index.md

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header	overlay_color overlay_filter overlay_image og_image cta_label cta_url caption #0a1428 0.35 /assets/images/index/microgen/tpms_cylinder.png /assets/images/index/microgen/tpms_cylinder.png Download https://github.com/3MAH/ Gyroid TPMS rendered with microgen
title	3MAH — Mechanics of Heterogeneous & Architectured Materials
description	Open-source scientific software for mechanics of materials and multiphysics. simcoon (constitutive modeling, micromechanics, UMAT), fedoo (nonlinear finite element analysis, periodic homogenization, PGD), and microgen (TPMS, lattices, polycrystals and microstructure meshing) in a single coherent workflow.
keywords	mechanics of materials computational mechanics constitutive modeling micromechanics finite element analysis nonlinear FEM periodic homogenization microstructure generation TPMS gyroid lattice structures polycrystal Voronoi tessellation plasticity hyperelasticity shape memory alloys composites Mori-Tanaka simcoon fedoo microgen Python C++ UMAT Abaqus open source
excerpt	Open-source scientific tools for the mechanics of materials and multiphysics: constitutive modeling, finite element analysis, and microstructure generation, in a single coherent workflow.
intro	excerpt The **3MAH** initiative brings together three complementary, interoperable open-source libraries: **simcoon** for constitutive modeling and micromechanics, **fedoo** for nonlinear finite element analysis, and **microgen** for microstructure generation and meshing. Together, they provide a complete pipeline from geometry to simulation for research in mechanics of heterogeneous and architectured materials.
simcoon_row	image_path alt title excerpt url btn_label btn_class /assets/images/logo_simcoon/simcoon_logo_text.png simcoon simcoon **Constitutive modeling and micromechanics** in C++ with Python bindings. Anisotropic elasticity, plasticity (isotropic, kinematic, Chaboche), viscoelasticity, hyperelasticity and phase transformation, with finite-strain support. https://3mah.github.io/simcoon-docs/ simcoon docs btn--primary image_path alt title excerpt url btn_label btn_class /assets/images/index/simcoon/simcoon_homog_mori_tanaka.png Mean-field homogenization Mean-field homogenization Effective properties of composites with **Mori-Tanaka** and self-consistent schemes, framed by Voigt and Reuss bounds and validated against experimental data. https://3mah.github.io/simcoon-docs/examples/heterogeneous/homogenization.html See example btn--primary image_path alt title excerpt url btn_label btn_class /assets/images/index/simcoon/simcoon_directional_stiffness.png Directional stiffness Analysis & identification Analyse **directional stiffness**, yield surfaces and cyclic response, then identify model parameters with hybrid genetic-gradient algorithms. https://3mah.github.io/simcoon-docs/examples/analysis/directional_stiffness.html See example btn--primary
fedoo_row	image_path alt title excerpt url btn_label btn_class /assets/images/logo_fedoo/fedoo_logo.png fedoo fedoo A **Python finite element solver** for nonlinear mechanics, with an emphasis on geometric and material nonlinearity, model reduction (PGD) and multiscale homogenization. https://3mah.github.io/fedoo-docs/ fedoo docs btn--primary image_path alt title excerpt url btn_label btn_class /assets/images/index/fedoo/fedoo_periodic_homog.png Periodic homogenization Periodic homogenization Apply **periodic boundary conditions** on representative volume elements to extract full anisotropic effective stiffness and nonlinear macroscopic response. https://3mah.github.io/fedoo-docs/examples/03-advanced/3D_periodic_BC_off_axis.html See example btn--primary image_path alt title excerpt url btn_label btn_class /assets/images/index/fedoo/fedoo_beam_lattice.png Beam and shell elements Beam, shell and solid elements From 2D plates with holes to 3D **beam lattices** and pressurised shells: a unified API for 1D, 2D and 3D structural analysis. https://3mah.github.io/fedoo-docs/ Read more btn--primary
fedoo_contact	image_path poster alt title excerpt url btn_label btn_class /assets/images/index/fedoo/fedoo_ipc_indentation.mp4 /assets/images/index/fedoo/fedoo_ipc_indentation.png Stiff disk progressively indenting a soft plate, von Mises stress field Contact with IPC Robust **incremental potential contact** (IPC) via the `ipctk` backend — barrier-method, intersection-free, **frictional or frictionless** contact for indentation, self-contact and lattice compression. The disk-on-plate example here is validated against the Hertzian half-space solution. https://3mah.github.io/fedoo-docs/ Read more btn--primary
microgen_morph	image_path alt title excerpt url btn_label btn_class /assets/images/index/microgen/microgen_morph.mp4 Continuous morphing through eleven TPMS surface families Continuous morphing between TPMS families Blend any two TPMS surface functions with a tanh weight to walk continuously through families: **gyroid → Schwarz P → Schwarz D → Neovius → Schoen IWP → Schoen FRD → Fischer-Koch S → PMY → honeycomb → Lidinoid → split P → gyroid**. The animated transition exposes the underlying surface-function arithmetic of microgen. https://3mah.github.io/microgen-docs/ Read more btn--primary
microgen_row	image_path alt title excerpt url btn_label btn_class /assets/images/logo_microgen/microgen_logo.png microgen microgen A **Python library for microstructure generation and meshing**: TPMS, lattices, polycrystals and hybrid architectures, exported to CAD or directly to periodic FE meshes. https://3mah.github.io/microgen-docs/ microgen docs btn--primary image_path alt title excerpt url btn_label btn_class /assets/images/index/microgen/gyroid_graded.png Graded TPMS Graded TPMS & lattices Generate **gyroids, Schwarz, Schoen** and other triply periodic minimal surfaces, with spatially graded thickness and mapping onto arbitrary CAD bodies. https://3mah.github.io/microgen-docs/ See example btn--primary image_path poster alt title excerpt url btn_label btn_class /assets/images/index/microgen/examples/voronoi_polycrystal.mp4 /assets/images/index/microgen/examples/voronoi_polycrystal.png Voronoi polycrystal grains assembling one by one Polycrystals & architectured cells **Voronoi** polycrystals, octet-truss lattices, honeycombs and hybrid architectures, ready for periodic homogenization in fedoo or Abaqus. https://3mah.github.io/microgen-docs/ Read more btn--primary
cta_row	title excerpt url btn_label btn_class Team Meet the researchers and labs behind 3MAH. /team/ About the team btn--inverse title excerpt url btn_label btn_class Gallery Explore simulations and renderings produced with the 3MAH stack. /gallery/ Open gallery btn--inverse

