From: mcbride Date: Thu, 16 Feb 2012 14:05:32 +0000 (+0000) Subject: changed definition of vol free energy to match standard X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=7d6a52532f842391417f7dc805b834ed64f606c7;p=dealii-svn.git changed definition of vol free energy to match standard git-svn-id: https://svn.dealii.org/trunk@25099 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-44/doc/intro.dox b/deal.II/examples/step-44/doc/intro.dox index ad84d560b9..572474a108 100644 --- a/deal.II/examples/step-44/doc/intro.dox +++ b/deal.II/examples/step-44/doc/intro.dox @@ -112,7 +112,7 @@ It is also symmetric and positive definite. The Green-Lagrange strain tensor is defined by @f[ \mathbf{E}:= \frac{1}{2}[\mathbf{C} - \mathbf{I} ] - = \underbrace{\frac{1}{2}[\textrm{Grad}^T\ \mathbf{U} + \textrm{Grad}\ mathbf{U}]}_{\boldsymbol{\varepsilon}} + = \underbrace{\frac{1}{2}[\textrm{Grad}^T \mathbf{U} + \textrm{Grad}\mathbf{U}]}_{\boldsymbol{\varepsilon}} + \frac{1}{2}[\textrm{Grad}^T\ \mathbf{U}][\textrm{Grad}\ \mathbf{U}] \, , @f] If the assumption of infinitesimal deformations is valid, then the second term @@ -242,7 +242,7 @@ The Helmholtz free energy corresponding to a compressible bulk modulus and // $\lambda$ is Lame's first parameter. template @@ -645,7 +645,7 @@ public: // Derivative of the volumetric free energy wrt $\widetilde{J}$ // return $\frac{\partial \Psi_{\text{vol}}(\widetilde{J})}{\partial \widetilde{J}}$ double get_dPsi_vol_dJ(void) const { - return kappa * (J_tilde - 1.0 / J_tilde); + return (kappa / 2.0) * (J_tilde - 1.0 / J_tilde); } // Second derivative of the volumetric free energy wrt $\widetilde{J}$ @@ -654,7 +654,7 @@ public: // We calculate // $\frac{\partial^2 \Psi_{\textrm{vol}}(\widetilde{J})}{\partial \widetilde{J} \partial \widetilde{J}}$ double get_d2Psi_vol_dJ2(void) const { - return kappa * (1.0 + 1.0 / (J_tilde * J_tilde)); + return ( (kappa / 2.0) * (1.0 + 1.0 / (J_tilde * J_tilde))); } // Return various data that we choose to store with the material