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Assumed stress finite elements are known for their extraordinary good performance in the framework of linear elasticity. In this contribution we propose a mixed variational formulation of the Hellinger-Reissner type for hyperelasticity. A family of hexahedral shaped elements is considered with a classical trilinear interpolation of the displacements and different piecewise discontinuous interpolation schemes for the stresses. The performance and stability of the new elements are investigateddoi:10.1186/s40323-019-0133-z fatcat:y557osxmyrepjjwkzljbtjqe7u