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Updated FEBio User Manual and Theory Manual
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Modified "front" and "back" shell faces to "top" and "bottom". Described plot variables "shell top/bottom stress/strain" and "shell top/bottom nodal stress/strain"
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gateshian committed Dec 12, 2024
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47 changes: 45 additions & 2 deletions Documentation/FEBio3.bib
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@@ -1,7 +1,7 @@
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% https://bibdesk.sourceforge.io/
%% Created for Gerard Ateshian at 2024-08-29 05:59:31 -0400
%% Created for Gerard Ateshian at 2024-12-12 16:41:35 -0500
%% Saved with string encoding Unicode (UTF-8)
Expand All @@ -11,6 +11,49 @@ @comment{jabref-meta:



@article{Coleman61,
author = {Coleman, Bernard D and Noll, Walter},
date-added = {2024-12-12 16:34:44 -0500},
date-modified = {2024-12-12 16:35:00 -0500},
journal = {Reviews of modern physics},
number = {2},
pages = {239},
publisher = {APS},
title = {Foundations of linear viscoelasticity},
volume = {33},
year = {1961}}

@book{Bland16,
author = {Bland, David Russell},
date-added = {2024-12-12 16:33:12 -0500},
date-modified = {2024-12-12 16:33:20 -0500},
publisher = {Courier Dover Publications},
title = {The theory of linear viscoelasticity},
year = {2016}}

@article{Brinkman49,
author = {Brinkman, Hendrik C},
date-added = {2024-12-12 16:28:33 -0500},
date-modified = {2024-12-12 16:28:42 -0500},
journal = {Flow, Turbulence and Combustion},
number = {1},
pages = {27--34},
publisher = {Springer},
title = {A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles},
volume = {1},
year = {1949}}

@article{Bowen69,
author = {Bowen, Ray M},
date-added = {2024-12-12 16:24:02 -0500},
date-modified = {2024-12-12 16:24:50 -0500},
journal = {Archive for Rational Mechanics and Analysis},
pages = {97--127},
publisher = {Springer-Verlag},
title = {The thermochemistry of a reacting mixture of elastic materials with diffusion},
volume = {34},
year = {1969}}

@article{Mullender94,
abstract = {Although the capacity of bone to adapt to functional mechanical requirements has been known for more than a century, it is still unclear how the bone adaptation processes are regulated. We hypothesize that osteocytes are sensitive to mechanical loading and control the regulation of bone mass in their environment. Recently, simulation models of such a process were developed, using the finite element method. It was discovered that these models produce discontinuous structures, not unlike trabecular bone. However, it was also found that severe discontinuities violate the continuum assumption underlying the finite element method and that the solutions were element mesh dependent. We have developed a simulation model (which is physiologically and mechanically more consistent) which maintains the self-organizational characteristics but does not produce these discontinuities. This was accomplished by separating the sensor density and range of action from the mesh. The results clearly show that predicted trabecular morphology, i.e. sizes and branching of struts, depend on the actual relationship between local load, sensor density and range of influence. We believe that the model is suitable to study the relationship between trabecular morphology and load and can also explain adaptation of morphology, in the sense of 'Wolff's law'.},
author = {Mullender, M G and Huiskes, R and Weinans, H},
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80 changes: 38 additions & 42 deletions Documentation/FEBio_Theory_Manual.lyx
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Expand Up @@ -5617,7 +5617,7 @@ where
\end_inset

When eigenvalues coincide,
L'Hospital's rule may be used to evalue the coefficient in the last term,
L'Hospital's rule may be used to evaluate the coefficient in the last term,

\begin_inset Formula
\begin{equation}
Expand Down Expand Up @@ -6007,7 +6007,7 @@ nolink "false"

can vary arbitrarily when enforcing the entropy inequality.
Instead,
we introduce the incompressbility constraint of eq.
we introduce the incompressibility constraint of eq.
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:incompressibility-redux"
Expand Down Expand Up @@ -8852,7 +8852,7 @@ apparent mass density
Following
\begin_inset CommandInset citation
LatexCommand citep
key "Bowen69,Ateshian07"
key "Bowen69,Ateshian07b"
literal "false"

\end_inset
Expand Down Expand Up @@ -13418,7 +13418,7 @@ nolink "false"
The complete theoretical framework for such materials can be found in
\begin_inset CommandInset citation
LatexCommand citep
key "Shim21a"
key "Shim22"
literal "false"

\end_inset
Expand Down Expand Up @@ -13733,7 +13733,7 @@ where
as shown in our earlier formulation of computational fluid dynamics
\begin_inset CommandInset citation
LatexCommand citep
key "Ateshian2018"
key "Ateshian18"
literal "false"

