# rctron's blog

## How to determine the reference rate of shearing and rate sensitivity for power-law rate dependent crystal plasticity formulation?

In single crystal plasticity, the material strain hardening is specified by the slip system strain hardness which is determined from the strain hardness function (Eqn 1, see attached). Its parameters can be determined by fitting the equation to the experimental stress-strain curve.

## How is this multiaxial relationship derived in this paper?

How did one arrive at the red-underlined part in the equation (2) from differentiating equation (1)? Please see the picture:

https://imgur.com/a/FZBUaY6

The paper referred here:

Chen, Y., Zhuang, W., Wang, S., Lin, J., Balint, D., & Shan, D. (2012). Investigation of FE model size definition for surface coating application. Chinese Journal of Mechanical Engineering, 25(5), 860-867.

## CP model

I am new to crystal plasticity simulations and have been studying the concepts from "Introduction to Crystal Plasticity" in Mechanics of Microstructured Materials book.

## Input file for the Single crystal plasticity subroutine Nonlinear Finite Elements for Continua and Structures by Ted Belytschko

Can anyone provide me with the input file for the example shown in the book Nonlinear Finite Elements for Continua and Structures by Ted Belytschko et al? The poly-slip, rate-dependent, single crystal plasticity VUMAT subroutine that is available publicly is attached in the following link. I have been trying to reproduce the results in Fig. 13.11 to Fig. 13.13. in the book, but am not successful in doing so. Can anyone please provide me with a working example input file for the problem?

https://gofile.io/d/xI9QSV

## Input file for the CPFE VUMAT in Nonlinear finite elements for continua and structure

I am learning crystal plasticity and its implementation as VUMAT subroutine from the book Nonlinear finite elements for continua and structure. I am aiming to gain more insight about the implementation by studying the poly-slip, rate-dependent, single crystal plasticity subroutine provided in the solution manual.

However, I couldn't reproduce the example in the book successfully, as I believe I have made errors in defining the material properties in the Abaqus input file. So, can someone please provide the input file for the associated VUMAT subroutine?

## How to include temperature effects on the shear rates in Dr. Huang's crystal plasticity code

I am using Dr. Huang's crystal plasticity code for an adiabatic process where temperature increase due to deformation need to be calculated. Dr. Huang's CP UMAT code does not consider the temperature effect of shear rate or hardening. Is there a way to include temperature effects in the current UMAT code?

http://www.columbia.edu/~jk2079/Kysar_Research_Laboratory/Single_Crystal...

## When to use equation of state models in modeling high velocity impacts?

Equation of state models (Mie-Gruneisen equation of state etc) have been widely used to study hydrodynamic response of material during explosive deformation, ballistic impacts for a long time. As far as I understand, a hydrodynamic response is required to be incorporated in a model if the pressure of impact leads to an increase volumetric strength. That is the stress wave speed in the material exceeds the speed of sound in the material (v = sqrt(elastic modulus/density)).  Ballistic impacts occur at strain rates close to 10^9 to 10^12/s.

## How to combine VUMAT an VUEOS in Abaqus

Hi,

I have written a VUMAT for Johnson Cook Model. I would like to use subroutine VUEOS to define linear Mie-Gruneisen equation of state. The USUP type VUEOS subroutine can be found at Abaqus Documentation.

However, I am not able to figure out how to combine the two subroutines. What needs to be called from VUEOS into VUMAT?

## finding contact time from maximum displacement for hertzian contact

While going through the derivation of contact time for a hertzian contact as given in problem 3 at the following link http://s17.postimg.org/t1kq6mlxr/Capture.png , I am not able to understand how the integral form for contact time has come into picture. Can anyone explain the in-between steps to get the same? I understand that this is a very trivial problem but it will be a great help to understand the steps. Thanks.

## Dependence of fracture energy of ceramic on loading condition?

Literature suggests that the fracture strength of the ceramic tends to be higher in a dynamic loading condition than in static condition. This relates to the increase in the fracture energy in dynamic processes. Literature refers to an inelastic response prior to failure (Hugoniot elastic limit) the reason behind increased strength. Can anyone explain the phenomenon in a more lucid way, or guide me to an appropriate reference to understand this?

## Which is the best model to capture brittle fracture and failure of ceramics at moderate velocities?

Several models have been developed over the past decades to capture the fracture and failure of ceramic materials. JH2, JHB models are widely used for simulating the behavior of armor plates upon ballistic impact. I have a doubt regarding these models. Are these models only valid when the impact velocity is in the order of 1000m/s, as under such circumstances material transitions from elastic to elastic-plastic regime defined by the HEL Pressure? But what about when the impact velocity of the ceramic is around 300-400 m/s (a fraction of ballistic impact)?