From cb4ca7c409ba4b172ad7388a955c32347e9a6a0a Mon Sep 17 00:00:00 2001 From: Gerard Ateshian Date: Thu, 12 Dec 2024 16:42:56 -0500 Subject: [PATCH] Updated FEBio User Manual and Theory Manual 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" --- Documentation/FEBio3.bib | 47 ++++- Documentation/FEBio_Theory_Manual.lyx | 80 ++++---- Documentation/FEBio_User_Manual.lyx | 276 ++++++++++++++++++++++++-- 3 files changed, 341 insertions(+), 62 deletions(-) diff --git a/Documentation/FEBio3.bib b/Documentation/FEBio3.bib index c6214bd55..65c12dd92 100644 --- a/Documentation/FEBio3.bib +++ b/Documentation/FEBio3.bib @@ -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) @@ -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}, diff --git a/Documentation/FEBio_Theory_Manual.lyx b/Documentation/FEBio_Theory_Manual.lyx index e1437162b..af50ebf4a 100644 --- a/Documentation/FEBio_Theory_Manual.lyx +++ b/Documentation/FEBio_Theory_Manual.lyx @@ -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} @@ -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" @@ -8852,7 +8852,7 @@ apparent mass density Following \begin_inset CommandInset citation LatexCommand citep -key "Bowen69,Ateshian07" +key "Bowen69,Ateshian07b" literal "false" \end_inset @@ -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 @@ -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 @@ -13900,7 +13900,7 @@ nolink "false" ) \begin_inset CommandInset citation LatexCommand citep -key "Ateshian2011,Ateshian2013,Shim2019" +key "Ateshian12,Ateshian13,Shim19" literal "true" \end_inset @@ -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 @@ -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 @@ -14369,7 +14369,7 @@ nolink "false" \begin_inset CommandInset citation LatexCommand citep -key "Hou1989" +key "Hou89" literal "false" \end_inset @@ -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 @@ -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 @@ -15583,7 +15583,7 @@ nolink "false" \begin_inset CommandInset citation LatexCommand citep -key "Ateshian2014" +key "Ateshian14" literal "false" \end_inset @@ -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" @@ -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 @@ -25904,7 +25904,7 @@ nolink "false" ) \begin_inset CommandInset citation LatexCommand citep -key "Ateshian2018" +key "Ateshian18" literal "true" \end_inset @@ -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 @@ -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 @@ -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. @@ -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" @@ -33985,7 +33985,7 @@ 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 @@ -33993,7 +33993,7 @@ We create a shell formulation by reducing a 3D element interpolation which is li \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 @@ -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 @@ -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 @@ -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 @@ -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 @@ -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 @@ -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}\\ @@ -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 @@ -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 @@ -55975,7 +55975,7 @@ literal "true" and reference \begin_inset CommandInset citation LatexCommand citep -key "Zimmerman21a" +key "Zimmerman22" literal "false" \end_inset @@ -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 @@ -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 ; diff --git a/Documentation/FEBio_User_Manual.lyx b/Documentation/FEBio_User_Manual.lyx index 0508180df..502fc2c38 100644 --- a/Documentation/FEBio_User_Manual.lyx +++ b/Documentation/FEBio_User_Manual.lyx @@ -12952,16 +12952,16 @@ q4eas By default, the nodes of a shell element define its \emph on -front +top \emph default face. The location of the shell element \emph on -back +bottom \emph default face is calculated from the nodal values of the shell thickness, along the opposite direction of nodal normals. - The nodal normal is evaluated by averaging the front face normal of all shell elements sharing that node. + The nodal normal is evaluated by averaging the top face normal of all shell elements sharing that node. When a shell element is attached to a solid element (e.g., when the shell nodes also represent the nodes of one face of the solid element), FEBio automatically accounts for the shell thickness, @@ -12977,7 +12977,7 @@ Prior to FEBio 2.6, \emph on middle \emph default - face (halfway between front and back, + face (halfway between top and bottom, such that the shell element extends above and below the face defined by the shell nodes). This older formulation can be recovered by setting \emph on @@ -12991,6 +12991,15 @@ Control This setting only works with compatible strain shell formulations. \end_layout +\begin_layout Standard +By default, + stresses and strains reported for a shell element are evaluated by averaging all the integration point values within the shell element, + thus producing values that reflect the response along the middle surface. + To display shell stresses or strains at the top or bottom faces, + use plot variables that start with 'shell top...' or 'shell bottom...', + such as 'shell top stress' or 'shell bottom nodal