Pedro M. Reis’s research while affiliated with Swiss Federal Institute of Technology in Lausanne and other places

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Publications (193)


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

October 2024

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18 Reads

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Florian Choquart

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Pedro M. Reis

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.



Fig. 1. Definition of the reference, intermediate and current configurations of volume  0 ,  í µí±– and , respectively, along with the different field variables defined therein.
Fig. 2. (a) Schematic of a magnetic particle subjected to a full cyclic magnetic load í µí°¡ = ℎ 1 í µí°ž 1 . (b) Normalized magnetization response versus the normalized field strength. Both ideal (í µí¼’ í µí±’ í µíº™ = 0; black dashed line) and actual (í µí¼’ í µí±’ í µíº™ = 0.1; blue solid line) hysteresis loops are shown along with the slopes of the í µí±š − ℎ response before and after magnetic switching, i.e., before and after reaching the value í µí± í µí± í µíº™ ∕í µí¼‡ í µí¿ ¶ í µí±š í µí± í µíº™ . (c) Normalized magnetization responses for finite (black dashed line) and zero (red solid line) coercivity í µí± í µí± í µíº™ ∕í µí¼‡ í µí¿ ¶ í µí±š í µí± í µíº™ lead to, respectively, hysteretic and energetic magnetization responses. Source: Both plots were adapted from the previous work of Mukherjee and Danas (2022).
Fig. 3. Results reproduced from Yan et al. (2023) for experiments and FEM simulations, the latter for both the í µí°‘í µí°Œ and the í µí° í µí°Œ models, for a fully clamped ℎ-MRE plate under combined pressure and magnetic loading. (a) Schematic diagram with a top view (into the í µí°ž 1 -í µí°ž 2 plane) and side view (into the í µí°ž 2 -í µí°ž 3 plane) of the system. (b,c) Normalized deflection, í µí»¿∕ℎ versus the applied pressure í µí±, for two values of the amplitude of the applied magnetic field, |í µí°›| = {80, 160} mT. The experimental results (solid symbols) are common to both plots. (b) Comparison between the experimental results and 3D FEM-simulations (open symbols) using the í µí°‘í µí°Œ model: circles and squares for 80 mT and 160 mT, respectively. (c) Comparison between the experimental results and 3D FEM-simulations (open symbols) using the í µí° í µí°Œ model: open diamonds and triangles for 80 mT and 160 mT, respectively. Source: This figure was adapted from the previous work of Yan et al. (2023).
Stretch-independent magnetization in incompressible isotropic hard magnetorheological elastomers
  • Article
  • Full-text available

July 2024

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168 Reads

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6 Citations

Journal of the Mechanics and Physics of Solids

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

January 2024

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89 Reads

Physical Review Research

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 interface aging. 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. Published by the American Physical Society 2024