\end_inset
Expand Down Expand Up @@ -13900,7 +13900,7 @@ nolink "false"
)
\begin_inset CommandInset citation
LatexCommand citep
key "Ateshian2011,Ateshian2013,Shim2019"
key "Ateshian12,Ateshian13,Shim19"
literal "true"

\end_inset
Expand Down Expand Up @@ -13974,7 +13974,7 @@ In this expression,
Based on the constitutive assumptions of our hybrid biphasic formulation
\begin_inset CommandInset citation
LatexCommand citep
key "Shim21a"
key "Shim22"
literal "false"

\end_inset
Expand Down Expand Up @@ -14196,7 +14196,7 @@ Jump conditions on the axioms of mass,
The full set of jump conditions for a hybrid biphasic material were derived in our recent study for the constitutive assumptions adopted in this formulation
\begin_inset CommandInset citation
LatexCommand citep
key "Shim21a"
key "Shim22"
literal "false"

\end_inset
Expand Down Expand Up @@ -14369,7 +14369,7 @@ nolink "false"

\begin_inset CommandInset citation
LatexCommand citep
key "Hou1989"
key "Hou89"
literal "false"

\end_inset
Expand Down Expand Up @@ -14746,7 +14746,7 @@ We model the domain
Unlike the standard (Darcy flow through a porous-deformable) multiphasic domain
\begin_inset CommandInset citation
LatexCommand citep
key "Ateshian2007,Ateshian13,Ateshian14"
key "Ateshian07b,Ateshian13,Ateshian14"
literal "false"

\end_inset
Expand Down Expand Up @@ -14987,8 +14987,8 @@ where

relative to an ideal solution
\begin_inset CommandInset citation
LatexCommand cite
key "Ogston1961,Laurent1964"
LatexCommand citep
key "Ogston61,Laurent63"
literal "false"

\end_inset
Expand Down Expand Up @@ -15583,7 +15583,7 @@ nolink "false"

\begin_inset CommandInset citation
LatexCommand citep
key "Ateshian2014"
key "Ateshian14"
literal "false"

\end_inset
Expand Down Expand Up @@ -15704,7 +15704,7 @@ nolink "false"

\begin_inset CommandInset ref
LatexCommand ref
reference "subsec:Salt-Dissociation-CFDSol"
reference "sec:Chemical-Reactions"
plural "false"
caps "false"
noprefix "false"
Expand All @@ -15720,7 +15720,7 @@ nolink "false"
can be determined as described in the previous standard multiphasic solver
\begin_inset CommandInset citation
LatexCommand citep
key "Ateshian2013,Ateshian2014"
key "Ateshian13,Ateshian14"
literal "false"

\end_inset
Expand Down Expand Up @@ -25904,7 +25904,7 @@ nolink "false"
)
\begin_inset CommandInset citation
LatexCommand citep
key "Ateshian2018"
key "Ateshian18"
literal "true"

\end_inset
Expand Down Expand Up @@ -25967,8 +25967,8 @@ where

in this case) is at the current time step
\begin_inset CommandInset citation
LatexCommand cite
key "Jansen2000a"
LatexCommand citep
key "Jansen00"
literal "true"

\end_inset
Expand Down Expand Up @@ -26828,7 +26828,7 @@ nolink "false"
The virtual work statement for a Galerkin finite element formulation
\begin_inset CommandInset citation
LatexCommand citep
key "Bonet2008"
key "Bonet97"
literal "true"

\end_inset
Expand Down Expand Up @@ -33315,9 +33315,9 @@ Starting with FEBio 2.6,
two shell formulations have become available:
The original formulation,
where nodes are located at the mid-surface through the thickness of the shell,
and a new formulation where nodes are located on the front face of the shell.
and a new formulation where nodes are located on the top face of the shell.
The original formulation uses nodal displacements and directors as degrees of freedom;
the new formulation uses front and back face nodal displacements.
the new formulation uses top and bottom face nodal displacements.
The new formulation is designed to properly accommodate shells attached to the surface of a solid element,
or shells sandwiched between two solid elements,
with minimal alterations to the rest of the code.
Expand Down Expand Up @@ -33969,7 +33969,7 @@ Different shell elements available in FEBio.
\end_layout

\begin_layout Subsection
Shells with front and back face nodal displacements
Shells with top and bottom face nodal displacements
\begin_inset CommandInset label
LatexCommand label
name "subsec:Shells-front-back"
Expand All @@ -33985,15 +33985,15 @@ We create a shell formulation by reducing a 3D element interpolation which is li
\end_inset

.
The nodal positions at the back of the shell (
The nodal positions at the bottom of the shell (
\begin_inset Formula $\xi_{3}=-1$
\end_inset

