Assignment 4
Objective
The aim of the project is to run 7 different cases for the given model and vary the parameter for the material & infer the results on each case.
Law 1
Law 1 defines an isotropic, linear elastic material using Hooke'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.
This material law is used to model purely elastic materials. The material stiffness is determined by only two values: Young's modulus (E), and Poisson's ratio ( υ">υ ). The shear modulus (G) can be computed using E and ν">ν, as:
| ρi - | Initial density. |
| E - | Young's modulus |
| υ - | Poisson ratio. |
Material Card
Law 2
This law represents an isotropic elastoplastic material using the Johnson-Cook material model. This model expresses material stress as a function of strain, strain rate, and temperature.
In this model, the material behaves as a linear-elastic material when the equivalent stress is lower than the plastic yield stress. For higher stress values, the material behavior is plastic and the stress is calculated as
Damage and rupture defined with 2 parameters for each principal direction.
Epsmax is the max plastic strain for element deletion for any loading.
εt - It is the beginning of tensile damage. From this point, the stress value defined in the curve is reduced by the factor.
Material Card
Results
Law 1
This law is used for the pure elastic material so the material undergoes the maximum deformation & return to its original state after the loading. The stress value is maximum in this method & it is not preferred for the loading which operates above the yield stress point.
The displacement value is 5mm. Strain value is 0.2021 & plastic strain is zero along with the thickness since it works only within the yield stress region. The energy error around 3% & for QEPH the error values is positive since we consider the hourglass error the error value is less.
Energy plot
The max total energy is 9e5 J & value keeps on increasing since it operates in the elastic region the energy raise occurs.
Law 2
In law 2 the failure value of the element is not provided & the maximum stress value is produced so above which the element can undergo stress. The element is not deleted & the element remains in the plastic region after it exceeds the yield stress value.
The displacement value is 5.011mm. Strain value is 0.3299 & plastic strain is 1.232 along with the thickness. The energy error around 3% & for QEPH the error values is positive since we consider the hourglass error the error value is less.
Energy plot
The max total energy is 70000 J & the value keeps on increasing since the element
Law 2 Epsmax Failure
The eps max value for the element is provided & once the element exceeds the stress limit the element gets deleted without any crack.
The displacement value is 27.58mm. Strain value is 0.1481 & plastic strain is 0.151 along with the thickness. The energy error around 3% & for QEPH the error values is positive since we consider the hourglass error the error value is less. The displacement value is high since the element doesn't crack & get deleted.
Energy plot
The max total energy is 26000 J & reaches its maximum value after 4ms.
Law 2 Epsmax Crack
The criteria for crack advancement are provided & the element undergoes deformation & once it exceeds the eps max value the element gets deleted.
The displacement value is 13.27 mm. Strain value is 0.1381 & plastic strain is 0.1489 along with the thickness. The energy error around 4% & for QEPH the error values is positive since we consider the hourglass error the error value is less.
Energy plot
The max total energy is 30000 J & reaches its maximum value after 4.5ms.
Law 2 Epsmax Nofail
The failure card is deleted to look for the variation of the stress value in the element.
The displacement value is 18.58 mm. Strain value is 0.1381 & plastic strain is 0.15 along with the thickness. The energy error around 1.2% & for QEPH the error values is positive since we consider the hourglass error the error value is less.
Energy plot
The max total energy is 26000 J & reaches its maximum value after 4ms.
Law 27
It is the combination of elastoplastic johnson cook material & it occurs only in the tension. The proper crack of the element & the element deletion occurs in this method.
The displacement value is 6.013 mm. Strain value is 0.1674 & plastic strain is 0.2038 along with the thickness. The energy error around 1.1% & for QEPH the error values is positive since we consider the hourglass error the error value is less.
Energy plot
The max total energy is 40000 J & reaches its maximum value after 4.5ms.
Law 36
Law 36 only need 2 input for the parameters & the values are calculated
The displacement value is 2416 mm. Strain value is 0.1416 & plastic strain is 0.1599 along with the thickness. The energy error around 0% & for QEPH the error values is positive since we consider the hourglass error the error value is less. The displacement is very high & the law is not accurate.
Energy plot
The max total energy is 1.4e10 J & the value keeps on increasing since the proper limits for the element are not set.
Inference
| Law | No of cycles | Energy error (%) | Mass error (%) | Simulation time (s) | Von mises stress | Strain | Displacement (mm) | Plastic Strain |
| Law 1 | 47969 | 0.3-3.6 | 0 | 129.04 | 1.09E+04 | 0.2021 | 5 | 0 |
| Law 2 | 48737 | (-0.3) - 3 | 0 | 127.62 | 4.25E+02 | 0.3299 | 5.011 | 1.232 |
| Law 2 epsmax failure | 49480 | (-0.6) - 1 | 0 | 127.88 | 3.28E+02 | 0.1481 | 27.58 | 0.151 |
| Law 2 epsmax crack | 49397 | (-1.1) - 4 | 0 | 121.07 | 2.95E+02 | 0.1381 | 13.27 | 0.1489 |
| Law 2 epsmax nofail | 49405 | (-0.6) - 1.2 | 0 | 126.5 | 3.11E+02 | 0.1381 | 18.58 | 0.15 |
| Law 27 | 49356 | (-0.6) - 1.1 | 0 | 125.53 | 3.29E+02 | 0.1674 | 6.013 | 0.2038 |
| Law 36 | 52691 | 0 - 0.7 | 0 | 146.75 | 4.84E+02 | 0.1416 | 2416 | 0.1599 |
The number of cycles for the law 2 & 27 is almost equal. Law 1 has the lowest number of cycles since no element is deleted & law 36 has the largest number of cycles. The energy error for all the cases is under the acceptable region. The mass error in all the cases is zero so it is not used for comparison. The Simulation time for law 36 is the highest & least for case 4.
Stress study
The highest value of stress in Law 1 is because the element working in the elastic region only. The eps max crack has the lowest stress value since the crack deformation factor also consider so the proper element deformation occurs. Law 2 has highest stress value in the johnson hook method since we delete the Eps max the element expands until the ultimate stress value.
Plastic Strain
In law 1 value is zero since element doesn't undergo plastic region & in law 2 the epsmax value is deleted so the element expands till the fracture so the strain value is high. The other methods value of the plastic strain is low since element gets deleted once it crosses the epsmax value.
Displacement
Law 36 the value of the displacement is unrealistic so it is neglected for comparison. The case 3,4 & 5 have high displacement value since the element gets deleted after it reaches the epsmax value. Law 1 & Law 2 value is due to the element operating regions & Law 27 provides accurate displacement results by considering all the parameters.
Conclusion
In case 1 is applicable if the element deforms within the elastic limits & Law 36 provides unrealistic this due to the value of the input provided & case 4 provides best results & to get more accurate results the input parameters are to be obtained from the physical testing. Law 27 is best suited for this simulation & it is generally used for the brittle material since the material used for the simulation is aluminum which is brittle so this law is preferred.