arXiv subjects

Pedro M. Reis

Publications and source records attributed to Pedro M. Reis.

At least 19 recordsLinked to original sources

arXiv2026

The Butterfly Defect Effect in Cylindrical Shell Buckling: Non-localized Interactions of Localized Imperfections

We investigate the buckling of axially compressed cylindrical shells containing localized defects, focusing on interactions among multiple defects and between them and the shell edges. Using high-fidelity finite-element simulations, we first characterize the parameter space of single-dimple sensitivity, defect-edge coupling, and pairwise defect-defect interactions. Building on this deterministic baseline, we run stochastic simulations of shells with randomly distributed imperfections whose amplitudes are sampled from a log-normal distribution. Post-buckling deformations form non-axisymmetric, butterfly-shaped patterns whose `wings' reach far across the shell surface. This spatial extent induces unavoidable interactions with neighboring defects and the clamped edges, so that buckling is not necessarily initiated by the deepest defect. A larger defect population raises the likelihood of an extreme defect, producing a statistical size effect: as the mean number of defects grows, the mean knockdown factor decreases asymptotically and its variability decays exponentially. The butterfly defect effect qualitatively explains the scatter in historical experimental data by correlating the knockdown factor with the cylinder length-to-thickness ratio ($H/t$) rather than the radius-to-thickness ratio ($R/t$) alone, thereby establishing $H$ as a key parameter for stability alongside $R$ and $t$. Nonetheless, the knockdown factors obtained here remain well above those reported in historical experiments, indicating that the localized Gaussian dimple, though nearly the worst-case imperfection for spherical shells, is not so for cylinders.

physics.app-ph↗

arXiv2026

Frictional sliding strength of knotted and capstan configurations along the axis of a cylinder

We investigate the sliding strength of thin filaments in frictional contact with a translating cylinder, perpendicular to the filaments' axes, in knotted (clove hitch) and unknotted (capstan) configurations. Recent work reported superlinear scaling for surgical knots with elasto-plastic filaments [1]. Testing the clove hitch with various materials (elastomeric rods, metallic wires, braided ropes) reveals similar nonlinear behavior, ruling out plasticity. To explore the source of the previously reported nonlinear behavior, we perform three-dimensional FEM simulations (resolving full 3D mechanics) and reduced-order DER simulations (isolating geometric effects by neglecting cross-sectional deformation). Both FEM and DER simulations reproduce the experimental scaling. Simplifying the knot topology by studying capstan angles from $π/4$ to $4π$ yields comparable superlinear behavior, transitioning to linearity at smaller angles. We rationalize the results by developing an analytical model based on planar elastica theory for the capstan configuration (which exhibits behavior similar to the clove hitch but with a simpler topology). The model reproduces the observed superlinear behavior and rationalizes it by coupling the evolution of normal forces and contact arclength during tightening. The analysis further predicts transition to linearity when full contact between the filament and the cylinder is established, providing a mechanical framework applicable across materials, geometries, and topologies.

cond-mat.soft↗

arXiv2026

Dynamic versus quasi-static response of a cantilevered beam rotated harmonically

We investigate a cantilevered elastic beam subjected to harmonic rotational motion. In the rotating frame, the beam experiences centrifugal and Euler fictitious forces, with negligible Coriolis effects. We validate a reduced-order \textit{elastica} model through precision experiments on slender beams rotating with a controlled sinusoidal angular velocity. Systematically exploring the parameter space, we identify regimes where inertial effects are negligible, enabling a quasi-static treatment despite harmonic driving. We characterize the transition to dynamic response using two dimensionless parameters, the Euler and centrifugal numbers, which compare centrifugal and Euler forces to bending forces. Counterintuitively, the quasi-static regime expands as rotational speed increases: faster rotation produces less dynamic response. The critical Euler number separating these regimes remains constant at low centrifugal numbers but follows square-root scaling at higher rotation rates, a transition driven by centrifugal stiffening. Our results establish the conditions under which quasi-static approximations remain valid for rotating flexible beams under harmonic driving.

cond-mat.soft↗

arXiv2025

High-throughput characterization of snap-through stability boundaries of bistable beams in a programmable rotating platform

