Applied PDE Group
Nonlinear Partial Differential Equations in Fluid and Solid Mechanics


On cavitation in nonlinear elastodynamics

​J. Giesselman, A.E. Tzavaras, On cavitation in nonlinear elastodynamics, In Hyperbolic Problems: Theory, Numerics, Applications, F. Ancona, A. Bressan, P. Marcati, A. Marson, eds; AIMS Series on Applied Mathematics, Vol 8, Springfield, 2014, pp. 599-606.
J. Giesselmann, A.E. Tzavaras
elastodynamics, cavitation
Motivated by the works of Ball (1982) and Pericak-Spector and Spector (1988), we investigate singular solutions of the compressible nonlinear elastodynamics equations. These singular solutions contain discontinuities in the displacement field and can be seen as describing fracture or cavitation. We explore a definition of singular solution via approximating sequences of smooth functions. We use these approximating sequences to investigate the energy of such solutions, taking into account the energy needed to open a crack or hole. In particular, we find that the existence of singular solutions and the finiteness of their energy is strongly related to the behavior of the stress response function for infinite stretching, i.e. the material has to display a sufficient amount of softening. In this note we detail our findings in one space dimension