MatTO

MatTO optimizes structural density, magnetic particle fraction and remanent magnetization direction together, rather than choosing a geometry first and then a material. It is built on FEniCSx with adjoint objective derivatives, density filtering and projection, and an MMA optimizer.

The design variables and the energy density are exposed through a generic interface, so a new constitutive model becomes an input rather than a fork. Worked examples cover magnetorheological and magnetoactive elastomers and liquid-crystal elastomers under prescribed stimulus.

Developed with Ian Galloway; version 0.2.0 credits both authors. The restorative-beam design behind Ian Galloway et al. (2026) was produced with it.

Current limits. Sensitivity analysis does not yet support state-dependent constraints, and contact and phase-field constraints are future work. No coupled-field solve or 3D validation is claimed.