Creep constitutive equations for damaged materials.

*(English)*Zbl 0728.73026The thermodynamics is developed in Section II. In Section III we examine each mechanism of void growth and in Section IV we briefly discuss the process of void nucleation. The analyzes of these sections results in constitutive equations with a large number of state variables. This can be partially overcome by formulating the problem in terms of the distribution of damage in the material. In Section VI we examine the strain-softening mechanism.

Sections II through VI are concerned primarily with the basic structure of the constitutive equations. When the damage is in the form of voids we need to know the distribution of these voids within the body before being able to obtain the exact constitutive laws. Constitutive equations are presented in Section VII for two simple distributions of voids that result in zero and full constraint. In Section IX we analyze the experimental data available to us to make decisions of the structure of the material laws. In general the amount of information available is quite limited and we must be content with sets of equations that contain a limited number of state variables. The type and physical nature of the state variables that prove appropriate in a given situation can change as the type of loading (monotonic, nonproportional, cyclic) is changed.

The remainder of the paper is devoted to the application of the material models to structural problems. It is found that when the rate of increase of damage is mathematically separable in expressions for stress and of damage that it is possible to obtain upper bounds to the life of a component.

Sections II through VI are concerned primarily with the basic structure of the constitutive equations. When the damage is in the form of voids we need to know the distribution of these voids within the body before being able to obtain the exact constitutive laws. Constitutive equations are presented in Section VII for two simple distributions of voids that result in zero and full constraint. In Section IX we analyze the experimental data available to us to make decisions of the structure of the material laws. In general the amount of information available is quite limited and we must be content with sets of equations that contain a limited number of state variables. The type and physical nature of the state variables that prove appropriate in a given situation can change as the type of loading (monotonic, nonproportional, cyclic) is changed.

The remainder of the paper is devoted to the application of the material models to structural problems. It is found that when the rate of increase of damage is mathematically separable in expressions for stress and of damage that it is possible to obtain upper bounds to the life of a component.

##### MSC:

74C99 | Plastic materials, materials of stress-rate and internal-variable type |

74R99 | Fracture and damage |

74A20 | Theory of constitutive functions in solid mechanics |