Deformation, Failure And Stability Of Strain-Softening Materials: Analytical And Numerical Analyses

Four aspects of investigations were carried out in this thesis:(1) Theoretical analysis of nonuniformities of physical and mechanical quantities in localized band due to the microstructural effectBased on nonlocal theory considering the interactions and interplaying among microstrcutures, the analytical solutions of the thickness of shear band and the local (plastic) shear strain, strain rate, deformation and velocity in shear band were derived using the isotropic assumption, the boundary condition, the assumption that the actual thickness of shear band corresponded to the maximum value of local plastic shear strain and the post-peak linear strain-softening constitutive relation.The relation between the gradient of local (plastic) shear deformation and the local (plastic) shear strain and that between the gradient of velocity and the strain rate were established. The theoretical results showed that the distributions of local (plastic) shear deformation and velocity in shear band exhibited nonlinear characteristics, which were different from the traditional assumption of linear distribution. The concept of constant shear strain point was proposed.The influences of strain rate, degradation of stiffness (damage) and weakening due to pore fluid on the distributions of local (plastic) shear strain and deformation in shear band were investigated. For dilative material in shear, the increment of local volumetric strain in shear band and the normal deformation of shear band due to shear dilatancy were derived. The constant shear strain point accounting for the degradation of stiffness was discussed. For dilative material in shear, the analytical solutions of local porosity, void ratio, increments of porosity and void ratio in shear band were proposed. The analytical solutions of maximum void ratio, average value of increment of maximum void ratio, average value of maximum void ratio and average value of maximum porosity were derived.For a specimen in uniaxial tension, the analytical solution of local plastic tensile strain in tensile localized band was proposed and compared with the previously numerical results. Based on nonlocal theory, the analytical solution of local damage variable in tensile localized band, nonlocal damage variable and their derivatives with respect to time and maximum values were proposed.For linearly strain-softening ductile metal material in uniaxial tension, the analytical solution of diameter in necked region was proposed. In direct shear condition, considering the residual shear strain at pre-peak and the propagation of deformed shear band, the analytical solutions of local plastic shear strain and deformation in deformed shear band were proposed for linearly strain-softening ductile metal material, respectively. The strain gradient was introduced into the John-Cook constitutive relation and then the distribution of temperature in adiabatic shear band and its evolution were calculated for linearly strain-softening ductile metal material.Using the widely used Johnson-Cook model and gradient-dependent plasticity, the distributions of local plastic shear strain and deformation in adiabatic shear band were analyzed. The effects of static shear strength, work to heat conversion factor, strain-hardening exponent, thermal-softening exponent, melting point, thermal capacity, mass density, strain rate sensitive...