The JC model is supposed to provide you with the effective plastic strain rate. Its implementation within a explicit FE solver is quite straight forward. You should use the following steps:

STEP 0: Get the stress tensor s, the damage variable D, the temperature T and the equivalent plastic strain ep,eq at the beginning of the time increment

STEP 1: Calculate the equivalent stress seq at beginning of the time increment with the yield criterion of your choice (e.g. von Mises, Tresca...)

seq=f(s)

STEP 2: Calculate the plastic flow direction n according to:

nij=dseq / dsij

STEP 3: Calculate the equivalent plastic strain rate dep,eq/dt from the JC constitutive equation

dep,eq/dt = f(seq, T, ep,eq)

STEP 4: Calculate the plastic strain rate tensor

dep,ij/dt=dep,eq/dt*nij

STEP 5: Calculate the stress rate tensor

dsij/dt=(1-D)*Cijkl *(dekl/dt -dep,kl/dt)

where C is the fourth rank stiffness tensor. For the specific case of isotropic elasticity, the above relation becomes:

dsij/dt=(1-D)*L *(dekk/dt -dep,kk/dt)*1ij+2*(1-D)*G *(deij/dt -dep,ij/dt)

where L and G are the Lamé coefficients. For the even more specific case of isotropic elasticity and purely deviatoric plasticity, the stress rate is given by:

dsij/dt=(1-D)*L dekk/dt*1ij+2*(1-D)*G *(deij/dt -dep,ij/dt)

STEP 6: Calculate the plastic strain tensor and equivalent plastic strain at the end of the time increment

ep,ij=ep,ij+dep,ij/dt*dt

ep,eq=ep,eq+dep,eq/dt*dt

STEP 7: Calculate the stress tensor at the end of the time increment

sij=sij+dsij/dt*dt

STEP 8: Calculate the damage indicator at the end of the time increment

D=ep,eq/ef

Hello

You can read all principal strains in your VUMAT then you have to calculate the Equivalent plastic strain using the formula regarding your constitutive equation.

I hope it helps

The JC model is supposed to provide you with the effective plastic strain rate. Its implementation within a explicit FE solver is quite straight forward. You should use the following steps:

STEP 0: Get the stress tensor s, the damage variable D, the temperature T and the equivalent plastic strain ep,eq at the beginning of the time increment

STEP 1: Calculate the equivalent stress seq at beginning of the time increment with the yield criterion of your choice (e.g. von Mises, Tresca...)

seq=f(s)

STEP 2: Calculate the plastic flow direction n according to:

nij=dseq / dsij

STEP 3: Calculate the equivalent plastic strain rate dep,eq/dt from the JC constitutive equation

dep,eq/dt = f(seq, T, ep,eq)

STEP 4: Calculate the plastic strain rate tensor

dep,ij/dt=dep,eq/dt*nij

STEP 5: Calculate the stress rate tensor

dsij/dt=(1-D)*Cijkl *(dekl/dt -dep,kl/dt)

where C is the fourth rank stiffness tensor. For the specific case of isotropic elasticity, the above relation becomes:

dsij/dt=(1-D)*L *(dekk/dt -dep,kk/dt)*1ij+2*(1-D)*G *(deij/dt -dep,ij/dt)

where L and G are the Lamé coefficients. For the even more specific case of isotropic elasticity and purely deviatoric plasticity, the stress rate is given by:

dsij/dt=(1-D)*L dekk/dt*1ij+2*(1-D)*G *(deij/dt -dep,ij/dt)

STEP 6: Calculate the plastic strain tensor and equivalent plastic strain at the end of the time increment

ep,ij=ep,ij+dep,ij/dt*dt

ep,eq=ep,eq+dep,eq/dt*dt

STEP 7: Calculate the stress tensor at the end of the time increment

sij=sij+dsij/dt*dt

STEP 8: Calculate the damage indicator at the end of the time increment

D=ep,eq/ef

plastic strain ( and damage) is local, stress tensor resulting from it is global, assuming the increment as linear (this presumes convexity) actual plastic strain+increment (epi+deltepi) result in a damage value (Di), that have to be in equilibrium for the global problem resulting in using them, iteration over i can converge using a criteria based on final damage value (convergence is not insured if non convex)