We introduce a high-throughput platform that enables simultaneous, parallel testing of six bistable beams via programmable motion of a rotating disk. By prescribing harmonic angular dynamics, the platform explores the phase space of angular velocity and acceleration $(Ω,\,\dotΩ)$, producing continuously varying centrifugal and Euler force fields that act as tunable body forces in our specimens. Image processing extracts beam kinematics with sub-pixel accuracy, enabling precise identification of snap-through events. By testing six beams in parallel, the platform allows systematic variation of beam thickness, pre-compression, tilt angle, and clamp orientations across 65 distinct configurations, generating 23,400 individual experiments. We construct stability boundaries and quantitatively parameterize them as parabolic functions, characterized by a vertical offset and a curvature parameter. Tilt angle provides the most robust mechanism for tuning the curvature parameter, while beam thickness and pre-compression modulate vertical offset. Modal decomposition analysis reveals that antisymmetric clamp configurations can trigger mode switching, in which competing geometric and inertial effects drive transitions through different deformation pathways. Our work establishes a scalable experimental framework for high-throughput characterization of dynamic nonlinear instabilities in mechanics. The complete experimental dataset is made publicly available to support data-driven design and machine learning models for nonlinear mechanics with applications to bistability-based metamaterials, mechanical memory, and electronics-free sensing systems.

cond-mat.soft↗

arXiv2025

Self-locking and Stability of the Bowline Knot

We investigate the self-locking of the bowline knot through numerical simulations, experiments, and theoretical analysis. Specifically, we perform two complementary types of simulations using the 3D finite-element method (FEM) and a reduced-order model based on the discrete-element method (DEM). For the FEM simulations, we develop a novel mapping technique that automatically transforms the centerline of the rod into the required knot topology prior to loading. In parallel, we conduct experiments using a nearly inextensible elastic rod tied into a bowline around a rigid cylinder. One end of the rod is pulled to load the knot while the other is left free. The measured force-displacement response serves to validate both the FEM and DEM simulations. Leveraging these validated computational frameworks, we analyze the internal tension profile along the rod's centerline, revealing that a sharp drop in tension concentrates around a strategic locking region, whose geometry resembles that observed in other knot types. By considering the coupling of tension, bending, and friction, we formulate a theoretical model inspired by the classic capstan problem to predict the stability conditions of the bowline, finding excellent agreement with our FEM and DEM simulations. Our methodology and findings offer new tools and insights for future studies on the performance and reliability of other complex knots.

cond-mat.soft↗

arXiv2024

A numerical study on the buckling of near-perfect spherical shells

We present the results from a numerical investigation using the finite element method to study the buckling strength of near-perfect spherical shells containing a single, localized, Gaussian-dimple defect whose profile is systematically varied toward the limit of vanishing amplitude. In this limit, our simulations reveal distinct buckling behaviors for hemispheres, full spheres, and partial spherical caps. Hemispherical shells exhibit boundary-dominated buckling modes, resulting in a knockdown factor of 0.8. By contrast, full spherical shells display localized buckling at their pole with knockdown factors near unity. Furthermore, for partial spherical shells, we observed a transition from boundary modes to these localized buckling modes as a function of the cap angle. We characterize these behaviors by systematically examining the effects of the discretization level, solver parameters, and radius-to-thickness ratio on knockdown factors. Specifically, we identify the conditions under which knockdown factors converge across shell configurations. Our findings highlight the critical importance of carefully controlled numerical parameters in shell-buckling simulations in the near-perfect limit, demonstrating how precise choices in discretization and solver parameters are essential for accurately predicting the distinct buckling modes across different shell geometries.

physics.app-ph↗

arXiv2024

The most severe imperfection governs the buckling strength of pressurized multi-defect hemispherical shells