Design, fabrication, and operation of a bistable Braille dot. a) Geometry: A word is formed by assembling a series of braille cells, each comprising 3 × 2 dots. “EPFL” is shown as an example. b) Fabrication: A bistable shell is fabricated by sandwiching a circular h‐MRE plate between two radially pre‐stretched boundary annuli. This pre‐stretch is then released to buckle the plate into a shell. c) Writing phase: an external magnetic field, Ba, sets each shell in one of its two stable states, either ON (bump) or OFF (dimple). d) Reading phase: an index finger applies an indentation force, F on each dot.
Validation of FEM simulations against the scaled‐up experiments. a) Phase diagram in the (t, D) parameter space. The experiments and simulations correspond to the cross and circle symbols, respectively. The smooth and wrinkled shells are represented by the blue and red symbols, respectively; the empirical phase boundary between the two is represented by the dashed line. The normalized b) shell height, h/t, c) critical magnetic field, BcaBr/(Eμ0)$B^\mathrm{a}_\mathrm{c}B^\mathrm{r}/(E \mu _0)$, and d) blocking force, FD/(Et³) are plotted as functions of the normalized base diameter of the shell, D/t, for ten different values of thickness, t. The error bars of the experimental data represent the standard deviation of six independent measurements on the same specimen. The different values of t are color‐coded (see adjacent color bar). The solid lines and data symbols correspond to FEM and experiments, respectively. The insets show the log‐log plots of the data. Throughout, the fabrication pre‐stretch is λ = 0.1.
Design of the real‐scale braille dot. The a) dot height, h, b) critical magnetic field, Bca$B^\mathrm{a}_\mathrm{c}$, and c) blocking force, F, are all plotted versus thickness, t, at different levels of pre‐stretching, λ = [0.05,0.2] (increments of 0.05). The horizontal dashed lines represent the design constraints of the corresponding quantities. d) Phase diagram in the (Bca$B^\mathrm{a}_\mathrm{c}$, F) parameter space, with the desired shaded region. e) Phase diagram in the (t, λ) parameter space for the geometry step and reading and writing phases, with the feasible design space indicated by the rectangle region. All results were obtained from FEM simulations.
Improved design of real‐scale braille dots with pneumatic system. a) Blocking force, F, and b) magnetic field, Bca$B^\mathrm{a}_\mathrm{c}$, plotted as a function of the pressure difference, ΔP. The thickness was varied in the range t = [0.075 − 0.3] mm (in increments of 0.025 mm) for a specific pre‐stretch λ = 0.15. The horizontal dashed lines represent the limiting bounds imposed by the braille standards. c) Phase diagram in the (Bca$B^\mathrm{a}_\mathrm{c}$, F) parameter space with the desired regions of viable parameters (shaded region), for different levels of pressure difference, 0 < |ΔP| < 120 kPa. All results were obtained from FEM simulations.
Fabrication and experimental apparatus for the scaled‐up model. a) A circular magnetic plate (diameter of Dp) is first b) folded along the x‐axis and then c) along the y‐axis to form a quarter‐circle shape. d) The folded plate is inserted into the pulse magnetizer at an angle α = 45°. The magnetizer generates a strong axial magnetic field, B, which induces a magnetic moment, m. e) The circular h‐MRE plate was magnetized while folded, yielding the magnetization profile described by Equation (1). f) Two VPS annuli serve to constrain the plate boundary. g) Cylinders pre‐stretched the annuli, which sandwich the h‐MRE plate. h) Upon release of the pre‐stretch, the plate buckles to form a shell. i) Photograph of the apparatus for the writing experiments. The shell is placed between two Helmholtz coils and loaded by a uniform magnetic field along ẑ$\hat{\mathbf {z}}$. j) Photograph of the apparatus for the reading experiments; a plate indents the shell, and the blocking force F is measured.
Leveraging the Snap Buckling of Bistable Magnetic Shells to Design a Refreshable Braille Dot

December 2023

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70 Reads

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6 Citations

A design concept is proposed 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. While the study is focused on experimentally validated numerical simulations, it is also identify several manufacturing challenges that need to be resolved for future physical implementations .


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

September 2023

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82 Reads

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2 Citations

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 analysed in this study.


FIG. 1. (a) A beam (1) is mounted on a rigid arm (2) inside an acrylic box (3). A torque motor (4) rotates the arm and a camera (5). (b) Representative time-series of the imposed angular velocity, Ω(t), and (c) angular acceleration, ˙ Ω(t), with α={5, 2.5} rad/s 2 (green/blue curves; see legend) and (Ω0, Ωe)=(5, 15)rad/s. Bottom panels: undeformed (top row) and deformed (lower row) specimens for (d) straight and (e) naturally curved cantilevers; and (f) pre-arched (doubleclamped) beam. Deformed configurations are taken at the instances labeled in panels (b, c). See also S.M. Video 1-3 [36].
FIG. 5. Solution to leading-order problem, Eq. (11), obtained by shooting. (Left) Solution for ϕ (0) (S) for different values of δ (see legend). (Right) Corresponding values of the eigenvalue C ⋆ and the constants c1, c2 and c3 (defined in Eq. (17)).
Gyrophilia: Harnessing Centrifugal and Euler Forces for Tunable Buckling of a Rotating Elastica

August 2023

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143 Reads

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.



FIG. 3. Design of the real-scale braille dot. The (a) dot height, h, (b) critical magnetic field, B a c , and (c) blocking force, F , are all plotted versus thickness, t, at different levels of pre-stretching, λ=[0.05, 0.2] (increments of 0.05). The horizontal dashed lines represent the design constraints of the corresponding quantities. (d) Phase diagram in the (B a c , F ) parameter space, with the desired shaded region. (e) Phase diagram in the (t, λ) parameter space for the geometry step and reading and writing phases, with the feasible design space indicated by the rectangle region. All results were obtained from FEM simulations.
Designing a braille reader using the snap buckling of bistable magnetic shells

July 2023

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135 Reads

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.


Citations (66)


... This behavior was recently demonstrated experimentally by Yan et al. [59], who investigated the deformation of a fully-clamped hMAE plate under combined pressure and magnetic loading. Furthermore, Danas and Reis [60] provided an in-depth analysis of the independence of remanent magnetization from the stretch of hMAEs. Liu et al. [61] developed a mesh-free model based on the radial point interpolation method to quantitatively predict large deformations of hMAEs. ...

