Homework, Quizzes, Simulation Examples — Volumetric and Deviatoric Behavior — Lesson 4

Simulation Examples

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

(1) Wine Cork Pullout Simulation

Cork material is widely used in wine sealing because of its impermeability and light weight. Another essential feature cork has is its almost zero Poisson’s ratio, which means squeezing or pulling in the longitudinal direction does not change its radius. This feature is important in providing good sealing. In this simulation, a wine cork being pulled out is simulated. The sealing pressure and the extraction force are used as parameters for evaluating the quality of sealing. Try to replicate the simulation and calculate these two values.  Download the zip file and extract the contents. Go through the Readme file. Follow along with the provided How To Video file.

(2) Hydraulic Lifting Jack

A hydraulic lifting jack uses hydraulic force to lift a weight that is several orders higher than the input force. This simulation uses hydrostatic fluid elements to model a hydraulic lifting jack and illustrate the concept of the bulk modulus. In practical applications, oil is usually used as the liquid in a hydraulic lifting jack, because the high bulk modulus of oil makes the liquid volume almost the same during the loading process. You are encouraged to follow the procedure in the Readme and video to replicate the model, and even take one step further to use the bulk modulus of air and check how that influences the lifting distance.  Download the zip file and extract the contents. Go through the Readme file. Follow along with the provided How To Video file.

(3) Air Shoe Simulation

This example uses a bladder-like air shoe to illustrate the concept of the bulk modulus. Hydrostatic fluid elements are used to model the air and the ideal gas law describes the air's behavior. Check out the model and find out what the difference is with and without air when the same amount of pressure is applied to the shoe base. Download the zip file and extract the contents. Go through the Readme file. Follow along with the provided How To Video file.

(4) Auxetic Design of a Shoe Base 

An auxetic structure expands in the transverse direction while being stretched in the longitudinal direction. Although the material could have a positive Poisson’s ratio, the overall geometry exhibits a negative Poisson’s ratio effect. Due to this unique property, the auxetic structure is widely applied to sports. This document illustrates a simulation of the auxetic structure of a shoe base. Download the zip file and extract the contents. Go through the Readme file. Follow along with the provided How To Video file.

Homework

(1) Bars under Tension (An Illustration of Poisson's Effect)

This simulation uses a uniaxial tension test to illustrate the effect of Poisson’s ratio. Five bars with the same dimension are stretched, and the transverse contraction is plotted. These bars have the same geometry and Young’s modulus, with the only difference being Poisson’s ratio. The Poisson’s ratio ranges from 0 to 0.5. Hand calculate the normal strain value in the transverse directions for each bar at time = 1 second (40.5% of strain in the longitudinal direction) and compare it to the simulation. Download the zip file and extract the contents. Go through the Readme file. Follow along with the provided How To Video file.

(2) Active Passive Lateral Earth Pressure Analysis  

Geomechanics is an area that studies the mechanical behavior of materials like soil, rock and aggregate materials. Understanding the behavior of geomechanical materials is crucial to civil engineering applications like foundations. This example shows the process of analyzing soil under passive and active earth-pressure. An active earth-pressure state is created by moving the retaining wall away from the soil, and the passive earth-pressure is produced by moving the wall against the soil. A Mohr-Coulomb material is used to study the plastic deformation of soil and its relationship with hydrostatic pressure. Go through the documentation file and answer the questions below.

 Download the zip file and extract the contents. Go through the Readme file. Follow along with the provided How To Video file.

The equation of Mohr-Coulomb's criterion of yielding is shown below, in which cohesive and friction angle are soil constants. If the left side of the equation (shear stress) is larger than the right side, yield happens.

(a) Explain why fewer soil yields occur in passive loading than active loading.

(b) What role does volumetric deformation play in the Mohr-Coulomb criterion? Hint: It helps if you plot the Mohr-Coulomb yield criterion in the x-y plane.