ABSTRACT

ABSTRACT: This contribution is concerned with the impact of configurational mechanics on computational mechanics. To this end we derive a generic hyperelastic ALE formulation embedded in a variational framework. The governing equations follow straightforwardly from the Dirichlet principle for conservative mechanical systems. Thereby, the key idea is the reformulation of the total variation of the potential energy at fixed referential coordinates in terms of its variation at fixed material and at fixed spatial coordinates. The corresponding Euler-Lagrange equations define the spatial and the material motion version of the balance of linear momentum, i.e. the balance of spatial and material forces, in a consistent dual format. In the discretised setting, the governing equations are solved simultaneously rendering the spatial and the material configuration which minimise the overall potential energy of the system. The remeshing strategy of this FE formulation is thus no longer user-defined but objective in the sense of energy optimisation. As the governing equations are derived from a potential, they are inherently symmetric, both in the continuous case and in the discrete case. The characteristic features of the derived approach will be demonstrated by means of selected examples.