From ff840d73dd2858404c455014a997b51b8eef0c4f Mon Sep 17 00:00:00 2001 From: wolf Date: Wed, 25 May 2005 16:03:24 +0000 Subject: [PATCH] Add some more documentation. git-svn-id: https://svn.dealii.org/trunk@10742 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/base/include/base/symmetric_tensor.h | 19 +++++++++++++++---- 1 file changed, 15 insertions(+), 4 deletions(-) diff --git a/deal.II/base/include/base/symmetric_tensor.h b/deal.II/base/include/base/symmetric_tensor.h index 3031dbf247..60fc732ed1 100644 --- a/deal.II/base/include/base/symmetric_tensor.h +++ b/deal.II/base/include/base/symmetric_tensor.h @@ -539,10 +539,21 @@ namespace internal * example for the 3x3x3x3 tensors of rank 4, only 36 instead of the full 81 * entries have to be stored. * - * Tensors of rank 4 are considered symmetric if they are operators mapping - * symmetric rank-2 tensors onto symmetric rank-2 tensors. This entails - * certain symmetry properties on the elements in their 4-dimensional index - * space. + * While the definition of a symmetric rank-2 tensor is obvious, + * tensors of rank 4 are considered symmetric if they are operators + * mapping symmetric rank-2 tensors onto symmetric rank-2 + * tensors. This entails certain symmetry properties on the elements + * in their 4-dimensional index space, in particular that + * Cijkl=Cjikl=Cijlk. However, + * it does not imply the relation + * Cijkl=Cklij. Consequently, symmetric + * tensors of rank 4 as understood here are only tensors that map + * symmetric tensors onto symmetric tensors, but they do not + * necessarily induce a symmetric scalar product a:C:b=b:C:a + * or even a positive (semi-)definite form a:C:a, where + * a,b are symmetric rank-2 tensors and the colon indicates + * the common double-index contraction that acts as a product for + * symmetric tensors. * * Symmetric tensors are most often used in structural and fluid mechanics, * where strains and stresses are usually symmetric tensors, and the -- 2.39.5