A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements. (English summary) Internat. J. Numer. Methods Engrg. 89 (2012), no. 6, 762–785.1097-0207 In this paper, the authors present an Eulerian formulation for large deformation hyperelasticity to address the shortcomings of the standard Lagrangian formulations in the presence of very large deformations. This approach allows one to model large deformations on a fixed mesh with the material moving relative to the mesh; in this case, the deformation gradient is transported to recover the deformation history at each point of the domain. The variational multiscale formulation for the transport equations improves accuracy and stability, and accelerates the convergence of the computational scheme. The formulation is accurate, stable and converges for compressible and nearly incompressible cases
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