[Study] Multi time resolution

[WeiyiVirtonomy]

A 2d test case of multi-time resolution contact problem

Description

The left brick represents a catheter with higher stiffness, while the right brick represents the softer arterial wall. The catheter and the aorta have contact interaction.

By using single time step size, the configuration is:

By using a dual loop, the aorta particles are strongly oscillating:

[WeiyiVirtonomy]

@Xiangyu-Hu I have pushed a 2D test case for multi-time-resolution problems. I would appreciate it if we could schedule some time to discuss how to deal with this problem.

[WeiyiVirtonomy]

@DongWuTUM Could you explain the left Cauchy damping to me again? Is the damping stress elastic_solid_.NumericalDampingLeftCauchy(...) * inverse_F.transpose()?

[DongWuTUM]

@DongWuTUM Could you explain the left Cauchy damping to me again? Is the damping stress elastic_solid_.NumericalDampingLeftCauchy(...) * inverse_F.transpose()?

If you use the Green-Lagrangian strain tensor $\mathbb{E}$ to calculate stress, then you should use the 'NumericalDampingRightCauchy(...)' which can be added directly to the second Piola-Kirchhoff stress $\mathbb{S}$.

If you use left Cauchy-Green deformation gradient tensor $\mathbb{b}$, then you should use the 'NumericalDampingLeftCauchy(...)' which can be added directly to the Kirchhoff stress $\mathbb{\tau}$.

[WeiyiVirtonomy]

@DongWuTUM Could you explain the left Cauchy damping to me again? Is the damping stress elastic_solid_.NumericalDampingLeftCauchy(...) * inverse_F.transpose()?

If you use the Green-Lagrangian strain tensor E to calculate stress, then you should use the 'NumericalDampingRightCauchy(...)' which can be added directly to the second Piola-Kirchhoff stress S .

If you use left Cauchy-Green deformation gradient tensor b , then you should use the 'NumericalDampingLeftCauchy(...)' which can be added directly to the Kirchhoff stress τ .

Thanks a lot!