A thermomechanical framework for constitutive models for rate-independent dissipative materials.

*(English)*Zbl 0958.74011Summary: A formulation of elastic-plastic theory for rate-independent materials is described, based on the use of thermodynamic potentials. The four energy functions commonly used in thermodynamics (internal energy, Helmholtz free energy, enthalpy and Gibbs free energy) are used to provide descriptions depending on which combinations of the stress, strain, temperature and entropy are taken as the independent variables. We use Legendre transformations in order to establish links between different energy functions. Dissipative behaviour is introduced through the use of kinematic internal parameters and their conjugate variables, which are termed generalised stresses. A dissipation function or a yield function is used to describe the irreversible behaviour, and these are related by a degenerate case of the Legendre transformation.

A central theme is that the constitutive behaviour is entirely determined by the knowledge of two scalar potentials. We make a systematic presentation of 16 possible ways of formulating constitutive behaviour within this framework. From four of these forms it is possible to establish the incremental response entirely by differentiation of two potentials and by standard matrix manipulation. We provide examples of the forms of potentials for certain simple cases.

A central theme is that the constitutive behaviour is entirely determined by the knowledge of two scalar potentials. We make a systematic presentation of 16 possible ways of formulating constitutive behaviour within this framework. From four of these forms it is possible to establish the incremental response entirely by differentiation of two potentials and by standard matrix manipulation. We provide examples of the forms of potentials for certain simple cases.

##### MSC:

74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |

74A15 | Thermodynamics in solid mechanics |

80A17 | Thermodynamics of continua |