Physical Fields and Scalars#

Overview#

Besides the primary solution of a physical problem, OpenPisco allows physical solvers to generate additional quantities such as stresses, strains or integrated energies.

These quantities are collectively referred to as auxiliary fields and auxiliary scalars.

Auxiliary Fields#

The capability of a solver to generate a given field is described through the attribute

  • OpenPisco.PhysicalSolvers.SolverBase.SolverBase.auxiliaryFieldGeneration

Useful methods include:

Auxiliary Scalars#

Scalar quantities follow a similar workflow through:

Field Naming Convention#

All field and scalar identifiers are defined in

This module provides a common vocabulary shared by all solver interfaces.

Available Fields#

Stress#

Cauchy stress tensor.

Strain#

Small-strain tensor:

\[e(u)=\frac{\nabla u + (\nabla u)^T}{2}\]

Von Mises Stress#

Equivalent stress defined by

\[\sigma_v=\sqrt{\frac32 s_{ij}s_{ij}}\]

Potential Energy#

Local strain energy density:

\[\frac12 \sigma(u):e(u)\]

Available Scalars#

Volume#

\[\int_\Omega dx\]

Mass#

\[\int_\Omega \rho \, dx\]

Integrated Potential Energy#

\[\int_\Omega \frac12 \sigma(u):e(u)\,dx\]

Field Availability#

N, C and IP denote respectively:

  • N: nodes

  • C: cell centroids

  • IP: integration points

Table 3 Fields available w.r.t. tools#

Field

Code_Aster

FreeFem++

Zset

Muscat

stress

N,C,IP

N

strain

N,C,IP

von_mises

N,C,IP

N

N,C,IP

potential_energy

N,C,IP

N

N

N,C,IP

Scalar Availability#

Table 4 Scalars available w.r.t. tools#

Scalar

Code_Aster

FreeFem++

Zset

Muscat

volume

False

False

False

False

mass

False

False

False

False

int_potential_energy

True

True

True

True