We perform a probabilistic investigation on the effect of systematically removing imperfections on the buckling behavior of pressurized thin, elastic, hemispherical shells containing a distribution of defects. We employ finite element simulations, which were previously validated against experiments, to assess the maximum buckling pressure, as measured by the knockdown factor, of these multi-defect shells. Specifically, we remove fractions of either the least or the most severe imperfections to quantify their influence on the buckling onset. We consider shells with a random distribution of defects whose mean amplitude and standard deviation are systematically explored while, for simplicity, fixing the width of the defect to a characteristic value. Our primary finding is that the most severe imperfection of a multi-defect shell dictates its buckling onset. Notably, shells containing a single imperfection corresponding to the maximum amplitude (the most severe) defect of shells with a distribution of imperfections exhibit an identical knockdown factor to the latter case. Our results suggest a simplified approach to studying the buckling of more realistic multi-defect shells, once their most severe defect has been identified, using a well-characterized single-defect description, akin to the weakest-link setting in extreme-value probabilistic problems.

cond-mat.soft↗

arXiv2024

Stretch-independent magnetization in incompressible magnetorheological elastomers

In this study, we perform a critical examination of the phenomenon where the magnetization is stretch-independent in incompressible hard-magnetic magnetorheological elastomers (h-MREs), as observed in several recent experimental and numerical investigations. We demonstrate that the fully dissipative model proposed by Mukherjee et al. (2021) may be reduced, under physically consistent assumptions, to that of Yan et al. (2023), but not that of Zhao et al. (2019). In cases where the h-MRE solid undergoes non-negligible stretching, the model of Zhao et al. (2019) provides predictions that are in disagreement with experimental observations, given that, by construction, that model produces a magnetization response that is not stretch-independent. By contrast, the other two models are able to describe this important feature present in h-MREs, as well as in incompressible magnetically soft s-MRES. Note that in cases where stretching is negligible, such as for inextensible slender structures under bending deformation, the Zhao et al. (2019) model provides accurate predictions despite its underlying assumptions. Additionally, our analysis reveals two key points about the magnetization vector in the context of the more general, fully dissipative model. First, the magnetization can be related to an internal variable in that theory. However, it cannot be formally used as an internal variable except in the special case of an ideal magnet, and, as such, it is subject to constitutive assumptions. Furthermore, we clarify that the magnetization vector alone is insufficient to describe entirely the magnetic response of an MRE solid; instead, the introduction of one of the original Maxwell fields is always necessary for a complete representation.

cond-mat.soft↗

arXiv2024

Stick-slip in a stack: how slip dissonance reveals aging

We perform physical and numerical experiments to study the stick-slip response of a stack of slabs in contact through dry frictional interfaces driven in quasistatic shear. The ratio between the drive's stiffness and the slab's shear stiffness controls the presence or absence of slip synchronization. A sufficiently high stiffness ratio leads to synchronization, comprising periodic slip events in which all interfaces slip simultaneously. A lower stiffness ratio leads to asynchronous slips and, experimentally, to the stick-slip amplitude becoming broadly distributed as the number of layers in the stack increases. We interpret this broadening in light of the combined effect of complex loading paths due to the asynchronous slips and creep. Consequently, the aging rate of the interfaces can be readily extracted from the stick-slip cycles, and it is found to be of the same order of magnitude as existing experimental results on a similar material. Finally, we discuss the emergence of slow slips and an increase in aging-rate variations when more slabs are added to the stack.

cond-mat.soft↗

arXiv2023

Twisting instabilities in elastic ribbons with inhomogeneous pre-stress: a macroscopic analog of thermodynamic phase transition

We study elastic ribbons subject to large, tensile pre-stress confined to a central region within the cross-section. These ribbons can buckle spontaneously to form helical shapes, featuring regions of alternating chirality (phases) that are separated by so-called perversions (phase boundaries). This instability cannot be described by classical rod theory, which incorporates pre-stress through effective natural curvature and twist; these are both zero due to the mirror symmetry of the pre-stress. Using dimension reduction, we derive a one-dimensional (1D) 'rod-like' model from a plate theory, which accounts for inhomogeneous pre-stress as well as finite rotations. The 1D model successfully captures the qualitative features of torsional buckling under a prescribed end-to-end displacement and rotation, including the co-existence of buckled phases possessing opposite twist, and is in good quantitative agreement with the results of numerical (finite-element) simulations and model experiments on elastomeric samples. Our model system provides a macroscopic analog of phase separation and pressure-volume-temperature state diagrams, as described by the classical thermodynamic theory of phase transitions.

