Abstract
Based on the thermodynamic framework for combined configurational and deformational changes, recently discussed in [1], we consider dissipative material response and emphasize the fact that it is possible to identify explicit energetic changes due to configurational changes for “frozen” spatial configuration and, in addition, the configuration-induced material dissipation. The classical assumption (previously adopted in the literature) is to ignore the latter. In this paper, however, we define configurational forces by considering the total variation of the total dissipation with respect to configurational changes. The key task is then to compute the sensitivity of the internal variable rates to such configurational changes. We restrict to quasistatic loading under isothermal conditions and elastic-plastic response, and we apply the theory to the simplest possible case of an interface of dissimilar materials in a single bar.
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Runesson, K., Larsson, F., Steinmann, P., On energetic changes due to configurational motion of standard continua, Int. J Solids Structures, 2008, accepted.
Eshelby, J., The force on an elastic singularity, Phil. Trans. Roy. Soc. Lond., 1951, 87–112.
Abeyaratne R., Knowles, J., On the driving traction acting on a surface of strain discontinuity in a continuum, J. Mech. Phys. Solids 38, 1990, 345–360.
Maugin, G., Material Inhomogeneities in Elasticity, Chapman & Hall, London, 1993.
Maugin, G., Material forces: Concepts, applications, Appl. Mech. Rev. 48, 1995, 213–245.
Maugin, G., Thermomechanics of inhomogeneous-heterogeneous systems: Application to the irreversible progress of two-, three-dimensional defects, ARI 50, 1997, 41–56.
Maugin, G., On shock waves, phase-transition fronts in continua, ARI 50, 1998, 141–150.
Maugin, G., Thermomechanics of forces driving singular pointsets, Arch. Mech. 50, 1998, 509–519.
Maugin, G., On the universality of the thermomechanics of forces driving singular sets, Arch. Mech. 69, 1999, 1–15.
Maugin, G., Trimarco, C., Pseudomomentum and material forces in nonlinear elasticity: variational formulations and application to brittle fracture, Arch. Mech. 94, 1992, 1–28.
Maugin, G., Trimarco, C., The dynamics of configurational forces at phase-transition fronts, Meccanica 30, 1995, 605–619.
Gurtin, M., On the nature of configurational forces, Arch. Rational Mech. Anal. 131, 1995, 67–100.
Gurtin, M., Configurational Forces as Basic Concepts of Continuum Physics, Springer, New York, 2000.
Kienzler, R., Herrmann, G., Mechanics in Material Space, Springer, Berlin, 2000.
Steinmann, P., On boundary potential energies in deformational, configurational mechanics, J. Mech. Phys. Solids 56, 2008, 772–800.
Simha, N., Fischer, F., Kolednik, O., Chen, C., Inhomogeneity effects on the crack driving force in elastic and elastic-plastic materials, J. Mech. Phys. Solids 51, 2003, 209–240.
Simha, N., Fischer, F., Shan, G., Chen, C., Kolednik, O., J-integral and crack driving force in elastic-plastic materials, J. Mech. Phys. Solids 56, 2008, 2876–2895.
Liebe, T., Denzer, R., Steinmann, P., Application of the material force method to isotropic continuum damage, Comput. Mech. 30, 2003, 171–184.
Menzel, A., Denzer, R., Steinmann, P., Material forces in computational single-slip crystal-plasticity, Computat. Mater. Sci. 32, 1995, 446–454.
Nguyen, T., Govindjee, S., Klein, P., Gao, H., A material force method for inelastic fracture mechanics, J. Mech. Phys. Solids 53, 2005, 91–121.
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Larsson, F., Runesson, K., Tillberg, J. (2009). Configurational Forces Derived from the Total Variation of the Rate of Global Dissipation. In: Steinmann, P. (eds) IUTAM Symposium on Progress in the Theory and Numerics of Configurational Mechanics. IUTAM Bookseries, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3447-2_5
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DOI: https://doi.org/10.1007/978-90-481-3447-2_5
Publisher Name: Springer, Dordrecht
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