On Finite Strains in Continua with Complex Rheology

Abstract

Abstract. The present study deals with the multiphysics modelling frameworks for the elasticcreep-plastic material. The proposed theory of large deformations is based on the classical formalism of nonequilibrium thermodynamics. Reversible and irreversible components of total deformations are derived by the constitutive differential equations. The development of this theory involves statements and solutions of the correct boundary value problems. The problem of deformation of the material in the vicinity of microdefect was considered. Resulting integrodifferential equations system was derived. Preliminary RemarksModern additive manufacturing technology [1,2] states the problem of creating and developing of new mathematical models of growth and deformation of structural materials. The calculation of stress-strain state parameters is needed during the forming processes of material [3]. In the design of ship hulls and aircraft are widely used panels and profiles of hardly-deformed aluminum alloys [4]. Traditional methods of formation of such structural elements often leads to the appearance of the plastic breaks, cracks and other damages. Thus, the effective way of this fabrication is metal forming under creep and low strain rates. These processes ensures the production of construction with high accuracy, which reduces the complexity of assembly and welding, and increase the residual life and the quality of construction.The mathematical description of the processes of thermomechanical treatment of contracture materials is faced with the necessity to consider the elastic properties of materials at all stages of the producing and utilization. Consideration of the problems in the classical models of small deformations is impossible when the relative shape of the body is strongly changed. Such problem is the process of deformation metals in vicinity of micropore under the intense pressure action. In this case, we are faced to assumption of large strains. Well known experiments [3,4] when the long-term strength of metal products after their treatment under hydrostatic pressure is significantly increased. Attempts to simulate such process of the micropores "healing" in the metal have been made repeatedly [4][5][6][7][8][9][10][11][12][13][14]. In [5] such problems are considered due to the model of large elastic-plastic deformation. In this case, the effect of adaptability to periodic loading on the cycle "loading and unloading" was shown in [6].