cond-mat.soft↗

arXiv2023

Gyrophilia: Harnessing Centrifugal and Euler Forces for Tunable Buckling of a Rotating Elastica

We investigate the geometrically nonlinear deformation and buckling of a slender elastic beam subject to time-dependent `fictitious' (non-inertial) forces arising from unsteady rotation. Using a rotary apparatus that accurately imposes an angular acceleration around a fixed axis, we demonstrate that centrifugal and Euler forces can be combined to produce tunable structural deformation. Specifically, using an imposed acceleration ramp, the buckling onset of a cantilevered beam can be precisely tuned and its deformation direction selected. In a second configuration, a pre-arched beam can be made to snap, on demand, between its two stable states. We also formulate a theoretical model rooted in Euler's elastica that rationalizes the problem and provides predictions in excellent quantitative agreement with the experimental data. Our findings demonstrate an innovative approach to programmable actuation of slender rotating structures.

cond-mat.soft↗

arXiv2023

Fluid--structure interactions of bristled wings: The trade-off between weight and drag

The smallest flying insects often have bristled wings resembling feathers or combs. We combined experiments and three-dimensional numerical simulations to investigate the trade-off between wing weight and drag generation. In experiments of bristled strips, a reduced physical model of the bristled wing, we found that the elasto-viscous number indicates when reconfiguration occurs in the bristles. Analysis of existing biological data suggested that bristled wings of miniature insects lie below the reconfiguration threshold, thus avoiding drag reduction. Numerical simulations of bristled strips showed that there exist optimal numbers of bristles that maximize the weighted drag when the additional volume due to the bristles is taken into account. We found a scaling relationship between the rescaled optimal numbers and the dimensionless bristle length. This result agrees qualitatively with and provides an upper bound for the bristled wing morphological data analyzed in this study.

physics.bio-ph↗

arXiv2023

Designing a braille reader using the snap buckling of bistable magnetic shells

A design concept is introduced for the building block, a dot, of programmable braille readers utilizing bistable shell buckling, magnetic actuation, and pneumatic loading. The design process is guided by Finite Element simulations, which are initially validated through precision experiments conducted on a scaled-up, single-shell model system. Then, the simulations are leveraged to systematically explore the design space, adhering to the standardized geometric and physical specifications of braille systems. The findings demonstrate the feasibility of selecting design parameters that satisfy both geometric requirements and blocking forces under moderate magnetic fields, facilitated by pneumatic loading to switch between the two stable states. The advantages of the proposed design include the reversible bistability of the actuators and fast state-switching via a transient magnetic field. While the study is focused on experimentally validated numerical simulations, several manufacturing challenges that need to be resolved for future physical implementations are identified.

cond-mat.soft↗

arXiv2023

Defect-Defect Interactions in the Buckling of Imperfect Spherical Shells

We perform finite element simulations to study the impact of defect-defect interactions on the pressure-induced buckling of thin, elastic, spherical shells containing two dimpled imperfections. Throughout, we quantify the critical buckling pressure of these shells using their knockdown factor. We examine cases featuring either identical or different geometric defects and systematically explore the parameter space, including the angular separation between the defects, their widths and amplitudes, and the radius-to-thickness ratio of the shell. As the angular separation between the defects is increased, the buckling strength initially decreases, then increases before reaching a plateau. Our primary finding is that the onset of defect-defect interactions, as quantified by a characteristic length scale associated with the onset of the plateau, is set by the critical buckling wavelength reported in the classic shell-buckling literature. Beyond this threshold, within the plateau regime, the buckling behavior of the shell is dictated by the largest defect.

cond-mat.soft↗

arXiv2022

Comparing the buckling strength of spherical shells with dimpled versus bumpy defects