Reference:

Magnetically tunable topological states in translational-rotational coupling metamaterials
Stretch-independent magnetization in incompressible isotropic hard magnetorheological elastomers

Journal of the Mechanics and Physics of Solids

... This instability occurs in various scenarios, including, e.g. during the abrupt closure of Venus flytrap leaves [11] and pneumatic-actuated soft jumping robots [12]. Snap-through of shells can be triggered through different stimuli, including indentation [13][14][15][16], pressure [9,10,12], magnetic actuation [17,18], chemical diffusion [19], strain mismatch [20] and mechanical contact [21], etc. In recent years, there has been growing interest in exploring snap-through instabilities due to their significant potential for applications such as robotic actuation [12,22]. ...

Leveraging the Snap Buckling of Bistable Magnetic Shells to Design a Refreshable Braille Dot

... Insect wing morphology may serve as a basic example of evolutionary variability, where distinct wing geometries can be observed in extant species occupying similar environments [3][4][5][6][7][8]. A specific example is the case of porous (bristled) and solid (membranous) wings in small flying insects (Fig 1A) [5,7,9]. ...

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

... It also includes the effect of the stored elastic strain energy which is not considered in the swelling-based mechanism. However, current study on the twisted helix focuses mostly on investigating the instability of the helical structure [29,[34][35][36][37][38][39], yet there is a notable gap in understanding the behavior of this system in parametric space, such as temperature. ...

Twisting instabilities in elastic ribbons with inhomogeneous pre-stress: A macroscopic analog of thermodynamic phase transition
  • Citing Article
  • August 2023

Journal of the Mechanics and Physics of Solids

... Extending beyond the single-defect case, Derveni et al. [33] explored the effect of interactions between defects by investigating spherical shells with two imperfections and unveiled a defect-defect interaction regime. Within this interaction regime, the knockdown factor can be either enhanced or reduced, the extent of which is dictated by the critical buckling wavelength of the shell [34]. ...

Defect-Defect Interactions in the Buckling of Imperfect Spherical Shells
  • Citing Article
  • June 2023

Journal of Applied Mechanics

... Assemblies of long, flexible, and intertwined fibers with frictional contacts are materials involved in various phenomena, including surgical or shoe knots [1,2], nests and self-assembled natural structures [3,4], nonwoven fabrics with a wealth of applications [5], or the degradation of ancient manuscripts [6]. Despite being essential for most applications, the mechanical response of fiber assemblies is intrinsically non-linear, dissipative, and historydependent, stemming from the fibers' slenderness and the frictional contacts. ...

The strength of surgical knots involves a critical interplay between friction and elastoplasticity

Science Advances

... During terrestrial locomotion, various aquatic species, including eels (Gillis, 1998a), ropefish (Pace & Gibb, 2011), and lungfish (Horner & Jayne, 2014), also exhibit large wave amplitudes along their body. Studies examining swimming behaviour in both viscous water (Horner & Jayne, 2008;Tytell et al., 2023) and sandy shallow water (Pace & Gibb, 2011) have advanced our understanding of how animals move in muddy environments. Notably, the lateral displacement surface gradually increases with higher viscosity and shallower water depth. ...

Regulation of the swimming kinematics of lampreys Petromyzon marinus across changes in viscosity
  • Citing Article
  • April 2023

Journal of Experimental Biology

... However, considerably less attention has been given to spherical multi-defect shells. Recently, Derveni et al. [41] examined the case of spherical shells with a random distribution of geometric imperfections on the surface of the shells. That work demonstrated that when the amplitude of the defects is sampled from a lognormal distribution, the resulting knockdown factor can be described using a 3-parameter Weibull distribution. ...

Probabilistic buckling of imperfect hemispherical shells containing a distribution of defects

... More in general, the design of mechanical metamaterials, materials displaying features not achievable from the classical ones, has been recently enhanced by considering the influence of structural flexibility [7] towards multistability [1,3,40,48], reconfigurable structures [25,36], wave guiding [11,18,27] and unidirectional wave propagation [43,45]. ...

Snap buckling of bistable beams under combined mechanical and magnetic loading

... ing shells with meticulously designed imperfections [25][26][27]. Subsequent studies have primarily focused on single imperfections localized at the shell pole via experiments and numerical simulations, including constant thickness geometrical imperfections, such as dimples [28][29][30] and bumps [31], or thickness variations [32]. ...

Comparing the Buckling Strength of Spherical Shells With Dimpled Versus Bumpy Defects
  • Citing Article
  • January 2023

Journal of Applied Mechanics