[image: grafik.png]
[image: grafik.png]
The only place I use Dev_P is to compute the above double contractions ('P'
in the above is what dealii returns as Dev_P)
As you can see, the fourth order tangent C_bar consists of outer products
of second order symmetric tensors:
boldsymbol 'I' is the second order unit tensor, C_bar is a symmetric second
order tensor, and blackboard 'I' is the general fourth order unit tensor,
the deltas are just scalars.In my opinion, the double contractions 'P : outer_product(C_bar, C_bar)' and 'P : I' produce different results if the fourth order symmetric unit tensor 'S' is used to define 'P' . The same holds also for doing the double contractions with P_T. Correct? Best Simon Am Mo., 8. Aug. 2022 um 12:54 Uhr schrieb Wolfgang Bangerth < [email protected]>: > On 8/7/22 06:00, Simon wrote: > > > > the fourth-order referential deviatoric tensor as returned by > > Physics::Elasticity::StandardTensors > > < > https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.dealii.org%2Fcurrent%2Fdoxygen%2Fdeal.II%2FclassPhysics_1_1Elasticity_1_1StandardTensors.html&data=05%7C01%7CWolfgang.Bangerth%40colostate.edu%7Cc7d0b41aa97a4f5bbf6a08da786c79b6%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C637954704552090273%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=u9Z1RfLeZdT2vdeD7%2BNYIXWA8h%2Bkvtdre4KIewAI0ws%3D&reserved=0>< > > > dim >::Dev_P > > includes the fourth-order referential/spatial unit *symmetric* tensor > > Physics::Elasticity::StandardTensors > > < > https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.dealii.org%2Fcurrent%2Fdoxygen%2Fdeal.II%2FclassPhysics_1_1Elasticity_1_1StandardTensors.html&data=05%7C01%7CWolfgang.Bangerth%40colostate.edu%7Cc7d0b41aa97a4f5bbf6a08da786c79b6%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C637954704552090273%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=u9Z1RfLeZdT2vdeD7%2BNYIXWA8h%2Bkvtdre4KIewAI0ws%3D&reserved=0>< > > > dim >::S = identity_tensor > > < > https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.dealii.org%2Fcurrent%2Fdoxygen%2Fdeal.II%2Fsymmetric__tensor_8h.html%23ab3e890348aa219805e84f7d367e098c3&data=05%7C01%7CWolfgang.Bangerth%40colostate.edu%7Cc7d0b41aa97a4f5bbf6a08da786c79b6%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C637954704552090273%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=3bQQR2Em7YyxuQuohp19IsBWntxKehAhRzin%2F0GFlBs%3D&reserved=0 > ><dim>(). > > > > In the literature, for instance G. A. Holzapfel: "Nonlinear solid > mechanics. A > > Continuum Approach for Engineering" (2007), > > however, the general fourth-order unit tensor > > I_{ijkl} = delta_{ik} delta_{jl} is used to compute Dev_P. > > > > I implemented a hyperelastic material model with a volumetric / > isochoric > > split of the strain energy function and it only converges when using 'S' > - as > > dealii does it. Using the general fourth-order unit tensor to define > Dev_P, > > my solver does not converge at all. > > > > Is it neccessary to use 'S' due to the way dealii stores and accesses > the > > elements of symmetric tensors? > > The question is what you apply I or S to. If you apply them to symmetric > rank-2 tensors, then they are the same. If you apply them to non-symmetric > tensors, then they are not. > > Best > W. > > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: [email protected] > www: http://www.math.colostate.edu/~bangerth/ > > -- > The deal.II project is located at http://www.dealii.org/ > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > --- > You received this message because you are subscribed to a topic in the > Google Groups "deal.II User Group" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/dealii/tHMjlrUqMYI/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/9c3d5b70-7fe0-9684-0f7e-c608baf72c50%40colostate.edu > . > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/CAM50jEvvyDyDO3aQepDSgkNdgm1qfH7xYgRJx1qJZmU4298CUQ%40mail.gmail.com.
