An energy-based method in phenomenological description of mechanical properties of nonlinear materials under plane stress

• Autorzy: Wegner T. , Kurpisz D.

Identyfikatory

DOI

10.15632/jtam-pl.55.1.129

• Języki publikacji: EN

Abstrakty

EN

A method based on energy is a very useful tool for description of mechanical properties of materials. In the current paper, on the base of geometrical interpretation of a deformation process, the strain energy density function for isotropic nonlinear materials has been constructed. On account of hydrostatic interpretation of the volumetric deformation, the elastic part of energy has been extracted. The initiation of the damage process due to plastic flow of the material under plane stress has been determined and the stability conditions have been formulated by using in the stability analysis the strain energy density function in addition to Sylvester’s theorem and assumption of zero volume change during pure plastic deformations. This concept is an original part of the work and continuation of the investigations previously carried out by Wegner and Kurpisz. The theoretical investigations have been illustrated on the example of aluminium.

Słowa kluczowe

EN

energy-based method; nonlinear material; phenomenological description; strain energy density function; Sylvester’s theorem

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2017
• Tom: Vol. 55 nr 1
• Strony: 129--139
• Opis fizyczny: Bibliogr. 15 poz., rys.

Twórcy

autor

Wegner T.

• Poznan University of Technology, Institute of Applied Mechanics, Poznań, Poland

autor

Kurpisz D.

• Poznan University of Technology, Institute of Applied Mechanics, Poznań, Poland

Bibliografia

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• 2. Dargazany R., Khiem V.N., Nawrath U., Istkov M., 2012, Network evolution model of anisotropic stress softening in filled rubber-like materials: Parameter identification and finite element implementation, Journal of Mechanics and Material and Structures, 7, 8/9, 861-885
• 3. Gajewska K., Maciejewska J., 2005, Energy based limit criteria for anisotropic elastic materials with constraints, Archives of Mechanics, 57, 2/3, 133-155
• 4. Petryk H., 1985, On the second-order work in plasticity, Archives of Mechanics, 37, 503-520
• 5. Petryk H., 1991, The energy criteria of instability in the time-independent inelastic solids, Archives of Mechanics, 43, 4, 519-545
• 6. Schroder J., Neff P., 2003, Invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions, International Journal of Solids and Structures, 40, 401-445
• 7. Silva E., Forst C., Li J., Lin X., Zhu T., Yip S., 2007, Multiscale material modelling: case studies at the atomistic and electronic structure levels, ESAIM: Mathematical Modelling and Numerical Analysis, 41, 2, 427-445
• 8. Speirs D.C.D., de Souza Neto E.A., Peri’c D., 2008, An approach to the mechanical constitutive modelling of arterial wall tissue based on homogenization and optimization, Journal of Biomechanics, 41, 2673-2680
• 9. Terada K., Inugai T., Hirayama N., 2008, A method of numerical material testing in nonlinear multiscale material analyses (in Japanese), Transactions of the Japan Society of Mechanical Engineering A, 74, 1084-1094, 2008
• 10. Wegner T., 1999, Methods Based On Energy in Strength of Materials (in Polish), Wydawnictwo Politechniki Poznańskiej, Poznań
• 11. Wegner T., 2000, Surface of limit state in nonlinear material and its relation with plasticity condition (in Polish), The Archive of Mechanical Engineering, 47, 3, 205-223
• 12. Wegner T., 2005, Mathematical modelling of mechanical properties of materials (in Polish), Biuletyn WAT, LIV, 12, 5-51
• 13. Wegner T., 2009, Modelling Based on Energy in Nonlinear Mechanics of Materials and Structures (in Polish), Wydawnictwo Politechniki Poznańskiej, Poznań
• 14. Wegner T., Kurpisz D., 2009, The conservation energy principle in description of stable and unstable states for aluminium, Proceedings in Applied Mathematics and Mechanics, PAMM, 9, 323-324
• 15. Wegner T., Kurpisz D., 2013, Phenomenological modeling of mechanical properties of metal foam, Journal of Theoretical and Applied Mechanics, 51, 203-214

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)