# Help about stress calculations in a ionic crystal

Dear Lammps Users

The unit cell of LiMn2O4 crystal considered in my simulations contains 56 ions (8 lithium atoms, 16 manganese atom and 32 oxygen atoms) .In my main refrence paper

# # “Molecular Dynamics Simulations of SOC-Dependent Elasticity of LixMn2O4 Spinels in Li-Ion Batteries”# Doi: 10.1149/2.147306jes# # That i want to reproduce the results of this paper. Specificly I want to calculate the virial stresses. But in the content of this paper I don’t understand some lines :# # Although we apply the strain to the equilibrated system, the resultant stresses fluctuate depending on which equilibrium point is chosen. In order to obtain a converged stress, convergence tests are conducted by increasing the number of selections. We find that 400 points are enough to reach convergence#

For each selected point, four different simulations are performed: three uniaxial deformations in the x, y, z directions and one hydrostatic deformation**. Stresses are calculated in the form of the virial stress**

Now my questions are :

1- What is the equlibrium point? What is the number of selection?

2- What is the hydrostatic deformation?

commencing with the easiest,

2 - i believe they mean isotropic - you apply the same amount of strain along x, y and z. the hydrostatic strain is the average of the three normal strains (exx, eyy, ezz).

have a look eg here
http://www.continuummechanics.org/cm/hydrodeviatoricstrain.html

1 - i didn’t read the paper carefully but i suspect they are taking different equilibrium configurations for each SOC and reporting Young’s modulus as the average over the set having size “number of selections”.

again, this is just a guess!

ciao,

luca

Dear Lammps Users

The unit cell of LiMn2O4 crystal considered in my simulations contains 56 ions (8 lithium atoms, 16 manganese atom and 32 oxygen atoms) .In my main refrence paper

# # “Molecular Dynamics Simulations of SOC-Dependent Elasticity of LixMn2O4 Spinels in Li-Ion Batteries”# Doi: 10.1149/2.147306jes# # That i want to reproduce the results of this paper. Specificly I want to calculate the virial stresses. But in the content of this paper I don’t understand some lines :# # Although we apply the strain to the equilibrated system, the resultant stresses fluctuate depending on which equilibrium point is chosen. In order to obtain a converged stress, convergence tests are conducted by increasing the number of selections. We find that 400 points are enough to reach convergence#

For each selected point, four different simulations are performed: three uniaxial deformations in the x, y, z directions and one hydrostatic deformation**. Stresses are calculated in the form of the virial stress**

Now my questions are :

1- What is the equlibrium point? What is the number of selection?

These questions are best asked to the authors.

2- What is the hydrostatic deformation?

Hydrostatic deformation is a deformation under a hydrostatic condition - meaning stress applied to all sides of the material is the same. If the material is isotropic, then it will result in an isotropic deformation, but if the material is anisotropic, then it will be an anisotropic deformation. So hydrostatic does not necessarily equal to isotropic.

Ray