Why do for some of the hyperelastic problems show better convergence trend with unsymmetric Newton Rapshon (NROPT,UNSYM) solver ? Does Mixed uP formulation result in unsymmetric stiffness matrix ?


March 17, 2023 at 9:00 amFAQParticipant
Mixed uP element formulation itself doesnâ€™t introduce unsymmetric stiffness matrix. The stress stiffening matrix is unsymmetric and pressure load stiffness matrix is also unsymmetric. Usually a procedure of symmetrizing the tangent stiffness matrix is invoked and then solved with symmetric Newton Rapshon (NROPT,FULL) solver. So when the contribution of stress stiffening and pressure load stiffness matrices are significant in resulting Consistent Tangent Stiffness Matrix for a problem, then NROPT,UNSYM shall lead to better convergence trend. But there is trade off. The inversion of an unsymmetric matrix takes longer and more memory to compute than a symmetric matrix, because we need to store the full matrix and not only the upper triangular half. Below two Ansys help theory manual links discuss this concept. (open Ansys help manual then Shift+Ctrl+D to paste this link) help/ans_thry/thy_geo2.html#geoconsistent (section : 3.3.8. Consistent Tangent Stiffness Matrix and Finite Rotation) help/ans_thry/thy_geo3.html#geopressure2 (section : 3.4.4. Pressure Load Stiffness

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