<CaribouMass />¶
Doxygen:
SofaCaribou::mass::CaribouMass
Implementation of a consistent Mass matrix. The assembly of this mass matrix takes the form of
where \(I\) and \(K\) are a pair of indices of the element \(K\) nodes. Here, \(\rho_0\) is the mass density as the mass per volume unit (ie \(\frac{m}{v}\)) at the undeformed configuration. Finally, \(N_I(\boldsymbol{\Psi})\) is the shape function of the \(I\)boldsymbol{Psi}` relative to the reference (canonical) element.
A diagonal consistent mass matrix is also constructed by scaling down the diagonal terms in a way that the mass is constant within the element. The procedure is the following:
With the scaling factor being
 See the following book for more information:
Peter Wriggers, Nonlinear finite element methods (2008), DOI: 10.1007/9783540710011_2
Requires a mechanical object. Requires a topology container.
Attribute 
Format 
Default 
Description 

printLog 
bool 
false 
Output informative messages at the initialization and during the simulation. 
lumped 
bool 
false 
Whether or not the mass matrix should be lumped by scaling the diagonal entries such that the mass is constant per element. Note that the lumped matrix is always computed. But this parameter will determine if it (the lumped) matrix should be used to solve the acceleration (a = M^(1).f). 
density 
double 
1 
Mass density of the material at the undeformed state formulated as the mass per volume unit, ie \(\rho_0 = m / v\). 
topology 
path 
Path to a either a SOFA mesh topology container (such as an HexahedronSetTopologyContainer or TetrahedronSetTopologyContainer) or a CaribouTopology component that contains the elements. 

template 
option 
The template argument is used to specified the element type on which to compute the mass. By default, the component will try to deduce its element type from the given topology.

Quick example¶
XML
<Node>
<RegularGridTopology name="grid" min="7.5 7.5 0" max="7.5 7.5 80" n="9 9 21" />
<MechanicalObject src="@grid" />
<HexahedronSetTopologyContainer name="topology" src="@grid" />
<CaribouMass density="2.5" lumped="true" topology="@topology" />
</Node>
Python
node.addObject("RegularGridTopology", name="grid", min=[7.5, 7.5, 0], max=[7.5, 7.5, 80], n=[9, 9, 21])
node.addObject("MechanicalObject", src="@grid")
node.addObject("HexahedronSetTopologyContainer", name="topology", src="@grid")
node.addObject("CaribouMass", density=2.5, lumped=True, topology="@topology")
Available python bindings¶
 class CaribouMass¶
 M()¶
 Returns
Copy of the consistent mass matrix as a compressed column sparse matrix
 Return type
 Note
The mass matrix must have been assembled beforehand. See the assemble_mass_matrix() methods to force an assembly.
Get the consistent mass matrix of a topology as a compressed sparse column major matrix.
 M_diag()¶
 Returns
Copy of the lumped mass matrix as a compressed column sparse matrix
 Return type
 Note
The mass matrix must have been assembled beforehand. See the assemble_mass_matrix() methods to force an assembly.
The diagonal lumped mass matrix is constructed by scaling down the diagonal terms in a way that the mass is constant within the element.
 assemble(x)¶
Assemble the mass matrix M.
This will force an assembly of the consistent mass matrix. Since the mass matrix is function of the the position vector at rest passed as an nx3 array parameter with n the number of nodes. If x is omitted, it will use the mechanical state vector “restPosition”.
A copy of the assembled consistent mass matrix M as a column major sparse matrix can be later obtained using the method M().