Topology-Optimized Pneumatic Soft Actuator: Design and Experimental Validation

Konstantinos Poulios; Sumit Mehta

arxiv: 2605.20101 · v1 · pith:SY5CD7NBnew · submitted 2026-05-19 · 💻 cs.RO

Topology-Optimized Pneumatic Soft Actuator: Design and Experimental Validation

Sumit Mehta , Konstantinos Poulios This is my paper

Pith reviewed 2026-05-20 04:38 UTC · model grok-4.3

classification 💻 cs.RO

keywords topology optimizationsoft pneumatic actuators3D designporohyperelasticitylarge deformationsstereolithographyexperimental validationbending actuators

0 comments

The pith

A 3D topology optimization method designs pneumatic soft actuators that maximize bending for a given pressure while respecting strain limits.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends an existing density-based topology optimization framework that incorporates porohyperelastic material behavior from two dimensions to three. This extension generates two distinct actuator geometries intended for stereolithography fabrication. Both designs aim to produce the largest possible tip bending angle under a fixed actuation pressure while staying below separate allowable strain thresholds. The optimization explicitly tracks the large shape changes that occur as the actuator inflates. Numerical results and physical experiments on the printed parts confirm that the predicted bending performance is achieved.

Core claim

Extending the density- and porohyperelasticity-based topology optimization framework from 2D to 3D produces two manufacturable actuator designs that maximize bending response for a prescribed actuation pressure under two different allowable strain limits; the designs are validated both numerically and through stereolithography fabrication and experimental testing.

What carries the argument

The 3D extension of the density- and porohyperelasticity-based topology optimization framework that accounts for large deformations throughout the optimization process.

If this is right

The same optimization procedure can be rerun for different pressure levels or strain limits to produce families of actuators.
The framework directly supplies printable 3D geometries that require no post-processing interpretation.
Numerical and experimental agreement demonstrates that the large-deformation effects are captured during design rather than corrected afterward.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The approach could be applied to other soft-robotics components such as grippers or crawling mechanisms by changing only the objective and boundary conditions.
Combining the method with multi-material printing might allow further performance gains by placing stiffer and softer regions where the optimization naturally concentrates them.
The resulting designs may serve as benchmarks for comparing different topology-optimization formulations or fabrication techniques.

Load-bearing premise

The porohyperelastic material model and large-deformation assumptions accurately represent how the stereolithography-fabricated elastomeric material behaves when pressurized.

What would settle it

Experimental measurement of tip bending angle and maximum strain in the fabricated actuators deviates substantially from the numerical predictions obtained with the optimized designs.

Figures

Figures reproduced from arXiv: 2605.20101 by Konstantinos Poulios, Sumit Mehta.

**Figure 2.** Figure 2: shows the fully converged design produced with the data from [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: Side view of the final design obtained for [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: Section of final design obtained for p 2Ψlim/E = 14% in the undeformed (a) and deformed (b) configurations. pressure at 2% of the elastomer’s initial Young’s modulus. The reader is referred to [26] for a parametric study with respect to source pressure and allowable strain energy density in 2D [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Section of final design obtained for p 2Ψlim/E = 11% in the undeformed (a) and deformed (b) configurations [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

**Figure 6.** Figure 6: Convergence history for the two optimization cases. [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: Flowchart for SLA 3D printing through Formlabs printers. [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗

**Figure 8.** Figure 8: Experimental testing device and instrumentation. [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗

**Figure 9.** Figure 9: a) Numerically obtained actuator design for [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗

**Figure 10.** Figure 10: a) Physical realization of the actuator design obtained for [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗

**Figure 11.** Figure 11: Evolution of individual contributions CA, Ci , CΨ, Cp, to the total objective. E Spring calibration [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗

**Figure 12.** Figure 12: shows the results of the cantilever spring calibration as well as the calibration setup. A height vernier gauge was used to measure deflections. Weights corresponding to 10 g, 20 g, 50 g, 70 g, and 100 g were used as loads. The free length of the cantilever was calibrated at 113 mm to reach the target stiffness of 0.045 N/mm, as shown in the force-deflection graph. 0 0.2 0.4 0.6 0.8 1 0 4 8 12 16 20 24 wi… view at source ↗

**Figure 13.** Figure 13: Measured displacement and pressure data over time. [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗

read the original abstract

This paper demonstrates the computational design of soft elastomeric pneumatic actuators using nonlinear topology optimization. An existing density- and porohyperelasticity-based topology optimization framework was extended from 2D to 3D and used to generate two manufacturable actuator designs, which were then studied numerically and experimentally. For both designs, the objective was to maximize the bending response for a prescribed actuation pressure under two different allowable strain limits. A key advantage of the employed topology optimization framework is that it can consistently, during the optimization, account for the very large deformations induced upon pressurization. The two optimized 3D designs were fabricated using stereolithography and experimentally tested to validate their performance.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This extends a 2D topology optimization framework to 3D for pneumatic actuators and adds experimental checks on two printed designs, but the porohyperelastic model lacks direct calibration to the actual SLA material.

