Assignment 4-RADIOSS Material Laws Challenge

AIM: To run the simulation for the plate and rigid ball by using johnson cook material and elastoplastic material with brittle failure as per the cases given in the question by using Radioss solver.

Objective:

• Run the simulation for all the cases given in the question
• Run the simulation by changing the material, shell properties, and failure parameters
• Run the simulation by converting the failure johnson model to LAW 1
• Tabulate the total number of cycles, energy error, Mass Error, and simulation time.
• Plot the graphs for all 7 cases.
• Compare all 7 Cases.

In FEA, the materials are specified to conduct simulation and analyze how a particular material behaves under stress and loading conditions.

Choosing the right material and providing reliable material data in performing a simulation is very important.

MATERIAL CARDS[LAWS]

• Law 1 - Elastic
• Law 2 - Johnson - cook
• Law 27 - Elastic - plastic-brittle
• Law 36 - Elastic-plastic - tabulated
• Law 42 - Ogden (Visco Hyperelastic)
• Law 70 - Foam

MATERIAL PROPERTIES

• Isotropic Elasticity
  
• Isotropic Elasto-plastic
• Composite and Anisotropic
• Viscuous
• Hydrodynamic
• Explosives

Law 1 [Isotropic Elasticity]:

• This law/MAT/ELAST defines an isotropic, linear elastic material using hook's law. This law represents a linear relationship between stress and strain. It is available for truss, beam(type 3 only), shell, and solid elements.
• Useful for elements attached to a rigid body. This material law is used to model purely elastic materials.
• This law is only applicable for small deformations.
• The material stiffness is determined by only two values: the youngs modulus(E), and Poisson's ratio(v). The shear modulus(G) can be computed using E and v.
• G = E/2(1+v)

Isotropic Elasto-plastic

• This law represents an isotropic elastoplastic material using the Jhonson -cook material mode
• This model expresses material stress as a function of strain. strain rate and temperature
• A built-in failure criterion based on the maximum plastic strain is available.

isotropic Elastic-Plastic Piecewise linear material [Law36]

• This is an isotropic elastoplastic material
• It's a user-defined function for the work-hardening portion of the stress-strain
• It's available for brick and shell element
• The elastic portion of material stress-strain curve defined by young modulus and Poisson's rat
• Material plasticity curves can be given for an arbitrary number of strain rates.
• Linear interpolation of strain-stress
• For a given strain rate.
• For a given plastic
• In order to avoid poor curve extrapolation during the strain calculation. a dummy curve defined for high strain rate value can be added in the model-typically the highest strain rate curve is r
• The curves have to be defined such as they don't intersect themselves in the strain range being used. Otherwise, the calculation may fail

There are 4 damage and rupture Parameters:

• Epsilon p max is the maximum plastic strain for element deletion for any loading(tensile, shear, or compression)
• Epsilon t is the beginning of tensile damage, from this point the stress value defined in the curve is reduced by the factor.

• Epsilon m is the end of the tensile damage. The stress value is null. but the element is not deleted
• Epsilon f is the tensile failure strain value for element del

Elasto-Plastic material with brittle failure [LAW27]

• This law combines an isotropic elastoplastic johnson-cook material model with an orthotropic brittle failure
• Material damage is accounted for prior to failure. Failure and damage occur only in tension. This law is applicable only for shells.
• Yield surface definition same as johnson-cook (LAW2)
• Useful for modeling brittle failure of glass.
• Damage and rupture are defined with 4 parameters for each principal direction

et= Strain at the beginning of tensile failure.

em= Maximum tensile strain at which the stress in the element is set to a value dependent on dmax1

dMax = Maximum damage factor

ef: maximum tensile strain for element deletion.

Viscous Material:

The viscous material is classified into two types called

• Hyperelastic [MAT/OGDEN or /MAT/LAW42:Ogde, Mooney-Rivlin]
• Tabulated foam [MAT/FOAM_TAB or /MAT/LAW70: Tabulated Foam]

Elastic [/MAT/OGDEN or /MAT/LAW42:Ogden,Mooney.-Rivlin]

• They are visco hyperelastic behavior (non-linear elastic).
• This law is generally used to model incompressible rubbers, polymers, foams, and elastomers.
• This material can be used with shell and solid elements
• Generally used to model polymers and elastomers

Tabulated foam [/MAT/FOAM _TAB or /MAT/LAW70: Tabulated Foam]

• Visco-elastic behavior
• The stress-strain relationship is defined by functions according to strain rate
• Unloading behavior is defined by: Curves and Hysteresis parameters.
  
  

CASES	ENERGY ERROR	INTERNAL ENERGY	KINECTIC ENERGY	EXTERNAL WORK	MASS ERROR	ELAPSED TIME	TOTAL NUMBER CYCLE	MATERIAL USED	CHANGES IN MATERIAL PARAMETERS	ELEMENT FAILURE BEHAVIOUR
CASE 1	0.8%	0.2730E+05	62.38	0.2721E+05	0.0	72.38	49407	LAW 2	Used default shell para and ran the simulation	Element deleted
CASE 2	4.1%	0.3082E+05	141.9	0.2980E+05	0.0	54.14	49407	LAW 2		the element will be cracked and deleted
CASE 3	0.8%	0.2744E+05	87.08	0.2736E+05	0.0	60.86	49216	LAW 2		element deleted
CASE 4	1.1%	0.3879E+05	3.931	0.3838E+05	0.0	64.03	49508	LAW 2		element deformed, cracked but not deleted
CASE 5	1.3%	0.8632E+06	3337.0	0.8658E+06	0.0	48.46	49508	LAW 1		element deformed, cracked but not deleted
CASE 6	0.8%	0.2954E+05	65	0.2940E+05	0.0	53.18	49508	LAW 27		element deleted
CASE 7	0.8%	0.7332E+05	44.42	0.7282EE+05	0.0	50.75	49508	LAW 36		element deleted

Result:

• Hence the simulation for all the cases was carried out with different materials laws.
• Hence the simulation for all the cases was run successfully
• Hence the simulation for all the cases was reviewed by
• Hence the graphs were plotted for all the cases success
• At last, compared all the results for those cases.

Conclusion and learning outcomes:

• I conclude that LAW36 is more suitable for real-world testing. cause it shows the behavior of elasticity and plasticity in the real world.
• In this challenge, I came to know about the different materials cards and their behavior.
• the failure criteria for the material cards
• how the deformation is happening for the elements from material cards.
• Damage and rupture parameters.
• How to define a plastic region curve with plastic strain and post-yield stress Values