Abstract
In the present work, we discuss configurational forces (also known as material forces) in the context of numerical simulations of short-time dynamical problems with an explicit finite element solver. In extension to the work presented in Kolling and Mueller (Comput Mech 35:392–399, 2005), the fully 3D-case for hyperelastic materials and large strains is shown. The intention of the present paper is the investigation of the influence of inertia effects, which become increasingly important at high strain rates. At first, the dynamical part of configurational forces will be discussed at moderate strain rates. Finally, we use configurational forces in the context of shockwave propagation.
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References
Kolling S, Mueller R (2005) On configurational forces in short-time dynamics and their computation with an explicit solver. Comput Mech 35: 392–399
Eshelby JD (1951) The force on an elastic singularity. Philos Trans R Soc A 244: 87–112
Eshelby JD (1970) Energy relations and the energy–momentum-tensor in continuum mechanics. In: Kanninen MF (eds) Inelastic behaviour of solids. McGraw-Hill, New York, pp 75–115
Braun M (1997) Configurational forces induced by finite-element discretization. Proc Estonian Acad Sci Math 46(1/2): 24–31
Steinmann P (2000) Application of material forces to hyperelastic fracture mechanics I: Continuum mechanical setting. Int J Solids Struct 37: 7371–7391
Steinmann P (2001) Application of material forces to hyperelastostatic fracture mechanics II: computational setting. Int J Solids Struct 38: 5509–5526
Mueller R, Maugin GA (2002) On material forces and finite element discretizations. Comput Mech 29: 52–60
Naeser B, Kaliske M, Mueller R (2007) Material forces for inelastic models at large strain – Application to fracture mechanics. Comput Mech 40: 1005–1013
Maugin GA (1993) Material inhomogeneities in elasticity. Chapman & Hall, London
Kienzler R, Herrmann G (2000) Mechanics in material space. Springer, Berlin
Gurtin ME (2000) Configurational forces as basic concept of continuum physics. Springer, New York
Kolling S, Ackermann D (2003) Applications of material forces in finite element simulations. In: Proceedings of the 4th European LS-DYNA Users Conference, D-II, pp 1–14
Schmidt I, Gross D (1997) The equilibrium shape of an elastically inhomogeneous inclusion. J Mech Phys Solids 45: 1521–1549
Gross D, Mueller R, Kolling S (2002) Configurational forces—morphology evolution and finite elements. Mech Res Commun 29: 529–536
Hugoniot H (1889) Sur la propagation du mouvement dans les corps et spécialement dansles gaz parfaits. J de L’École Polytech 58: 1–126
Maugin GA (1998) On shock waves and phase transition fronts in continua. ARI 50: 141–150
Maurer D (2002) Simulation of shockwaves in explicit finite element methods. http://people.freenet.de/fetool/shocks.htm
Von Neumann J, Richtmyer RD (1950) A method for the numerical calculation of hydrodynamic shocks. J Appl Phys 21: 232–237
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Timmel, M., Kaliske, M., Kolling, S. et al. On configurational forces in hyperelastic materials under shock and impact. Comput Mech 47, 93–104 (2011). https://doi.org/10.1007/s00466-010-0537-6
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DOI: https://doi.org/10.1007/s00466-010-0537-6