User's Material Law for Shell Elements Example

A Johnson-Cook elasto-plastic material law is defined for shell elements. Input user data includes density, Young’s modulus, Poisson ratio, yield stress, hardening parameters, hardening modulus, maximum stress, and maximum strain.

The Johnson Cook model:(1)
σ = A + B ε p N MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacPqpw0le9v8qqaqFD0xXdHaVhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aabaGaam4Wdiaad2dacaWGbbGaam4kaiaadkeacaWG1oWaa0baaSqa aiaadchaaeaacaWGobaaaaaaaa@4267@

Maximum stress and plastic strain are taken into account. Shell thickness is variable.

Two methods are available to compute plastically admissible stresses:
  • Projection by return radial
  • Iterative projection with three Newton iterations
This model is made of shell elements.

Figure 1.