THE THEORY OF HYPERELASTIC-VISCOPLASTICITY, WHICH TAKES INTO ACCOUNT THE MICRODEFORMATION - Shneider, V. P. (Computer Science and Applied Mathematics, 2017)
Introduction. The plastic flow caused by the slip of dislocations is closely related to the mechanism of thermal activation over a wide range of strain rates. On the other hand, plastic deformation at high speed can lead to an obvious increase in temperature. Therefore, the effects of strain rate and temperature should be taken into account simultaneously when studying the behavior of materials. A number of theories have been proposed to describe the plastic deformation of materials over a wide range of strain rates and temperatures over the past three decades. These theories are conditionally divided into two main groups; Physical and phenomenological. A small number of material constants and simple calibration characterizes phenomenological models, but they have a limited scope of applicability. Physical theories usually contain a larger number of material constants, and thus their use is more complex than using phenomenological theories, but their scope is much broader. The main point, of the construction of the defining relations of the theory of large viscoplastic deformations, is the separation of total deformations and their velocities into elastic and plastic components. The solution of this question is related to the configuration in which the theory is formulated. Two main approaches are usually used. In the first one, the defining relations in the current configuration (hypoelasticity) are stated, and in the second relationship the relationships are formed with respect to the intermediate unloaded configuration (hyperelasticity). In work [7] the theory of hypoelastic-viscoplasticity, taking into account microdeformation was formulated. The disadvantages of this approach are known. These include: the work of stresses on a closed cycle by deformation is not exactly zero; The requirement of isotropy of elastic relations; Isotropy of the yield function; The need to integrate the hypoelastic relationships over time to determine the stresses. In the present paper, these shortcomings are eliminated by introducing a hyperelastic-viscoplastic formulation, in which the elastic behavior is given by a hyperelastic potential. This allows to eliminate some disadvantages of the hypoelastic approach. Сonclusions.To eliminate imperfections of the previously proposed theory of hypoelasticviscoplasticity, a variant of the hyperelastic-viscoplastic theory, taking into account microdeformation, is developed, in which the elastic behavior is given by the hyperelastic potential. An algorithm for numerical investigation of viscoplastic flow for a given deformation gradient trajectory is proposed. Preliminary calculations showed the effectiveness of the proposed version of the theory.