arXiv subjects

Marco Picchi Scardaoni

Publications and source records attributed to Marco Picchi Scardaoni.

5 recordsLinked to original sources

arXiv2026

When Volumetric Growth Selects Surface Growth

We investigate the relationship between volumetric and surface growth within a recently proposed optimization-driven framework for linearly elastic solids. In this approach, growth is not prescribed through an evolution law; instead, the growth distribution is determined as the solution of a constrained optimization problem. Focusing on processes driven by the minimization of the work performed by external loads in one-dimensional and axisymmetric settings, we derive explicit analytical solutions for the resulting growth distributions. Although growth is initially formulated as a volumetric process through a distributed growth strain tensor, we show that the optimal growth distributions are singular and concentrate on boundaries or internal interfaces. These results provide a variational mechanism through which, under certain conditions, surface growth is selected as the optimal realization of volumetric growth.

math-ph↗

arXiv2026

Surface Growth Driven by an Optimality Criterion

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.

math-ph↗

arXiv2026

Volumetric Growth in Linear Elasticity Driven by an Optimality Criterion

Using linearized elasticity as a convenient mechanical framework, we show that volumetric growth can be formulated as an optimization-driven process in which the growth tensor is determined implicitly by constrained optimization rather than prescribed through phenomenological evolution laws. At each incremental step, the displacement and growth fields satisfy equilibrium, mass-balance constraints, and an irreversibility condition enforcing accretive growth, while an objective functional encodes the driving mechanism of the process. Finite element discretization leads to a finite-dimensional constrained minimization problem in the growth variables alone and makes explicit the interpretation of the evolution as a projected gradient flow. Numerical examples illustrate the proposed framework.

math-ph↗

arXiv2021

Linear Models of a Stiffened Plate via $Γ$-convergence

We consider a family of three-dimensional stiffened plates whose dimensions are scaled through different powers of a small parameter $\varepsilon$. The plate and the stiffener are assumed to be linearly elastic, isotropic, and homogeneous. By means of $Γ$-convergence, we study the asymptotic behavior of the three-dimensional problems as the parameter $\varepsilon$ tends to zero. For different relative values of the powers of the parameter $\varepsilon$, we show how the interplay between the plate and the stiffener affects the limit energy. We derive twenty-three limit problems.

math-ph↗

arXiv2021

Aircraft turnaround time estimation in early design phases: simulation tools development and application to the case of box-wing architecture

This work deals with the problem of estimating the turnaround time in the early stages of aircraft design. The turnaround time has a significant impact in terms of marketability and value creation potential of an aircraft and, for this reason, it should be considered as an important driver of fuselage and cabin design decisions. Estimating the turnaround time during the early stages of aircraft design is therefore an essential task. This task becomes even more decisive when designers explore unconventional aircraft architectures or, in general, are still evaluating the fuselage design and its internal layout. In particular, it is of paramount importance to properly estimate the boarding and deboarding times, which contribute for up the 40% to the overall turnaround time. For this purpose, a tool, called SimBaD, has been developed and validated with publicly available data for existing aircraft of different classes. In order to demonstrate SimBaD capability of evaluating the influence of fuselage and cabin features on the turnaround time, its application to an unconventional box-wing aircraft architecture, known as PrandtlPlane, is presented as case study. Finally, considering standard scenarios provided by aircraft manufacturers, a comparison between the turnaround time of the PrandtlPlane and the turnaround time of a conventional competitor aircraft is presented.

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