# Homework, Quizzes, Simulation Examples — Large Deformation in Structural Mechanics — Lesson 5

### Simulation Examples

Several simulation examples are provided here. Each of them comes with a description file, video instruction, and Ansys simulation file. All of the simulations are conducted using Ansys Mechanical. Download the student version of the software here.

#### (1) Fishing rod

A fishing rod is a typical example of large deflection. Review this fishing rod simulation and try to explain why avoiding the use of large deflections make a difference in the result.

#### (2) Crack growth in a CT specimen

Sometimes when the deformation is too large or when it changes the topology of the geometry, it requires remeshing the model during a simulation. Crack propagation is a good example in which remeshing is needed. Check this simulation and pay attention to the meshes around the crack tip.  What could possibly happen when there is no remeshing?

#### (3) Driveshaft under rotation

This is another vivid example illustrating the importance of considering large deflection in a simulation. Can you explain why the radius of the drive shaft is expanding under torsion without large deflection? Is it realistic?

This bladder like air shoe model considers a situation where gas is contained within a solid upon which loads are applied. Due to the localized deformation, the large deflection effect needs to be considered. Explore the simulation and see how different the result is without large deflection.

#### (5) Plucked guitar strings

Tuning guitar strings is a process of applying stress to the strings. For a pre-stressed analysis, it is recommended that you turn on the large deflection. Why is that the case? You are encouraged to explore the simulation by excluding the large deflection and see how the string’s displacement versus time curve changes.

### Homework

#### (1) Calibrating hyperelastic material

Hyperelasticity is a characteristic material behavior of polymers and biological materials including, for example, rubber, veins and brain tissue. One common feature is that hyperelastic material usually undergoes large deformation. It requires a special material model and calibration of the material properties to account for the hyperelastic behavior.

In this homework, hyperelasticity is modeled using the Mooney-Rivlin material model. Several sets of experimental test data are provided for material property calibration. Follow the instruction files to reproduce the calibration process. After that, conduct a tension and torsion simulation on a specimen and obtain the moment versus rotation curve. Compare the result to the experiment result and see if they match. Answer the following questions:

a. What is the maximum strain level in the simulation? How does it compare to the yield strain of metal (for example steel)?

b. Assuming the maximum strain level is 100% in question (a), apply it to a one-dimensional bar of length 1 mm. First find out the deformed length with the large strain equation, then compare it to the value calculated using small strain equation. How much error is there in the small strain equation?