Published Paper

Inserted: 19 may 2025

Journal: Math. Mech. Solids
Volume: 30
Number: 6
Pages: 1249-1281
Year: 2025
Doi: 10.1177/10812865241275568

Abstract:

A variational scheme of evolution (minimizing movements) is applied to a sequence of discrete functionals converging, as the mesh size tends to zero, to the prototypical second-order functional with free-discontinuities. At fixed mesh size, a discrete evolution can be defined, depending on a (small) time parameter. We study the limit problem when both the mesh size and the time step tend to zero. The method provides a function which matches the expected evolution of the free-discontinuity limit functional. From a mechanical point of view, the model can be interpreted as the evolution from a non-equilibrium state, of a rod with possible crease discontinuities and fracture.