read the letter

The main point is that the authors took their prior density-based topology optimization setup, which already used a porohyperelastic model in 2D, and moved it to 3D to generate two actuator geometries. These are optimized to maximize bending at a set pressure while staying under different strain limits, then built with stereolithography and tested against the simulations. The consistent treatment of large deformations inside the optimizer is a practical plus that avoids some common simplifications in soft actuator work. The experimental results on the fabricated parts give direct evidence that the designs function as intended under pressure. That combination of 3D extension plus physical validation is what is actually new here. The soft spot sits with the material model. The optimization depends on the porohyperelastic assumptions holding for the printed elastomer under large strains, yet the provided details do not show calibration against specimens from the same resin batch and process. A mismatch in shear modulus or compressibility would affect both the optimality of the shapes and how well the numerics match the tests. This is not fatal on its own, but it is the load-bearing assumption that needs checking. The paper is aimed at soft robotics researchers who use computational design tools for actuators. Someone working on topology optimization or 3D printed soft devices would get concrete value from the geometries and the sim-to-exp comparison. It has enough substance and validation to deserve a serious referee rather than a desk reject. I would recommend sending it for review, with specific attention to the material characterization and the 3D implementation details.

Referee Report

1 major / 2 minor

Summary. The paper extends a density-based topology optimization framework that incorporates porohyperelasticity from 2D to 3D and applies it to generate two manufacturable pneumatic soft actuator designs. The objective is to maximize bending displacement under a fixed actuation pressure subject to two different allowable strain limits; the designs are then fabricated via stereolithography and their performance is assessed both numerically (using the same constitutive model) and experimentally.

Significance. If the porohyperelastic constitutive model is representative of the SLA-printed elastomer under large strains, the work demonstrates a practical route to computationally designing high-performance soft actuators that explicitly account for geometric nonlinearity during optimization. The direct numerical-experimental comparison on fabricated prototypes supplies concrete evidence that the 3D extension produces realizable, high-bending designs.

major comments (1)

[Constitutive model and topology optimization framework] The porohyperelastic material parameters employed throughout the 3D topology optimization are not calibrated against uniaxial or biaxial test data obtained from specimens printed with the identical SLA resin batch and process parameters used for the final actuators. Because the optimizer relies on this model to evaluate both the objective (bending) and the strain-limit constraints under finite deformations, any mismatch in shear modulus, bulk modulus, or strain-stiffening behavior directly affects the optimality of the generated topologies and the reported numerical-experimental agreement.

minor comments (2)

[Problem formulation] Specify the exact numerical values of the two allowable strain limits and the rationale for their selection; this information is needed to interpret the relative performance gains of the two optimized designs.
[Experimental validation] In the experimental results, report the number of repeated tests per actuator and the observed variability (standard deviation or range) in bending angle to allow quantitative assessment of experimental repeatability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comment point by point below.

read point-by-point responses

Referee: [Constitutive model and topology optimization framework] The porohyperelastic material parameters employed throughout the 3D topology optimization are not calibrated against uniaxial or biaxial test data obtained from specimens printed with the identical SLA resin batch and process parameters used for the final actuators. Because the optimizer relies on this model to evaluate both the objective (bending) and the strain-limit constraints under finite deformations, any mismatch in shear modulus, bulk modulus, or strain-stiffening behavior directly affects the optimality of the generated topologies and the reported numerical-experimental agreement.

Authors: We thank the referee for this observation. The porohyperelastic parameters were taken directly from the 2D framework paper on which this work builds, where they were calibrated to uniaxial tension data for SLA-printed specimens of the same resin family and similar process parameters. We acknowledge that batch-specific recalibration for the exact resin lot used here would be preferable and could further strengthen claims of optimality. To address the concern, we will revise the manuscript to (i) explicitly state the provenance of the parameters with reference to the prior calibration data, (ii) add a short sensitivity study demonstrating that the optimized topologies and predicted bending displacements remain qualitatively unchanged under modest variations in shear and bulk moduli consistent with typical SLA batch variation, and (iii) note the close numerical-experimental agreement as supporting evidence that the chosen model remains representative for the designs considered. We believe these additions will clarify the modeling choices without requiring new physical testing. revision: partial

