r5.03.33 Laws of plastic and viscoplastic behavior with nonlinear isotropic work hardening VMIS_ISOT_NL and VISC_ISOT_NL

Summary:

This document describes the elasto-visco-plastic behavior model with nonlinear isotropic work hardening, available in a local version and with a gradient of internal variables (GRAD_VARIou GRAD_INCO). A modeling of large deformations is accessible via kinematics GDEF_LOG. The work hardening function combines several terms (an affine term, two exponential terms, a power term, a Lüders plateau) capable of covering most of the non-linear responses of a metallic material; each can easily be cancelled out, which offers a form of modularity to the behavioral relationship (for example: linear work hardening or work-hardening under power law only). Finally, the behavior can be independent of time (VMIS_ISOT_NL) or viscoplastic (VISC_ISOT_NL). In the latter case, plasticity evolves according to a Norton model in which the threshold function intervenes.

• 1. Field of application
  • 1.1. Purpose
  • 1.2. Material parameters
  • 1.3. Internal variables
• 2. Continuous model
  • 2.1. Behavioral equations: local plastic model
  • 2.2. Taking viscosity into account
  • 2.3. Taking into account the work-hardening gradient
• 3. Digital integration
  • 3.1. Discretized equations
  • 3.2. Solving the discretized problem — Plastic case without viscosity
  • 3.3. Solving the discretized problem: viscoplastic case
  • 3.4. Tangent matrix
• 4. Bibliography