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.
Variational evolution of discrete one-dimensional second-order functionals / Defranceschi, Anneliese; Lussardi, Luca; Vitali, Enrico. - In: MATHEMATICS AND MECHANICS OF SOLIDS. - ISSN 1081-2865. - ELETTRONICO. - 2024 online first:(2024), pp. 1-33. [10.1177/10812865241275568]
Variational evolution of discrete one-dimensional second-order functionals
Defranceschi, Anneliese
Primo
;
2024-01-01
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.File | Dimensione | Formato | |
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