Circularity Check

0 steps flagged

No significant circularity; optimization and experimental validation are independent

full rationale

The paper extends an existing 2D density- and porohyperelasticity-based topology optimization framework to 3D to generate actuator geometries that maximize bending under prescribed pressure and strain limits. These geometries are then fabricated via stereolithography and tested experimentally. No equation or step reduces a performance metric to a fitted parameter or self-definition by construction. The porohyperelastic constitutive law is an input to the optimizer, but the final claims rest on physical measurements outside the model, satisfying the self-contained benchmark criterion. Minor self-citation of the prior framework is present but not load-bearing for the 3D extension or validation results.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The work rests on an existing topology-optimization framework whose material model and large-deformation handling are taken as given and extended to 3D; experimental validation supplies an external check rather than deriving performance from fitted constants.

free parameters (1)

allowable strain limits
Two different strain limits are prescribed as constraints in the optimization; their specific numerical values are design choices that affect the resulting geometries.

axioms (1)

domain assumption The elastomeric material obeys a porohyperelastic constitutive law under large deformations
Invoked by the density-based topology optimization framework to model actuator inflation.

pith-pipeline@v0.9.0 · 5636 in / 1220 out tokens · 34591 ms · 2026-05-20T04:38:34.576427+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

An existing density- and porohyperelasticity-based topology optimization framework was extended from 2D to 3D ... employing the theory of porohyperelasticity from [27] ... Neo-Hookean constitutive law
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean J_uniquely_calibrated_via_higher_derivative unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

maximize the bending response for a prescribed actuation pressure under two different allowable strain limits

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

34 extracted references · 34 canonical work pages

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[1] [1]

Ilievski, A

F. Ilievski, A. D. Mazzeo, R. F. Shepherd, X. Chen, G. M. Whitesides, Soft robotics for chemists, Angewandte Chemie International Edition 50 (8) (2011) 1890–1895

work page 2011

[2] [2]

Shintake, V

J. Shintake, V. Cacucciolo, D. Floreano, H. Shea, Soft robotic grippers, Advanced Materials 30 (29) (2018) 1707035

work page 2018

[3] [3]

S. Chen, Y. Cao, M. Sarparast, H. Yuan, L. Dong, X. Tan, C. Cao, Soft crawling robots: design, actuation, and locomotion, Advanced Materials Technologies 5 (2) (2020) 1900837

work page 2020

[4] [4]

Arleo, G

L. Arleo, G. Stano, G. Percoco, M. Cianchetti, I-support soft arm for assistance tasks: a new manufacturing approach based on 3D printing and characterization, Progress in Additive Manufacturing 6 (2) (2021) 243–256

work page 2021

[5] [5]

Polygerinos, Z

P. Polygerinos, Z. Wang, K. C. Galloway, R. J. Wood, C. J. Walsh, Soft robotic glove for combined assistance and at-home rehabilitation, Robotics and Autonomous Systems 73 (2015) 135–143

work page 2015

[6] [6]

Runciman, A

M. Runciman, A. Darzi, G. P. Mylonas, Soft robotics in minimally invasive surgery, Soft Robotics 6 (4) (2019) 423–443

work page 2019

[7] [7]

X. Hu, A. Chen, Y. Luo, C. Zhang, E. Zhang, Steerable catheters for minimally invasive surgery: a review and future directions, Computer Assisted Surgery 23 (1) (2018) 21–41. 18

work page 2018

[8] [8]

Umedachi, V

T. Umedachi, V. Vikas, B. Trimmer, Softworms: the design and control of non-pneumatic, 3D-printed, deformable robots, Bioinspiration & Biomimetics 11 (2) (2016) 025001

work page 2016

[9] [9]

D. Li, J. Li, P. Wu, G. Zhao, Q. Qu, X. Yu, Recent advances in electrically driven soft actuators across dimensional scales from 2D to 3D, Advanced Intelligent Systems 6 (2) (2024) 2300070

work page 2024

[10] [10]

H. Wang, Z. Zhu, H. Jin, R. Wei, L. Bi, W. Zhang, Magnetic soft robots: Design, actuation, and function, Journal of Alloys and Compounds 922 (2022) 166219

work page 2022

[11] [11]

Mosadegh, P

B. Mosadegh, P. Polygerinos, C. Keplinger, S. Wennstedt, R. F. Shepherd, U. Gupta, J. Shim, K. Bertoldi, C. J. Walsh, G. M. Whitesides, Pneumatic networks for soft robotics that actuate rapidly, Advanced Functional Materials 24 (15) (2014) 2163–2170

work page 2014

[12] [12]

