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Murat Güven

Microstructure designer

Design a periodic microstructure for a target stiffness, or pick one of hundreds already optimized on the property map, then export it for cutting or printing.

Pick a target and press Run: material moves, step by step, until the cell meets it. Or open the property map and start from one of hundreds of finished cells.

Set a target and run the optimizer, or browse finished cells on the property map.

0.40
2.00

Converged at iteration 143

Objective

min⁡ρ  C12H−w (C11H+C22H)\min_{\rho}\;C^{\mathrm{H}}_{12}-w\,(C^{\mathrm{H}}_{11}+C^{\mathrm{H}}_{22})
subject toV≤0.40\text{subject to}\quad V\le 0.40

Homogenized stiffness

CHE=[0.086−0.0600.000−0.0600.0860.0000.0000.0000.003]\dfrac{C^{\mathrm{H}}}{E}=\left[\begin{array}{rrr}0.086 & -0.060 & \textcolor{#4F5D68}{0.000} \\ -0.060 & 0.086 & \textcolor{#4F5D68}{0.000} \\ \textcolor{#4F5D68}{0.000} & \textcolor{#4F5D68}{0.000} & \textcolor{#4F5D68}{0.003}\end{array}\right]

Properties

E1=0.044 EE_{1}=0.044\,E
G12=0.003 EG_{12}=0.003\,E
ν12=−0.70\nu_{12}=-0.70
κ=0.013 E=0.09 κHS\kappa=0.013\,E=0.09\,\kappa_{\mathrm{HS}}

Seed 316760

Export

Exports use the design on screen.

Panel: the cell tiled, with no frame. SVG and DXF hold cutting outlines; STL holds the undeformed solid in millimetres.

Panel 160 × 160 mm

Method

Energy-based homogenization of a periodic unit cell on a square mesh of bilinear elements, after Andreassen and Andreasen (2014). Base material E = 1, ν = 0.3, plane stress.

Densities follow SIMP (p = 3) with a density filter and a Heaviside projection that sharpens during the run; MMA updates the design under the volume constraint. The cell keeps the square’s symmetries, so it tiles in both directions.

The property map holds cells from the same solver, on a 48 × 48 mesh, run from random starts for each target at volume fractions 0.30, 0.40 and 0.50; only runs that converged to a crisp design in one piece are kept. Its vertical axis divides the stiffness E1E_{1} by its Voigt bound VEVE, so cells of different volume fractions compare on one scale; no cell can pass 1.

Because of those symmetries the stiffness is solved on a quarter of the cell. My paper combines the same pieces, SIMP, MMA and a domain reduced by symmetry, for nonlinear elastic microstructures; this tool runs the linear case.

My paperReferencesCode

Assumptions and limits

Linear elastic, small strains, plane stress; stiffness in units of the base material’s E. A research demo, not a design check.

A link reproduces the settings. Another browser engine can end a run in a slightly different design.

The map shows what this optimizer found from those starts, not the limits of what is possible.

Cutting files trace density 0.5 after light smoothing. Check the thinnest features against your cutter’s kerf before cutting.

Cite

@software{guven_unit_cell,
  author = {Güven, Murat},
  title  = {Microstructure designer},
  year   = {2026},
  url    = {https://likemaestro.github.io/tools/unit-cell}
}

References

  1. Andreassen, E., & Andreasen, C. S. (2014). How to determine composite material properties using numerical homogenization. Computational Materials Science, 83, 488–495. doi:10.1016/j.commatsci.2013.09.006
  2. Bendsøe, M. P. (1989). Optimal shape design as a material distribution problem. Structural Optimization, 1(4), 193–202. doi:10.1007/BF01650949
  3. Bruns, T. E., & Tortorelli, D. A. (2001). Topology optimization of non-linear elastic structures and compliant mechanisms. Computer Methods in Applied Mechanics and Engineering, 190(26–27), 3443–3459. doi:10.1016/S0045-7825(00)00278-4
  4. Güven, M., & Özdemir, İ. (2026). Topology optimization of nonlinear elastic micro-structures by a domain reduction technique. Finite Elements in Analysis and Design, 260, Article 104599. doi:10.1016/j.finel.2026.104599
  5. Hashin, Z., & Shtrikman, S. (1963). A variational approach to the theory of the elastic behaviour of multiphase materials. Journal of the Mechanics and Physics of Solids, 11(2), 127–140. doi:10.1016/0022-5096(63)90060-7
  6. Svanberg, K. (1987). The method of moving asymptotes—a new method for structural optimization. International Journal for Numerical Methods in Engineering, 24(2), 359–373. doi:10.1002/nme.1620240207
  7. Voigt, W. (1889). Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper. Annalen der Physik, 274(12), 573–587. doi:10.1002/andp.18892741206
  8. Wang, F., Lazarov, B. S., & Sigmund, O. (2011). On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization, 43(6), 767–784. doi:10.1007/s00158-010-0602-y