Bartels

A lightweight collection of routines for physics simulation.

External Dependencies

None so far

Included Submodules (Installed Automatically)

1. Libigl https://github.com/libigl/libigl
2. Eigen >= 3.2 (By Default Bartels uses the libigl Eigen install)

To get started: Clone this repository and all its submodule dependencies using:

git clone --recursive https://github.com/dilevin/Bartels.git

Compilation

Bartels is a header only library but includes somethings that need to be compiled or use.

Tests

To compile the included tests do the following:

cd ${BARTELS_SOURCE_DIRECTORY}/tests
mkdir build
cd build
cmake ..
make all

MATLAB Interface

Bartels includes MATLAB wrappers for usefull functions. To compile the MATLAB wrappers do the following:

cd ${BARTELS_SOURCE_DIRECTORY}/matlab
mkdir build
cd build
cmake ..
make all

To enable Bartels in MATLAB open MATLAB and issue the following commands:

addpath('${BARTELS_SOURCE_DIRECTORY}/matlab')
addpath('${BARTELS_SOURCE_DIRECTORY}/matlab/mex')
savepath

Here is an example of using Bartels to compute the first 20 deformation modes of a Neo-Hookean bunny:

>> [V,T,F] = readMESH('/Users/dilevin/Documents/Research/Development/bartels/data/meshes_mesh/coarser_bunny.mesh');
>> M = linear_tetmesh_mass_matrix(V,T, 0.1*ones(size(T,1),1), vol);
>> YM = 2e6; %in Pascals
>> pr =  0.45
>> [lambda, mu] = emu_to_lame(YM*ones(size(T,1),1), pr*ones(size(T,1),1));
>>  H = linear_tetmesh_neohookean_dq2(V,T, q, dX, vol, [0.5*mu, 0.5*lambda]);
>> [modes, freq] = eigs(-H, M, 20, 'smallestabs');

NOTE: I use GPToolbox by Alec Jacobson for file I/O (i.e readMESH) and geometry processing.

Conventions

I try to obey some naming conventions when I implement new functions in Bartels which makes it, in some sense, self documenting. Below are some of these conventions:

• Finite element methods are prefaced by element type i.e linear_tet_.... indicates this method applies to a single tetrahedral element with linear shape functions.

• There are seperate methods which apply per element functions to an entire computational mesh. These take the form i.e. linear_tetmesh_...

• q refers to the degrees of freedom of a mechanical system, no matter what they are. For FEM they are the vertices of the simulation mesh

• F refers to the deformation gradient at point in space

• psi refers to a potential energy function for a constitutive model

• phi referes to shape functions

• lower case d is used to represent differential operations.

• when taking derivatives with respect to matrix quantities (like F), the matrix quantitiy is flattened to a column vector. *i.e the 3x3 matrix F = [F00 F01 F02; F10 F11 F12; F20 F21 F22] becomes a 9x1 vector [F00 F10 F20 F01 F11 F21 F02 F12 F22]'.

Some examples of putting it all together:

• dpsi_neohookean_dF2 computes the second derivative of the neohookean potential energy, with respect to the deformation gradient.

• linear_tet_dphi_dX computes the derivative of the linear tetrahedron shape functions with respect to the reference space

• linear_tetmesh_dphi_dX computes the above over the entire tetmesh

• linear_tetmesh_neohooken_dq2 computes the sparse Hessian of the neohookean energy over an entire tetmesh

• linear_tetmesh_stvk_dq computes the gradient of the stvk energy over an entire tetmesh

• linear_tetmesh_arap_q computes the energy of the As-Rigid-As-Possible energy over an entire tetmesh