This paper presents a method for frame-based finite element model in order to develop fast personalised cardiac electromechanical models. Its originality comes from the choice of the deformation model: it relies on a reduced number of degrees of freedom represented by affine transformations located at arbitrary control nodes over a tetrahedral mesh. This is motivated by the fact that cardiac motion can be well represented by such poly-affine transformations. The shape functions use then a geodesic distance over arbitrary Voronoï-like regions containing the control nodes. The high order integration of elastic energy density over the domain is performed at arbitrary integration points. This integration , which is associated to affine degrees of freedom, allows a lower computational cost while preserving a good accuracy for simple geometry. The method is validated on a cube under simple compression and preliminary results on simplified cardiac geometries are presented, reducing by a factor 100 the number of degrees of freedom.