From: Daniel Arndt Date: Sun, 12 May 2019 16:17:28 +0000 (+0200) Subject: Revert #8082 X-Git-Tag: v9.1.0-rc1~46^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=7e0489428d287ccd787546624bb9fa1db0e52cf9;p=dealii.git Revert #8082 This reverts commit f6c96c520478d963cd9ebb6f4877d59e3ddb8b01. --- diff --git a/include/deal.II/base/symmetric_tensor.h b/include/deal.II/base/symmetric_tensor.h index ed2b550596..f164142472 100644 --- a/include/deal.II/base/symmetric_tensor.h +++ b/include/deal.II/base/symmetric_tensor.h @@ -31,15 +31,15 @@ DEAL_II_NAMESPACE_OPEN template class SymmetricTensor; -template +template SymmetricTensor<2, dim, Number> unit_symmetric_tensor(); -template +template SymmetricTensor<4, dim, Number> deviator_tensor(); -template +template SymmetricTensor<4, dim, Number> identity_tensor(); @@ -3310,6 +3310,23 @@ unit_symmetric_tensor() +/** + * Return a unit symmetric tensor of rank 2, i.e., the dim-by-dim identity + * matrix. This specialization of the function uses double as the + * data type for the elements. + * + * @relatesalso SymmetricTensor + * @author Wolfgang Bangerth, 2005 + */ +template +inline SymmetricTensor<2, dim> +unit_symmetric_tensor() +{ + return unit_symmetric_tensor(); +} + + + /** * Return the tensor of rank 4 that, when multiplied by a symmetric rank 2 * tensor t returns the deviator $\textrm{dev}\ t$. It is the @@ -3351,6 +3368,29 @@ deviator_tensor() +/** + * Return the tensor of rank 4 that, when multiplied by a symmetric rank 2 + * tensor t returns the deviator dev t. It is the operator + * representation of the linear deviator operator. + * + * For every tensor t, there holds the identity + * deviator(t)==deviator_tensor<dim>()*t, up to numerical + * round-off. The reason this operator representation is provided is that one + * sometimes needs to invert operators like identity_tensor<dim>() + + * delta_t*deviator_tensor<dim>() or similar. + * + * @relatesalso SymmetricTensor + * @author Wolfgang Bangerth, 2005 + */ +template +inline SymmetricTensor<4, dim> +deviator_tensor() +{ + return deviator_tensor(); +} + + + /** * Return the fourth-order symmetric identity tensor which maps symmetric * second-order tensors to themselves. @@ -3399,6 +3439,36 @@ identity_tensor() +/** + * Return the tensor of rank 4 that, when multiplied by a symmetric rank 2 + * tensor t returns the deviator dev t. It is the operator + * representation of the linear deviator operator. + * + * Note that this tensor, even though it is the identity, has a somewhat funny + * form, and in particular does not only consist of zeros and ones. For + * example, for dim=2, the identity tensor has all zero entries + * except for id[0][0][0][0]=id[1][1][1][1]=1 and + * id[0][1][0][1]=id[0][1][1][0]=id[1][0][0][1]=id[1][0][1][0]=1/2. + * To see why this factor of 1/2 is necessary, consider computing A=Id . + * B. For the element a_01 we have a_01=id_0100 b_00 + + * id_0111 b_11 + id_0101 b_01 + id_0110 b_10. On the other hand, we need + * to have a_01=b_01, and symmetry implies b_01=b_10, + * leading to a_01=(id_0101+id_0110) b_01, or, again by symmetry, + * id_0101=id_0110=1/2. Similar considerations hold for the three- + * dimensional case. + * + * @relatesalso SymmetricTensor + * @author Wolfgang Bangerth, 2005 + */ +template +inline SymmetricTensor<4, dim> +identity_tensor() +{ + return identity_tensor(); +} + + + /** * Invert a symmetric rank-2 tensor. *