From b9e8665e094fb4e201086b4065147a47a0ce93ef Mon Sep 17 00:00:00 2001 From: Daniel Arndt Date: Sat, 7 Dec 2019 11:39:08 -0500 Subject: [PATCH] Typeset Lame correctly --- examples/step-18/doc/results.dox | 2 +- examples/step-18/step-18.cc | 16 ++++++++-------- examples/step-42/doc/intro.dox | 2 +- examples/step-42/step-42.cc | 3 ++- examples/step-44/doc/intro.dox | 2 +- examples/step-44/step-44.cc | 4 ++-- include/deal.II/differentiation/ad/ad_helpers.h | 2 +- include/deal.II/numerics/error_estimator.h | 4 ++-- 8 files changed, 18 insertions(+), 17 deletions(-) diff --git a/examples/step-18/doc/results.dox b/examples/step-18/doc/results.dox index 93b1c9db80..80a08a9cdb 100644 --- a/examples/step-18/doc/results.dox +++ b/examples/step-18/doc/results.dox @@ -463,7 +463,7 @@ Incompressibility is characterized by Poisson's ratio @f[ \nu = \frac{\lambda}{2(\lambda+\mu)}, @f] -where $\lambda,\mu$ are the Lam\'e constants of the material. +where $\lambda,\mu$ are the Lamé constants of the material. Physical constraints indicate that $-1\le \nu\le \frac 12$ (the condition also follows from mathematical stability considerations). If $\nu$ approaches $\frac 12$, then the material becomes incompressible. In that diff --git a/examples/step-18/step-18.cc b/examples/step-18/step-18.cc index 5175afacb8..638192dc2e 100644 --- a/examples/step-18/step-18.cc +++ b/examples/step-18/step-18.cc @@ -112,8 +112,8 @@ namespace Step18 // in the form $C_{ijkl} = \mu (\delta_{ik} \delta_{jl} + \delta_{il} // \delta_{jk}) + \lambda \delta_{ij} \delta_{kl}$. This tensor maps // symmetric tensor of rank 2 to symmetric tensors of rank 2. A function - // implementing its creation for given values of the Lame constants $\lambda$ - // and $\mu$ is straightforward: + // implementing its creation for given values of the Lamé constants + // $\lambda$ and $\mu$ is straightforward: template SymmetricTensor<4, dim> get_stress_strain_tensor(const double lambda, const double mu) @@ -134,11 +134,11 @@ namespace Step18 // tensor. Note that in more elaborate programs, this will probably be a // member variable of some class instead, or a function that returns the // stress-strain relationship depending on other input. For example in - // damage theory models, the Lame constants are considered a function of the - // prior stress/strain history of a point. Conversely, in plasticity the - // form of the stress-strain tensor is modified if the material has reached - // the yield stress in a certain point, and possibly also depending on its - // prior history. + // damage theory models, the Lamé constants are considered a function + // of the prior stress/strain history of a point. Conversely, in plasticity + // the form of the stress-strain tensor is modified if the material has + // reached the yield stress in a certain point, and possibly also depending on + // its prior history. // // In the present program, however, we assume that the material is // completely elastic and linear, and a constant stress-strain tensor is @@ -696,7 +696,7 @@ namespace Step18 // Now for the implementation of the main class. First, we initialize the // stress-strain tensor, which we have declared as a static const - // variable. We chose Lame constants that are appropriate for steel: + // variable. We chose Lamé constants that are appropriate for steel: template const SymmetricTensor<4, dim> TopLevel::stress_strain_tensor = get_stress_strain_tensor(/*lambda = */ 9.695e10, diff --git a/examples/step-42/doc/intro.dox b/examples/step-42/doc/intro.dox index 3baec04389..aaabb4fbc7 100644 --- a/examples/step-42/doc/intro.dox +++ b/examples/step-42/doc/intro.dox @@ -72,7 +72,7 @@ relationship between strain $\varepsilon(\mathbf u)=\frac{1}{2}\left(\nabla \mat the fourth-order compliance tensor $A$; $\varepsilon^p$ provides the plastic component of the strain to ensure that the stress does not exceed the yield stress. We will only consider isotropic -materials for which $A$ can be expressed in terms of the Lam\'e moduli +materials for which $A$ can be expressed in terms of the Lamé moduli $\lambda$ and $\mu$ or alternatively in terms of the bulk modulus $\kappa$ and $\mu$. The second equation is the force balance; we will here diff --git a/examples/step-42/step-42.cc b/examples/step-42/step-42.cc index 1633eb8fda..044b125f13 100644 --- a/examples/step-42/step-42.cc +++ b/examples/step-42/step-42.cc @@ -137,7 +137,8 @@ namespace Step42 // The constructor of the ConstitutiveLaw class sets the required material // parameter for our deformable body. Material parameters for elastic // isotropic media can be defined in a variety of ways, such as the pair $E, - // \nu$ (elastic modulus and Poisson's number), using the Lame parameters + // \nu$ (elastic modulus and Poisson's number), using the Lamé + // parameters // $\lambda,mu$ or several other commonly used conventions. Here, the // constructor takes a description of material parameters in the form of // $E,\nu$, but since this turns out to these are not the coefficients that diff --git a/examples/step-44/doc/intro.dox b/examples/step-44/doc/intro.dox index 9218481a30..95ce4fe00d 100644 --- a/examples/step-44/doc/intro.dox +++ b/examples/step-44/doc/intro.dox @@ -286,7 +286,7 @@ The Helmholtz free energy corresponding to a compressible bulk // modulus and $\lambda$ is Lame's first - // parameter. + // href="http://en.wikipedia.org/wiki/Lam%C3%A9_parameters">Lamé's + // first parameter. // // The following class will be used to characterize the material we work with, // and provides a central point that one would need to modify if one were to diff --git a/include/deal.II/differentiation/ad/ad_helpers.h b/include/deal.II/differentiation/ad/ad_helpers.h index a41e6c0b28..55c87fa82f 100644 --- a/include/deal.II/differentiation/ad/ad_helpers.h +++ b/include/deal.II/differentiation/ad/ad_helpers.h @@ -3011,7 +3011,7 @@ namespace Differentiation * // This example is sufficiently complex to warrant the use of AD to, * // at the very least, verify an unassisted implementation. * const double mu_e = 10; // Shear modulus - * const double lambda_e = 15; // Lame parameter + * const double lambda_e = 15; // Lamé parameter * const double mu_0 = 4*M_PI*1e-7; // Magnetic permeability constant * const double mu_r = 5; // Relative magnetic permeability * diff --git a/include/deal.II/numerics/error_estimator.h b/include/deal.II/numerics/error_estimator.h index e8be29c6a8..485b7bd526 100644 --- a/include/deal.II/numerics/error_estimator.h +++ b/include/deal.II/numerics/error_estimator.h @@ -157,8 +157,8 @@ namespace hp * finite element field and each component of the error estimator will then be * weighted by the respective component in this coefficient function. In the * other case, when all components have the same meaning (for example the - * displacements in Lame's equations of elasticity), you can specify a scalar - * coefficient which will then be used for all components. + * displacements in Lamé's equations of elasticity), you can specify a + * scalar coefficient which will then be used for all components. * * *

Boundary values

-- 2.39.5