A data-driven approach to nonlinear elasticity

- The distance-minimizing data-driven method is extended for nonlinear elasticity.
- Physical constraints are enforced by the use of Lagrange multipliers.
- Insight into the algorithm and the implementation is provided.
- The proposed scheme is validated against several numerical convergence studies.

The so-called distance-minimizing data-driven computing method is extended to deal with boundary-value problems of continuum mechanics within the finite strain theory. In the merit of a data-driven model the solution process is carried out by using directly the experimental data instead of the conventional constitutive laws. Thus it bypasses the uncertainties in fabricating the stress-strain functional relationships from material data. Consequently, the mathematical formulation involves an optimization problem with equality constraints consisting of the equilibrium equations in continuum mechanics and the compatibility conditions on the displacement field. In the framework of finite element formulation the element tangent stiffness, the generalized internal force and the generalized external force can be computed, which renders it amenable to the implementation of finite element procedures. The proposed scheme is validated through the applications to continuum elements and convergence studies of the data-driven solution in regard to the interpolation order, the mesh size as well as the data size. The variational structure allows to recognize the overall pattern of the system of equations to be solved. This includes the structural tangent stiffness and the generalized force vectors.