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README.md

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   <p align="center">Material Definition with Automatic Differentiation.</p>
 </p>
 
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 matADi is a 3.8+ Python package for the definition of a constitutive hyperelastic material formulation by a strain energy density function. Both [gradient](https://en.wikipedia.org/wiki/Gradient) (stress) and [hessian](https://en.wikipedia.org/wiki/Hessian_matrix) (elasticity tensor) are carried out by [**Automatic Differentiation (AD)**](https://en.wikipedia.org/wiki/Automatic_differentiation) using [casADi](https://web.casadi.org/) [[1](https://doi.org/10.1007/s12532-018-0139-4)] as a backend. A high-level interface for hyperelastic materials based on the deformation gradient exists. Several isotropic hyperelastic material formulations like the Neo-Hookean or the Ogden model are included in the model library. Gradient and hessian methods allow input data with trailing axes which is especially useful for Python-based finite element modules, e.g. [scikit-fem](https://scikit-fem.readthedocs.io/en/latest/) or [FElupe](https://github.com/adtzlr/felupe). Mixed-field formulations suitable for nearly-incompressible material behavior are supported as well as single-field formulations based on the deformation gradient. A numerical lab is included to run, plot and analyze homogeneous uniaxial, equi-biaxial, planar shear and simple shear load cases.