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In this article, we present the port-Hamiltonian representation, thestructure preserving discretization and the resulting finite-dimensional statespace model of geometrically nonlinear mechanical systems based on a mixedfinite element formulation. This article focuses on St. Venant-Kirchhoffmaterials connecting the Green strain and the second Piola-Kirchhoff stresstensor in a linear relationship which allows a port-Hamiltonian representationby means of its co-energy (effort) variables. Due to treatment of bothDirichlet and Neumann boundary conditions in the appropriate variationalformulation, the resulting port-Hamiltonian state space model features both ofthem as explicit (control) inputs. Numerical experiments generated with FEniCSillustrate the properties of the resulting FE models.

Explicit port-Hamiltonian FEM models for geometrically nonlinear mechanical systems