Papers by Keyword: Logarithmic Strain

Abstract: The logarithmic strain is more suitable for analyzing large strain problems because the volume invariability condition in small deformation is equivalent to volume invariability condition in large deformation when using the logarithmic strain. Large simple shear deformation has always been used in the analysis of large strain problems. In this paper, elastic large strain constitutive model was introduced based on the logarithmic strain and large simple shear deformation was analyzed by using the constitutive model given in the paper. The stress responses to large simple shear deformation were derived corresponding to four objective rates of tensors. The results show that normal stresses may maintain good monotonicity, but there exists different levels of oscillation of shear stress corresponding to various objective rates, and there was the most severe oscillation of stress when adopting Jaumann rate. The objective rate should not be the only factor bringing about oscillation of shear stress.

Abstract: In this paper, a finite strain constitutive model was proposed by the additive decomposition of the logarithmic strain rate and the generalization of small deformation constitutive model and a complete analysis was made for an isotropic hardening J2 flowing finite strain constitutive model based on torsion experiments. Logarithmic strain and Jaumann stress rate were discussed in solid circular shaft torsion deformation. Utilizing the results obtained from solid circular shaft torsion experiments, the plastic rigidity function in constitutive model was determined. The simple shear problem was studied by using the constitutive model given in this paper. The results shows that the plastic rigidity function corresponding to logarithmic strain was different from one to Green strain and finite strain constitutive model should be analyzed by logarithmic strain and torsion experiments.

Abstract: In order to analyze the dynamic mechanical property of steel 4340 during its micro-milling, finite element method is used to simulate the process of elastic-plastic micro-milling. The curves of logarithmic strain, plastic strain, strain rate changing as cutting time goes on are shown in the process of simulation, with the distribution of logarithmic strain, plastic strain, equivalent plastic stain and stain rate analyzed. The results provide a basis for the further reaserch of materials’ dynamic mechanical properties during their cutting process.