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arXiv · 2605.13602

Surface Growth Driven by an Optimality Criterion

Rohan Abeyaratne·Roberto Paroni·Marco Picchi Scardaoni
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Abstract

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.

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Rohan Abeyaratne, Roberto Paroni, Marco Picchi Scardaoni. 2026-05-13. Surface Growth Driven by an Optimality Criterion. https://arxiv.org/abs/2605.13602

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