## TContinuumMechanics

swMATH ID: | 16766 |

Software Authors: | J. F. Gouyet, R. Cabrera, D. Park |

Description: | The package TContinuumMechanics is devoted to the manipulation of tensors in the context of Continuum Mechanics problems. The present version is TContinuumMechanics 3.0, which needs Mathematica (version 6 and later). TContinuumMechanics version 3.0 is now free in Researchgate. I give here all the outputs after calculation of each functions and tutorials using Mathematica 8.0. To perform calculations using the functions present in TContinuumMechanics you need the basic program Tensorial 5.0 which can be downloaded via: https://www.dropbox.com/sh/ve1kphwvmyocw8i/AAAORzwclBuHbKfZ2GH5WCIHa?dl=0. Another program, Presentations, is also needed to draw the graphics. It is available at: https://www.dropbox.com/sh/mn0dlqrnosp0v9i/AAAs6nwVcz6Sjg8urdf5dM_Ma?dl=0. The functions necessary to use TContinuumMechanics are listed in TContinuumMechanics>Documentation>English>ReferencePages>Symbols. The Tutorials of TContinuumMechanics are composed of the twelve chapters of the well known book of Wilhelm Flügge ”Tensorial Analysis and Continuum Mechanics”, Wilhelm Flügge, Springer, 1972. It shows how TContinuumMechanics 3.0 can be used in continuum mechanics problems. In this program, I closely followed Flügge’s book all along the chapters, as it is to my opinion one of the clearest presentation of Continuum Mechanics using tensors extensively. It demonstrates how the Mathematica, Tensorial and TContinuumMechanics packages, permit to express in a very clear manner the tensorial structure of the equations of Continuum Mechanics. Tensorial, can be used to manipulate tensors in a way which corresponds to the manner tensors are written in standard text books. Many applications have already been performed in the fields of relativity and general relativity. Two examples of applications of TContinuumMechanics are included in the package: In example a) we give the method to calculate the operators gradient, divergence, curl and laplacian in curvilinear coordinates. We apply the method to the case of spherical coodinates, but the procedure is general. In example b) we apply Tensorial and TContinuumMechanics, to the case of distortions in a nematic single liquid crystal. |

Homepage: | http://www.jfgouyet.fr/tcm/tcm.html |

Dependencies: | Mathematica |

Related Software: | Tensorial; GeneralVectorAnalysis; MathGR; ORTHOVEC; VEST; MathTensor; xAct; xTensor; VEST; xPerm; Mathematica; Maple; Invar; Cadabra |

Referenced in: | 2 Publications |

### Referenced by 3 Authors

1 | Burby, J. W. |

1 | Flügge, Wilhelm |

1 | Squire, John M. |

### Referenced in 1 Serial

1 | Computer Physics Communications |

### Referenced in 4 Fields

1 | Linear and multilinear algebra; matrix theory (15-XX) |

1 | Differential geometry (53-XX) |

1 | Mechanics of particles and systems (70-XX) |

1 | Mechanics of deformable solids (74-XX) |