) are denoted by
\begin_inset Formula $\mathbf{y}_{a}$
\end_inset

and those on the front of the shell (
and those on the top of the shell (
\begin_inset Formula $\xi_{3}=+1$
\end_inset

Expand Down Expand Up @@ -34231,22 +34231,22 @@ For this formulation,

.
Similarly,
prescribed pressures and contact pressures act on the shell front face.
prescribed pressures and contact pressures act on the shell top face.
\end_layout

\begin_layout Standard
When a shell element is sandwiched between two solid elements,
the nodal displacements of the solid element facing the shell back face are set to coincide with the shell back-face nodal displacements
the nodal displacements of the solid element facing the shell bottom face are set to coincide with the shell back-face nodal displacements
\begin_inset Formula $\mathbf{w}_{b}$
\end_inset

,
whereas the nodal displacements of the solid element facing the shell front face are set to coincide with the shell front-face nodal displacements
whereas the nodal displacements of the solid element facing the shell top face are set to coincide with the shell front-face nodal displacements
\begin_inset Formula $\mathbf{u}_{a}$
\end_inset

.
If the shell thickness exceeds the thickness of the solid element connected to its back face,
If the shell thickness exceeds the thickness of the solid element connected to its bottom face,
results become unpredictable.
\end_layout

Expand Down Expand Up @@ -34418,7 +34418,7 @@ External work of surface forces
\end_layout

\begin_layout Standard
We assume that surface forces are applied on the shell front face (
We assume that surface forces are applied on the shell top face (
\begin_inset Formula $\xi_{3}=+1$
\end_inset

Expand All @@ -34443,7 +34443,7 @@ Shell on top of solid element

\begin_layout Standard
When a shell is coincident with the face of a solid element,
we assume that the face of the solid element coincides with the back face (
we assume that the face of the solid element coincides with the bottom face (
\begin_inset Formula $\xi_{3}=-1$
\end_inset

Expand Down Expand Up @@ -34480,7 +34480,7 @@ When a shell is sandwiched between two solid elements,
\begin_inset Formula $\mathbf{u}_{b}$
\end_inset

displacements facing the back of the shell to those of the shell
displacements facing the bottom of the shell to those of the shell
\begin_inset Formula $\mathbf{w}_{b}$
\end_inset

Expand All @@ -34489,7 +34489,7 @@ When a shell is sandwiched between two solid elements,
\begin_inset Formula $\mathbf{u}_{b}$
\end_inset

displacements facing the front of the shell remain unchanged;
displacements facing the top of the shell remain unchanged;
they will coincide with those of the corresponding solid element nodes.
\end_layout

Expand All @@ -34500,7 +34500,7 @@ Rigid-Shell Interface
\begin_layout Standard
When the node of a deformable shell belongs to a rigid body,
we need to substitute the nodal degrees of freedom with the rigid body degrees of freedom.
The positions of the shell front face and back face nodes are
The positions of the shell top face and bottom face nodes are
\begin_inset Formula
\begin{equation}
\begin{aligned}\mathbf{x}_{b} & =\mathbf{r}+\boldsymbol{\Lambda}\cdot\left(\mathbf{X}_{b}-\mathbf{R}\right)\equiv\mathbf{r}+\mathbf{a}_{b}\\
Expand Down Expand Up @@ -41369,7 +41369,7 @@ nolink "false"
often called a Voigt model in linear viscoelasticity
\begin_inset CommandInset citation
LatexCommand citep
key "Bland60,Coleman61"
key "Bland16,Coleman61"
literal "false"

\end_inset
Expand Down Expand Up @@ -50627,7 +50627,7 @@ nolink "false"
For second-order systems these parameters may be evaluated from
\begin_inset CommandInset citation
LatexCommand citep
key "Bazilevs2008"
key "Bazilevs08"
literal "true"

\end_inset
Expand Down Expand Up @@ -55975,7 +55975,7 @@ literal "true"
and reference
\begin_inset CommandInset citation
LatexCommand citep
key "Zimmerman21a"
key "Zimmerman22"
literal "false"

\end_inset
Expand All @@ -55984,7 +55984,7 @@ literal "false"
The presentation here follows that of
\begin_inset CommandInset citation
LatexCommand citep
key "Zimmerman21a"
key "Zimmerman22"
literal "false"

\end_inset
Expand Down Expand Up @@ -65783,11 +65783,7 @@ The position of a node shared by any number of deformable finite elements is den
\end_inset

by
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq34"
nolink "false"

\begin_inset Formula $\mathbf{x}=\mathbf{X}+\mathbf{u}$
\end_inset

;
Expand Down
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