Submitted Paper
Inserted: 14 feb 2025
Last Updated: 14 feb 2025
Year: 2025
Abstract:
We study the existence and regularity of minimizers of an energy functional which in the physical $3$D dimension corresponds to the so--called generalized Varga materials and includes an additional term accounting for surface tension. Due to the linear growth of the strain energy, we relax the problem in a suitable class of extended graphs of radially symmetric functions of bounded variations. Besides cavitation at the origin, a new phenomenon due to the occurrence of a spherical fracture inside the body is observed.
Keywords: functions of bounded variation, fracture, cavitation, Generalized Varga materials, Radially symmetric deformations
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