Polygerinos, Z

P. Polygerinos, Z. Wang, J. T. Overvelde, K. C. Galloway, R. J. Wood, K. Bertoldi, C. J. Walsh, Modeling of soft fiber-reinforced bending actuators, IEEE Transactions on Robotics 31 (3) (2015) 778–789

work page 2015

[13] [13]

M. S. Xavier, C. D. Tawk, A. Zolfagharian, J. Pinskier, D. Howard, T. Young, J. Lai, S. M. Harrison, Y. K. Yong, M. Bodaghi, et al., Soft pneumatic actuators: A review of design, fabrication, modeling, sensing, control and applications, IEEE Access 10 (2022) 59442–59485

work page 2022

[14] [14]

S. Kim, C. Laschi, B. Trimmer, Soft robotics: a bioinspired evolution in robotics, Trends in Biotechnology 31 (5) (2013) 287–294

work page 2013

[15] [15]

Sarker, T

A. Sarker, T. Ul Islam, M. R. Islam, A review on recent trends of bioinspired soft robotics: actuators, control methods, materials selection, sensors, challenges, and future prospects, Advanced Intelligent Systems 7 (3) (2025) 2400414

work page 2025

[16] [16]

D. Guo, Z. Kang, Chamber layout design optimization of soft pneumatic robots, Smart Materials and Structures 29 (2) (2020) 025017

work page 2020

[17] [17]

F. Chen, Z. Song, S. Chen, G. Gu, X. Zhu, Morphological design for pneumatic soft actuators and robots with desired deformation behavior, IEEE Transactions on Robotics 39 (6) (2023) 4408–4428

work page 2023

[18] [18]

E. M. de Souza, E. C. N. Silva, Topology optimization applied to the design of actuators driven by pressure loads, Structural and Multidisciplinary Optimization 61 (5) (2020) 1763–1786

work page 2020

[19] [19]

Y. Lu, L. Tong, Optimal design and experimental validation of 3d printed soft pneumatic actuators, Smart Materials and Structures 31 (11) (2022) 115010

work page 2022

[20] [20]

J. C. Chi, C. H. Liu, Topology optimization of a soft pneumatic actuator considering design-dependent loads, IEEE/ASME Transactions on Mechatronics (2025)

work page 2025

[21] [21]

Kumar, J

P. Kumar, J. S. Frouws, M. Langelaar, Topology optimization of fluidic pressure-loaded structures and compliant mechanisms using the Darcy method, Structural and Multidis- ciplinary Optimization 61 (2020) 1637–1655

work page 2020

[22] [22]

Kumar, M

P. Kumar, M. Langelaar, On topology optimization of design-dependent pressure-loaded three-dimensional structures and compliant mechanisms, International Journal for Numer- ical Methods in Engineering 122 (9) (2021) 2205–2220. 19

work page 2021

[23] [23]

Kumar, C

P. Kumar, C. Prakash, J. Pinskier, D. Howard, M. Langelaar, Soft pneumatic grippers: Topology optimization, 3D-printing and experimental validation (2026).arXiv:2511. 19211

work page 2026

[24] [24]

Caasenbrood, A

B. Caasenbrood, A. Pogromsky, H. Nijmeijer, A computational design framework for pressure-driven soft robots through nonlinear topology optimization, in: 2020 3rd IEEE international conference on soft robotics (RoboSoft), IEEE, 2020, pp. 633–638

work page 2020

[25] [25]

Dalklint, M

A. Dalklint, M. Wallin, D. Tortorelli, Simultaneous shape and topology optimization of in- flatable soft robots, Computer Methods in Applied Mechanics and Engineering 420 (2024) 116751

work page 2024

[26] [26]

Mehta, K

S. Mehta, K. Poulios, Topology optimization of pneumatic soft actuators based on poro- hyperelasticity, Computer Methods in Applied Mechanics and Engineering 444 (2025) 118123

work page 2025

[27] [27]

Simon, M

B. Simon, M. Kaufmann, M. McAfee, A. Baldwin, Porohyperelastic theory and finite element models for soft tissues with application to arterial mechanics, Mechanics of Poroe- lastic Media (1996) 245–261

work page 1996

[28] [28]

G. L. Bluhm, O. Sigmund, K. Poulios, Internal contact modeling for finite strain topology optimization, Computational Mechanics 67 (2021) 1099–1114

work page 2021

[29] [29]

Stolpe, K

M. Stolpe, K. Svanberg, An alternative interpolation scheme for minimum compliance topology optimization, Structural and Multidisciplinary Optimization 22 (2001) 116–124

work page 2001

[30] [30]

J. Simo, R. L. Taylor, K. Pister, Variational and projection methods for the volume con- straint in finite deformation elasto-plasticity, Computer Methods in Applied Mechanics and Engineering 51 (1-3) (1985) 177–208

work page 1985

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