Salvato in:
| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2605.13602 |
| Tags: |
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Sommario:
- We propose a variational framework for accretive surface growth driven by an optimality principle. Rather than prescribing a kinetic law, the configuration at each time step is obtained, within a time-discrete setting, as the solution of a constrained minimization problem. Growth is modeled as an irreversible surface deposition process subject to a global mass constraint, while the driving mechanism is encoded in an objective functional, here taken to be the structural mean compliance. The approach is illustrated on a linearly elastic cantilever beam whose cross-sectional height evolves through layered accretion, possibly involving prestrain and precurvature. Growth-induced residual stresses can alter the convexity of the compliance functional, leading to nonuniqueness and localization phenomena. We explore the possibility of adding a regularization term penalizing deviations from the previous-step configuration. Finally, through a formal limiting procedure, we derive from the time-discrete formulation a time-continuous limit in the form of a constrained gradient flow.