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simcoon — Constitutive modeling & micromechanics

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Parameter identification from cyclic experiments

Identify seven Chaboche parameters — initial yield σ_y, Voce isotropic hardening (Q, b) and two non-linear Armstrong-Frederick backstresses (C₁, D₁, C₂, D₂) — from three cyclic uniaxial tests at increasing strain amplitudes. simcoon's EPCHA UMAT is the forward model, driven through sim.solver; the new simcoon.identify module wraps SciPy's differential evolution with a key-based file-templating workflow that generalises to any optimiser or external simulator.

EPCHA UMAT · E = 140 GPa, ν = 0.3 (fixed) · 7 parameters identified · cost = NMSE-per-response, balanced across the three tests · optimiser: scipy.optimize.differential_evolution (popsize 15, maxiter 80, seed 42) · final cost ≈ 8 × 10⁻³.

fedoo — Nonlinear finite element analysis

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Nonlinear and finite-strain mechanics

Plastic buckling of a thin tube under axial compression — 2D axisymmetric model with updated-Lagrangian finite strain, self-contact, and a simcoon EPICP elasto-plastic UMAT. Line-search Newton with adaptive stiffness drives the tube from undeformed to fully folded in a single nonlinear solve.

Initial

Evolution

Final

E = 200 GPa · σ_y = 300 MPa · power-law isotropic hardening σ = σ_y + k·pm (k = 1000, m = 0.3) · 240 axial elements · 3D revolution from the axisymmetric solution · field shown: equivalent plastic strain p.

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microgen — Microstructure generation & meshing

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Graded and periodic meshes

microgen drives Gmsh and MMG from Python to deliver two complementary mesh styles for architectured materials: graded structures with spatially varying thickness, and seamlessly periodic unit cells ready for periodic-homogenisation BCs in fedoo or Abaqus.

Graded — tanh-graded gyroid, thickness varying along x.

Periodic — unit cell tiled 3 × 2, no seam visible.

Open CASCADE / CadQuery for geometry · Gmsh for the conforming triangulation · MMG for adaptive remeshing · exported as .vtk /.msh for fedoo, Abaqus and others.

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From microstructure to simulation

The same Kelvin (truncated-octahedron) unit cell is generated and meshed with microgen, exported as a conforming periodic mesh, then loaded directly into fedoo to run a periodic homogenization with simcoon constitutive models. One workflow, three libraries — geometry, mesh and simulation kept in lock-step.

Same Kelvin unit cell — left: periodic conforming mesh from microgen; right: periodic homogenization (shear E_YZ, σ_YZ field) in fedoo.

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