Viscoplastic Unified Constitutive Theory And Its Application To Concrete

The typical viscoplastic unified constitutive model is mainly applied for the constitutive analysis of metallic materials. In order to construct the viscoplastic unified constitutive models for the materials which its deformation characteristic is different from metallic materials, it is necessary to change the constructing method based on analyzing and generalizing its constructing theory. The traditional method for constructing unified constitutive models is typically phenomenological. The inelastic strain rate equation is derived from the expressions which is based on the three categories of steady-state creep functions for metallic materials. The basic forms of internal state variable evolution equations of kinematic hardening and isotropic hardening are assumed mainly based on the characteristic of plasticity and creep for metallic materials, and the ultimate forms are determined in terms of experiment data. There are not the concepts of plastic potential and yield surface in the viscoplastic unified constitutive model, so the achievements of classical plasticity can not applied to its theory, and so it can not be applied to the stress-strain analysis of the materials which its deformation characteristic is different from metallic materials, such as geo-materials.The flow rule is firstly taken into the phenomenological viscoplastic unified constitutive model based on analyzing the traditional constructing method of viscoplastic unified constitutive theory, and simultaneously the inelastic multiplier which includes the relational information of yield surface is constructed, and finally a method which develops the typical viscoplastic unified constitutive model is given. The presented inelastic multiplier can describe not only the plastic deformation as a substitute for plastic multiplier, but also the behavior of viscosity. The continue function of inelastic multiplier is in more accord with the deformation feature than the piece-wise function, moreover it not need to judge the stress state in applying. The introducing of the plasticity potential and yield surface enable that the correlation of classic plasticity and the unified viscoplasticity constitutive theory is discovered. Then, the viscoplastic unified constitutive model of other nonmetal materials could be developed by means of the theoretic achievements of classic plastic.Based on the presented inelastic multiplier and taking into account damage, a new inelastic multiplier which is fit for the behavior of concrete is proposed, and simultaneously a viscoplastic unified constitutive model for concrete is proposed by means of the achievements of classical plasticity theory and unified constitutive theory. The existence of a yield surface is not the basic assumption and reason for constructing the presented model. A set of coupled internal state variable evolution equations is used to describe the changes in the microstructure of concrete materials and the inelastic strain rate. Results from numerical simulation show that this model is capable of reproducing the significant deformation phenomena, including the different behavior under compression and tension loading, volume dilatancy under compression, strain-rate sensitivity, and stiffness degradation and strain-softening behavior beyond the peak stress which are brought by damages and fractures.The irreversible thermodynamics provide the method for constructing the constitutive model. In order to construct the constitutive model within the framework of irreversible thermodynamics based on the state variable, the rule that state variables must meet is obtained through studying the thermodynamics condition that the irreversible behavior of internal structure must meet. The irreversible behavior of internal structure is represented through the state variables. Then, the evolution approach of irreversible thermodynamics state variables for the specific materials which is in the specific condition is given, and subsequently this the constitutive feature of the materials respond is prescribed, and finally the expression of constitutive equation is given. A general and integrated theoretic framework is developed based on irreversible thermodynamics and the presented inelastic multiplier. The internal state variables which can describe the behavior of kinematic hardening and isotropic hardening are chosen, and simultaneously the corresponding expressions of Helmholtz free energy function and a flow potential function are given, from which the flow equation and the evolution equations of the internal state variables are derived. Moreover, this theoretic framework not only provides a new theoretical foundation for further development of the unified viscoplasticity constitutive model, but also gives a way for the stress-strain analysis of more materials.A viscoplasticity unified constitutive model for metallic materials is developed based on the presented theoretic framework. Results from the equation format and numerical simulation show that the presented model is reasonable. The damage is taken into account, and subsequently the viscoplastic damage unified constitutive model is developed by means of extending the presented theoretic framework. Moreover, the viscoplastic damage unified constitutive model for concrete is constructed. The means, which the presented model can describe the deformation features of the concrete without the formal hypotheses of yield criterion and failure criteria, is very reasonable because there are inconspicuous yield surface and initial damage in existence for concrete. Results from numerical simulation show that the proposed model can describe the important deformation characteristic of concrete.