Extension of the viscoplasticity theory based on overstress (VBO) to capture non-standard rate dependence in solids
The authors proposed a new VBO model. The constitutive equations are rate-dependent, which means that no loading and unloading conditions are used in the evolution of state variables. Only isothermal processes are considered, and the constitutive functions inferred in the model are identified from uniaxial experimental data. The uniaxial constitutive equations are first introduced in section 2, while the extension to a three-dimensional tensor representation is given at the end of the paper. The internal tensorial variables involved in the model are the equilibrium stress deviator \({\mathbf g}\) and the kinematic stress \({\mathbf f,}\) which allows to model the Bauschinger effect. The scalar material functions which characterize the inelastic flow law are decreasing viscosity function, or increasing flow function, considered to be dependent on the intensity of the overstress and on the drag stress, that is kept constant in the model. The overstress is defined as the difference between the stress and the equilibrium stress. The growth law for equilibrium stress is linearly dependent on the rate of stress and on the rate of kinematic stress, respectively, with the coefficients involving a viscoplastic like term. A scalar shape function controls the transition between initial quasi-elastic behaviour and fully established inelastic flow, being dependent on the intensity of the overstress and bounded by the tangent modulus and Young modulus. The viscoplastic term characterizes the long term behaviour. The authors explain that the long term solution is thought to apply when the inelastic flow is fully established. Two dimensionless function \(\lambda\) and \(\beta\) are inferred in the viscoplastic term, modeling the unusual rate dependence. The augmentation function \(\beta\) is dependent on the accumulated inelastic strain, while \(\lambda\) is considered to be equal to 1. The evolution equation for \({\mathbf f}\) is expressed in Prager hardening form. Numerical simulations emphasize the new capabilities of the model in uniaxial tests. The results of the modeling are reported in a number of suggestive figures.
scientific article; zbMATH DE number 1797343