Stabileo Research

Computational-mechanics papers you can run. We reproduce the authors’ code, re-implement the method on Stabileo’s engine, validate it against that reference, and let you run it here with your own parameters, in Stabileo’s viewer.

Research, not a design tool. Nothing here is an engineering result; agreement with a reference code is not a certification. Contributions: CONTRIBUTING.md.

Run it

• 
  Fracture and damageNumerically validated

  Phase-field fracture of a notched plate

  Pull a notched plate apart and watch an AT2 phase-field crack form and run, solved in your browser and checked step by step against the author’s code.

  Less than 500 lines self-contained Python finite element implementation of the phase-field method for fracture mechanics. Nathan Shauer, Advances in Engineering Software, 2025.

  Read & run Paper ↗ Code ↗

Coming next

• in progress
  Topology optimization of an MBB beam
  SIMP with density filter and optimality criteria, against the 88-line reference results
• in progress
  Mechanics of spring networks
  Truss networks against the paper’s published numbers (no reference code)

On our list: papers we plan to reproduce

• Metamaterials · 2026Proposed

  Predicting the mechanical properties of spring networks

  Doron Grossman, Arezki Boudaoud · Physical Review Research · doi:10.1103/17sg-gzhl

  Derives the elastic continuum model of an arbitrary network of Hookean springs from its geometry and topology alone, including the nonaffine displacements, and checks it against simulations of crystalline and disordered networks.

  Summary in our words, from the abstract.

• Metamaterials · 2026Proposed

  Snapping and switching of elastic arches with patterned preferred curvature

  Michał Zmyślony, Ammar Khan, John S. Biggins · Physical Review Research · doi:10.1103/56f8-8gsx

  Elastica theory and photomechanical experiments on an arch whose preferred curvature varies along its length and in time. A shallow-arch theory projects the curvature pattern onto Euler buckling modes; overlap with the fundamental mode makes the arch snap, other patterns give a continuous switch to a higher mode. Patterns with the largest energy release and the lowest threshold are found, and the same control applies to passive pre-curved arches loaded at the boundaries.

  Summary in our words, from the abstract.

• Metamaterials · 2026Proposed

  Controlling the snap-through behavior of an elastica strip by cuts

  Eszter Fehér · European Journal of Mechanics - A/Solids · doi:10.1016/j.euromechsol.2026.106217

• Optimization · 2026Proposed

  Differentiable force density method for the design of lightweight structures

  Rafael Pastrana, Deniz Oktay, Kai-Uwe Bletzinger et al. · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2026.118783

  The JAX FDM library computes equilibrium shapes of pin-jointed bar systems with the force density method and solves inverse design problems by tuning force densities, loads and support positions with gradient-based optimization against goals and constraints; written in JAX, so the simulation is differentiable and JIT-compiled.

  Summary in our words, from the code’s README.

  Code: arpastrana/jax_fdm (MIT)

• Optimization · 2026Proposed

  Topology and geometry optimization of grid-shells incorporating design-dependent self-weight loading

  Helen E. Fairclough, Karol Bołbotowski, Linwei He et al. · Computers & Structures · doi:10.1016/j.compstruc.2025.107997

• Optimization · 2025Proposed

  Optimization of the Initial Post‐Buckling Response of Trusses and Frames by an Asymptotic Approach

  Federico Ferrari, Ole Sigmund · International Journal for Numerical Methods in Engineering · doi:10.1002/nme.70082

  Uses Koiter's asymptotic post-buckling expansion in sizing and topology optimization of trusses and frames. Constraining the first two asymptotic coefficients (initial post-buckling slope and curvature) shapes the post-buckling response and lowers imperfection sensitivity, and the same expansion approximates the nonlinear response so that measures such as end-compliance can be optimized.

  Summary in our words, from the abstract.

• Optimization · 2023Proposed

  A framework for structural shape optimization based on automatic differentiation, the adjoint method and accelerated linear algebra

  Gaoyuan Wu · Structural and Multidisciplinary Optimization · doi:10.1007/s00158-023-03601-0

  Code: GaoyuanWu/JaxSSO (MIT)

• Optimization · 2022Proposed

  On benchmarking and good scientific practise in topology optimization

  Ole Sigmund · Structural and Multidisciplinary Optimization · doi:10.1007/s00158-022-03427-2

• Optimization · 2017Proposed

  Giga-voxel computational morphogenesis for structural design

  Niels Aage, Erik Andreassen, Boyan S. Lazarov et al. · Nature · doi:10.1038/nature23911

• Metamaterials · 2014Proposed

  Ultralight, ultrastiff mechanical metamaterials

  Xiaoyu Zheng, Howon Lee, Todd H. Weisgraber et al. · Science · doi:10.1126/science.1252291

  Octet-truss microlattices made by projection microstereolithography from polymers, metals and ceramics. Because their struts carry load axially instead of bending, the materials are very stiff and strong for their low density.

  Summary in our words, from the abstract.

• Metamaterials · 2013Proposed

  Topological boundary modes in isostatic lattices

  C. L. Kane, T. C. Lubensky · Nature Physics · doi:10.1038/nphys2835

• Optimization · 2010Proposed

  Efficient topology optimization in MATLAB using 88 lines of code

  Erik Andreassen, Anders Clausen, Mattias Schevenels et al. · Structural and Multidisciplinary Optimization · doi:10.1007/s00158-010-0594-7

• Seismic and dynamics · 2005Proposed

  Crowd synchrony on the Millennium Bridge

  Steven H. Strogatz, Daniel M. Abrams, Allan McRobie et al. · Nature · doi:10.1038/438043a

• Optimization · 2003Proposed

  Layout optimization of large-scale pin-jointed frames

  Matthew Gilbert, Andrew Tyas · Engineering Computations · doi:10.1108/02644400310503017

  Ground-structure layout optimization of trusses is limited by the number of potential members. The paper presents an iterative member-adding method, built on linear-programming column generation, that starts from a sparsely connected ground structure and adds members as needed until the provably optimal layout is reached, handling problems with very large numbers of potential members.

  Summary in our words, from the abstract.

• Optimization · 1988Proposed

  Generating optimal topologies in structural design using a homogenization method

  Martin Philip Bendsøe, Noboru Kikuchi · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(88)90086-2

• Metamaterials · 1978Proposed

  Buckminster Fuller's “Tensegrity” structures and Clerk Maxwell's rules for the construction of stiff frames

  C.R. Calladine · International Journal of Solids and Structures · doi:10.1016/0020-7683(78)90052-5

• Optimization · 1974Proposed

  The force density method for form finding and computation of general networks

  H.-J. Schek · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(74)90045-0

• Shells and buckling · 1966Proposed

  The stone skeleton

  Jacques Heyman · International Journal of Solids and Structures · doi:10.1016/0020-7683(66)90018-7

• Numerical methods · 1956Proposed

  Stiffness and Deflection Analysis of Complex Structures

  M. J. TURNER, R. W. CLOUGH, H. C. MARTIN et al. · Journal of the Aeronautical Sciences · doi:10.2514/8.3664

• Optimization · 1904Proposed

  LVIII. The limits of economy of material in frame-structures

  A.G.M. Michell · The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science · doi:10.1080/14786440409463229

• Metamaterials · 1864Proposed

  L. On the calculation of the equilibrium and stiffness of frames

  J. Clerk Maxwell · The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science · doi:10.1080/14786446408643668

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