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Lesson 4: Johnson-Cook Plasticity30 minutesLesson content:IntroductionElasticityYield Function and Plastic FlowHardeningStrain Rate DependenceAnnealing or MeltingHeat GenerationDynamic FailureExample: Oblique Impact of a Copper RodIntroductionThe Johnson-Cook plasticity model is particularly well suited to model high-strain-rate deformation of metals.This model is a particular type of Mises plasticity that includes analytical forms of the hardening law and rate dependence.The Johnson-Cook model, like the classical Mises plasticity model, uses a deviatoric stress measure to determine if inelastic behavior occurs.It is generally used in adiabatic transient dynamic simulations.The Johnson-Cook model was developed originally for high-speed impact simulations.The Johnson-Cook plasticity model can be used with any stress/displacement element in Abaqus. Elasticity (1/3)The elastic behavior of materials modeled with the Johnson-Cook model must be defined aslinear elastic, or an equation of state material model (Abaqus/Explicit only)Usage:*EOSElasticity (2/3)Equation of state modelsAbaqus/Explicit onlyHydrodynamic material modelThe material’s deviatoric and volumetric strengths are determined by an equation of state.The deviatoric (shear) elastic behavior is defined with the *ELASTIC, TYPE=SHEAR option.The elastic shear modulus, G, is given on the data lines.Temperature and/or field variable dependencies can be defined for the shear modulus, G (q, fi ).Elasticity (3/3)Equations of state govern the material’s volumetric response. Eitheran ideal gas law, ora Jones-Wilkens-Lee (or JWL) equation of state model, or a Mie-Gruniesen (Us-Up) equations of state, oran ignition and growth equation of state, or a tabulated equation of state (linear in energy), ora user-defined equations of state (via user subroutine VUEOS) can be defined. For details about these models see the Abaqus Analysis User’s Guide.The equation of state material models can be used with any stress/displacement co