strain'. +\end_layout + \begin_layout Standard When shell domains intersect such that three or more shell elements share the same edge, as in a T-connection, @@ -13003,7 +13012,7 @@ shell_normal_nodal ShellDomain \emph default section. - This setting ensures that the back face of a shell element is calculated using the front face normal, + This setting ensures that the bottom face of a shell element is calculated using the top face normal, instead of nodal normals, since the latter would be ill-defined for nodes belonging to such an edge. \end_layout @@ -17135,7 +17144,7 @@ shell velocity \begin_inset Text \begin_layout Plain Layout -Set the initial value for the shell (back) nodal velocities. +Set the initial value for the shell (bottom) nodal velocities. \end_layout @@ -17641,7 +17650,7 @@ zero shell displacement \begin_layout Plain Layout Fix the x, y, - or z shell (back) displacement dof + or z shell (bottom) displacement dof \end_layout \end_inset @@ -17812,7 +17821,7 @@ prescribed shell displacement \begin_layout Plain Layout Prescribe the x, y, - or z shell (back) displacement dof + or z shell (bottom) displacement dof \end_layout \end_inset @@ -32167,7 +32176,7 @@ literal "true" and in \begin_inset CommandInset citation LatexCommand citep -key "Zimmerman21a" +key "Zimmerman22" literal "true" \end_inset @@ -34928,7 +34937,7 @@ shell_bottom_primary \begin_inset Text \begin_layout Plain Layout -contact with back of shell on primary surface +contact with bottom of shell on primary surface \end_layout \end_inset @@ -35026,7 +35035,7 @@ shell_bottom_secondary \begin_inset Text \begin_layout Plain Layout -contact with back of shell on secondary surface +contact with bottom of shell on secondary surface \end_layout \end_inset @@ -35816,7 +35825,7 @@ implementation for sliding interfaces can deal with biphasic contact surfaces (i biphasic-on-rigid) \begin_inset CommandInset citation LatexCommand citep -key "Ateshian10b,Zimmerman21a" +key "Ateshian10b,Zimmerman22" literal "true" \end_inset @@ -35885,7 +35894,7 @@ When either contact surface is biphasic, As detailed in \begin_inset CommandInset citation LatexCommand citep -key "Zimmerman21a" +key "Zimmerman22" literal "true" \end_inset @@ -47371,7 +47380,7 @@ An asterisk (*) in the Category column denotes that the attribute is required an \begin_inset Tabular - + @@ -50324,7 +50333,6 @@ Element \begin_layout Plain Layout The Cauchy stress, projected to the nodes. - \end_layout \end_inset @@ -51288,6 +51296,122 @@ Average element solid-bound molecule referential apparent density \begin_inset Text +\begin_layout Plain Layout +shell bottom nodal strain +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Node +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Shell Lagrange strain extrapolated to bottom nodes +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +shell bottom nodal stress +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Node +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Shell Cauchy stress extrapolated to bottom nodes +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +shell bottom strain +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Element +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Average of shell Lagrange strain extrapolated to bottom surface +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +shell bottom stress +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Element +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Average of shell Cauchy stress extrapolated to bottom surface +\end_layout + +\end_inset + + + + +\begin_inset Text + \begin_layout Plain Layout shell director \end_layout @@ -51347,7 +51471,7 @@ Relative volume of shell element \begin_inset Text \begin_layout Plain Layout -shell strain +shell strain \end_layout \end_inset @@ -51397,6 +51521,122 @@ Node Shell thickness \end_layout +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +shell top nodal strain +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Node +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Shell Lagrange strain extrapolated to top nodes +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +shell top nodal stress +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Node +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Shell Cauchy stress extrapolated to top nodes +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +shell top strain +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Element +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Average of shell Lagrange strain extrapolated to top surface +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +shell top stress +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Element +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Average of shell Cauchy stress extrapolated to top surface +\end_layout + \end_inset @@ -63464,7 +63704,7 @@ Donnan equilibrium and the external bathing environment consists of a salt solution of monovalent counter-ions \begin_inset CommandInset citation LatexCommand citep -key "OVERBEEK56,Lai91" +key "Overbeek56,Lai91" literal "true" \end_inset @@ -77776,7 +78016,7 @@ where represents the unit sphere (for 3D fiber distributions) or unit circle (for 2D fiber distributions) over which the integration is performed \begin_inset CommandInset citation LatexCommand citep -key "Hou2016" +key "Hou16" literal "true" \end_inset