We investigate the effect of defect geometry in dictating the sensitivity of the critical buckling conditions of spherical shells under external pressure loading. Specifically, we perform a comparative study between shells containing dimpled (inward) versus bumpy (outward) Gaussian defects. The former has become the standard shape in many recent shell-buckling studies, whereas the latter has remained mostly unexplored. We employ finite-element simulations, which were validated previously against experiments, to compute the knockdown factors for the two cases while systematically exploring the parameter space of the defect geometry. For the same magnitudes of the amplitude and angular width of the defect, we find that shells containing bumpy defects consistently exhibit significantly higher knockdown factors than shells with the more classic dimpled defects. Furthermore, the relationship of the knockdown as a function of the amplitude and width of the defect is qualitatively different between the two cases, which also exhibit distinct post-buckling behavior. A speculative interpretation of the results is provided based on the qualitative differences in the mean-curvature profiles of the two cases.

cond-mat.soft↗

arXiv2022

Probabilistic buckling of imperfect hemispherical shells containing a distribution of defects

The buckling of spherical shells is plagued by a strong sensitivity to imperfections. Traditionally, imperfect shells tend to be characterized empirically by the knockdown factor, the ratio between the measured buckling strength and the corresponding classic prediction for a perfect shell. Recently, it has been demonstrated that the knockdown factor of a shell containing a single imperfection can be predicted when there is detailed a priori knowledge of the defect geometry. Still, addressing the analogous problem for a shell containing many defects remains an open question. Here, we use finite element simulations, which we validate against precision experiments, to investigate hemispherical shells containing a well-defined distribution of imperfections. Our goal is to characterize the resulting knockdown factor statistics. First, we study the buckling of shells containing only two defects, uncovering nontrivial regimes of interactions that echo existing findings for cylindrical shells. Then, we construct statistical ensembles of imperfect shells, whose defect amplitudes are sampled from a lognormal distribution. We find that a 3-parameter Weibull distribution is an excellent description for the measured statistics of knockdown factors, suggesting that shell buckling can be regarded as an extreme-value statistics phenomenon.

cond-mat.soft↗

arXiv2022

Snap buckling of bistable beams under combined mechanical and magnetic loading

We investigate the mechanics of bistable, hard-magnetic, elastic beams, combining experiments, finite element modeling (FEM), and a reduced-order theory. The beam is made of a hard magneto-rheological elastomer, comprising two segments with antiparallel magnetization along the centerline, and is set into a bistable curved configuration by imposing an end-to-end shortening. Reversible snapping is possible between these two stable states. First, we experimentally characterize the critical field strength for the onset of snapping, at different levels of end-to-end shortening. Second, we perform 3D FEM simulations using the Riks method to analyze high-order deformation modes during snapping. Third, we develop a reduced-order centerline-based beam theory to rationalize the observed magneto-elastic response. The theory and simulations are validated against experiments, with an excellent quantitative agreement. Finally, we consider the case of combined magnetic and mechanical-indentation loading, examining how the applied field affects the bistability and quantifying the maximum load-bearing capacity. Our work provides a set of predictive tools for the rational design of one-dimensional, bistable, magneto-elastic structural elements.

cond-mat.soft↗

arXiv2022

A reduced-order, rotation-based model for thin hard-magnetic plates

We develop a reduced-order model for thin plates made of hard magnetorheological elastomers (hard-MREs), which are materials composed of hard-magnetic particles embedded in a polymeric matrix. First, we propose a new magnetic potential, as an alternative to an existing torque-based 3D continuum theory of hard-MREs, obtained by reformulating the remnant magnetization of a deformed hard-MRE body. Specifically, the magnetizations in the initial and current configurations are related by the rotation tensor decomposed from the deformation gradient, independently of stretching deformation. This description is motivated by recently reported observations in microscopic homogenization simulations. Then, we derive a 2D plate model through the dimensional reduction of our proposed rotation-based 3D theory. For comparison, we also provide a second plate model derived from the existing 3D theory. Finally, we perform precision experiments to thoroughly evaluate the proposed 3D and 2D models on hard-magnetic plates under various magnetic and mechanical loading conditions. We demonstrate that our rotation-based modification of the magnetic potential is crucial in correctly capturing the behavior of plates subjected to an applied field aligned with the magnetization, and undergoing in-plane stretching. In all the tested cases, our rotation-based 3D and 2D models yield predictions in excellent quantitative agreement with the experiments and can thus serve as predictive tools for the rational design of hard-magnetic plate structures.

cond-mat.soft↗