscoplastic flow“ Arch. Mechanics 29, 1977, pp. 607-624. [3] P. Perzyna, “The thermodynamical theory of elasto-viscoplasticity“ Engineering Transactions 53, 2005, pp. 235-316. [4] H. Petryk, “On the second-order work in plasticity” Archives of Mechanics, 37. Warszawa 1985, pp. 503-520. [5] H. Petryk, “The energy criteria of instability in the time-independent inelastic solids” Archives of Mechanics, 43. 4. Warszawa 1991, pp. 519-545. [6] H. Petryk, “On stability and symmetry conditions in time independent plasticity” Archives of Mechanics, 43. 2 -3. Warszawa 1991, pp. 377-397. [7] J. Schroder, P. Neff, “Invariant Formulation of Hyperelastic Transverse Isotropy Based on Polyconvex Free Energy Functions” International Journal of Solids and Structures, Vol. 40, 2003, pp. 401-445. [8] D.R. Wagner, J.C. Lotz, “A non-linear anisotropic strain energy function for the annulus fibrosus” San Francisco: Orthopaedic Research Society; 2001. [9] T. Wegner, D. Kurpisz “Phenomenological modeling of mechanical properties of metal foam” Journal of Theoretical and Applied Mechanics JTAM (in press).
[1] R.W. Ogden, “Non-linear elastic deformations” Dover Publications, Mineola, New York 1997. [2] P. Perzyna, “Coupling of dissipative mechanisms of viscoplastic flow“ Arch. Mechanics 29, 1977, pp. 607-624. [3] P. Perzyna, “The thermodynamical theory of elasto-viscoplasticity“ Engineering Transactions 53, 2005, pp. 235-316. [4] H. Petryk, “On the second-order work in plasticity” Archives of Mechanics, 37. Warszawa 1985, pp. 503-520. [5] H. Petryk, “The energy criteria of instability in the time-independent inelastic solids” Archives of Mechanics, 43. 4. Warszawa 1991, pp. 519-545. [6] H. Petryk, “On stability and symmetry conditions in time independent plasticity” Archives of Mechanics, 43. 2 -3. Warszawa 1991, pp. 377-397. [7] J. Schroder, P. Neff, “Invariant Formulation of Hyperelastic Transverse Isotropy Based on Polyconvex Free Energy Functions” International Journal of Solids and Structures, Vol. 40, 2003, pp. 401-445. [8] D.R. Wagner, J.C. Lotz, “A non-linear anisotropic strain energy function for the annulus fibrosus” San Francisco: Orthopaedic Research Society; 2001. [9] T. Wegner, D. Kurpisz “Phenomenological modeling of mechanical properties of metal foam” Journal of Theoretical and Applied Mechanics JTAM (in press).