Resumen de On the mechanics of strain localization in plasticity. Isotropic and orthotropic, cohesive and frictional, associated and non-associated models
In this thesis, two main topics have been covered: the mechanics of strain localization in plasticity and the performance of several mixed finite elements subjected to plastic strain localization.
Throughout the thesis, incompressible and cohesive-frictional, isotropic and orthotropic, elasto- and rigid-plastic solids are analyzed using associated or non-associated flow rules, both in the continuum and the discrete settings.
Plastic yielding, strain bifurcation and strain localization are identified in the failure process prior to conducting a detailed analysis of strain localization.
The mechanics of strain localization in the continuum and discrete settings, including the constitutive relations, the kinematics for strong and weak discontinuities, and the strain localization conditions are presented. Maxwell’s kinematic condition, the traction rate continuity and the stress rate constraints are explained, thereby distinguishing the correlations and differences between strain bifurcation and strain localization conditions.
The analytical prediction of strain localization derived from the stress boundedness condition is proposed and numerically verified through independent simulations. Unlike predicted in classical strain bifurcation analysis, strain localization is independent from the elasticity behavior and is only related to plastic flow. Specifically, the strain localization angle depends on the stress state and plastic potential but not on the yield surface.
Uniaxial computational experiments on strips subjected to uniaxial stretching and compressing in plane stress and plane strain to assess the theoretical analysis and Prandtl’s flat punch tests are performed.
Numerical results for incompressible and cohesive-frictional, isotropic and orthotropic, associated and non-associated plasticity, with or without inclination angles between the material local axes and the global axes are compelling evidence for the proposed theoretical framework.
Various mixed finite elements are used in this thesis. By comparing the numerical outputs, the advantages and disadvantages of the performance of the several mixed finite elements are shown regarding enhanced accuracy, computational efficiency, mesh sensitivity and stress locking.
