### Abstract

The elastic-plastic material model for porous material
proposed by Gurson and Tvergaard is evaluated. First a
general description is given of constitutive equations
for solid materials by thermomechanics with internal
variables. The role and definition of internal variables
are briefly discussed and the following definition is
given: The independent variables present (possibly
hidden) in the basic laws for thermomechanics are called
controllable variables. The other independent variables
are called internal variables. An internal variable is
shown always to be a state variable. This work shows that
if the specific dissipation function is a homogeneous
function of degree one in the fluxes, a description for a
time-independent process is obtained.
When damage to materials is evaluated, usually a
scalar-valued or tensorial variable called damage is
introduced in the set of internal variables. A problem
arises when determining the relationship between
physically observable weakening of the material and the
value for damage. Here a more feasible approach is used.
Instead of damage, the void volume fraction is inserted
into the set of internal variables. This allows use of an
analytical equation for description of the mechanical
weakening of the material.
An extension to the material model proposed by Gurson and
modified by Tvergaard is derived. The derivation is based
on results obtained by thermomechanics and damage
mechanics. The main difference between the original
Gurson-Tvergaard material model and the extended one lies
in the definition of the internal variable 'equivalent
tensile flow stress in the matrix material' denoted by
M. Using classical plasticity theory, Tvergaard elegantly
derived an evolution equation for M. This is not
necessary in the present model, since damage mechanics
gives an analytical equation between the stress tensor
and M. Investigation of the Clausius-Duhem inequality
shows that in compression, states occur which are not
allowed.

Original language | English |
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Place of Publication | Espoo |

Publisher | VTT Technical Research Centre of Finland |

Number of pages | 180 |

ISBN (Electronic) | 951-38-5061-7 |

ISBN (Print) | 951-38-5060-9 |

Publication status | Published - 1997 |

MoE publication type | Not Eligible |

### Publication series

Series | VTT Publications |
---|---|

Number | 312 |

ISSN | 1235-0621 |

### Keywords

- thermomechanical analysis
- thermodynamics
- plasticity
- porous medium
- Gurson-Tvegaard model

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## Cite this

Santaoja, K. (1997).

*Thermomechanics of solid materials with application to the Gurson-Tvergaard material model*. VTT Technical Research Centre of Finland. VTT Publications, No. 312