# Implicit vs explicit result in damage-mechanics+plasticity model

Hello experts, I am trying to model the response (damage+plasticity) and compare with commercial FE codes. I chose to follow explicit scheme and compare with available implicit solution. Attached image shows the comparison between implicit (commerical FE software) and explicit (my Python program).

As it can be observed, near the failure, i.e. applied strain > 0.05, there is a noise in the explicit solution. When I decrease the time step, the noise infact decreases.

(a) Is this noise is a result of explicit procedure ? or some thing wrong with my algorithm ?

(b) Some times, I can observed that the plastic strain increment is higher than total strain increment (this can be observed for an applied strain value > 0.06). This is absurd.

Can some one explain me the reasons for these two abnormalities? If I use smaller time step, I am going closer to the implicit solution. However, even at smaller time step, I am seeing some negative elastic strain increments (caused due to the use of eij_elastic = eij_total - eij_plastic).

In analytical world, how can I get critical time step. While code stress-strain equations, we assume unit dimensions: 1x1x1 mm3, while we dont need density of the material, Rho.

Recalling that critical time step, Dt = 1/(sqrt(E/rho)). For a typical material with E = 160e3 MPa and nu = 0.3, rho = 1200 kg/m3 I get Dt = 0.00271 (using rho in ton/mm3).  However, using 1.4e-7  as increment, I am not able to achieve better results with explicit results.

In the attached image, Dt = 1.4e-7 is used to get explicit response.

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