Week - 9 Material Modeling from Raw Data

Aim :

Use the diagram of the true stress-strain curve of graphite iron casting. Two curves are there for different material structures. Students need to pick any one of them and use the data to create either a MAT_024 or MAT_018 material model and then validate it. 

Solution :

 It is very important to convert the material data into a material law that the solver can understand.To model the linear behaviour of a material we just need the density , youngs modulus and poisson ratio.LS Dyna consists of the following materials cards as shown below :

1.Elastic 

a.Linear : Isotropic (MAT00)

b.Non Linear : Hyperelastic(MAT*077):Orthod aniso trophic :Their properties changes with direction.

2.Elastic -Plastic :These can rate dependent or rate independent .The following laws are used :

a.MAT003:PLASTIC KINEMATIC:

b.MAT0012:Isotropic Elastic Plastic:

c.MAT0015:Mat_Johnson_Cook:This considers the thermal and damage effects.

d.MAT098:Simplified_Johnson_Cook: This does not consider the thermal and damaging effects.

The following material cards are used the most to model metals :

mat_024,mat_18 and mat098

3.For a rigid material we can use mat 20

Elastic materials can be defined as shown below :

Strain rate is the rate of deformation caused by strain in a material within a corresponding time. This gauges the rate where distances of materials change within a respective period of time.

In order to input the model the material we have to convert the engineering stress -strain into true stress and strain by the following formula :

Once we get the true stress strain curve we convert it into plastic strain curve and feed this data into the material modelling.

Now we will discuss about hyperelastic material :

Hyperelastic material models are regularly used to represent the large deformation behavior of materials with FEA. They are commonly used to model mechanical behaviors of unfilled/filled elastomers. In addition to elastomers, hyperelastic material models are also used to approximate the material behavior of biological tissues, polymeric foams, etc.

Linearly elastic materials are described through two material constants (like Young’s modulus and Poisson ratio). In contrast, hyperelastic materials are described through a strain-energy density function. The strain-energy density can be used to derive a nonlinear constitutive model (i.e., stresses as a function of large strain deformation measures like deformation gradient or Cauchy-Green tensors, etc.). There are several models proposed in the literature such as the Neo-Hookean, Mooney-Rivlin and Signorini models, 

Now we will extract data from the following image using data digizer as shown below :

Using the digitizer app we get the following curve :

We will apply this to the following :

We will set up the boundary condition as shown below :

We are constraining the following nodes in the x and z directions in translation as shown below :

Now we will apply the y constrain in translation on the middle node as shown below :

Now we will apply the displacement condition on using the prescribed motion card as shown below :

 We have defined the displacement curve as shown below :

Now we will define the prescribed motion card as shown below :

Now we will define the curve set id 2 which will be the curve for the material :

Now we will define the general cards as shown below :

We have defined the material card as shown below :

Therefore we have applied the following cards :

We have got the following results :

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