Determine a unique set of the constant values
Course:- Mechanical Engineering
Reference No.:- EM132187179

Assignment Help
Expertsmind Rated 4.9 / 5 based on 47215 reviews.
Review Site
Assignment Help >> Mechanical Engineering

Applied Elasticity and Plasticity Project -

Use a computer program to draw the yield surfaces of the yield criteria given in the table below (a) on deviatoric planes at ρ = 0 and four other different values, where ρ = I1/√3 = √3σm = √3σoct; (b) on meridain planes at θ = 0o, 15o, 30o, 45o, and 60o. (c) Also draw the 3-D perspective views of the yield surfaces in the principal-stress space from three different angles.

Yield Criteria

Uniaxial Compressive Yield Stress

Uniaxial Tensile Yield Stress

von Mises

50,000 psi

50,000 psi


2,000 psi

200 psi

Yield criterion defined below

2,000 psi

200 psi

The yield surface of the yield criterion is expressed in the form:

F(σ) = √3τ0 - r(θ, σ0yc, ks) = 0 (1)

where σ is the stress tensor whose Cartesian components are σij, σ0 = I1/3, I1 = σkk = first invariant of stress tensor, τ0 = √(2J2/3), J2 = sijsij/2 = second invariant of the stress deviator sij = σij - 1/3 δijσkk, δij = Kronecker delta, θ = 1/3 cos-1((3√3)/2)J3J2-3/2) = similarity angle which represents the polar angle in the deviatoric section, J3 = 1/3 sijsjkski = third invariant of sij, σyc is the uniaxial compressive yield stress, ks is a constant which determines the size of the yield surface, and function r(θ, σ0yc, ks) represents the deviatoric section of the yield surface which can be expressed by the formula


where rt and rc represent the tensile and compression meridians, respectively, which are defined as:


The equations above involve eight parameters α0, · · ·, α3, β0,· · · , β3. These eight parameters and constant ks can be determined based on the following conditions:

1. The two apices of each curve of Eq. 3 and Eq. 4 on the horizontal axis must be common to both curves.

2. The point representing the yield stress under uniaxial tension has to be on the yield surface.

3. The point representing the yield stress under uniaxial compression has to be on the yield surface too.

The above conditions are not enough to determine a unique set of the constant values. Use any set of constants fulfill the above conditions for your project. Include a section in your project report to show the values you use and explain and show calculations how you determine the constants.

Note - It has to be done in Matlab. As for the report of 1000 words need Abstract, intro, procedure, discussion of results, conclusion.

Attachment:- Assignment File.rar

Put your comment
View Conversion
  1. user image

    It has to be done in matlab, as for the report of 1000 words i need Abstract, intro, procedure, discussion of results, conclusion. The project is due on the day of the last lecture of this class. Hand in a hardcopy of typed project report by the due date. The report should at least include your thinking and explanation in working out the problem, the computer software you used, how to generate the input data, how to run the program, the computer-generated plots of the yield surfaces, your comments and discussions, and appendixes for the computer printouts of your input data and output results with essential information highlighted.

  2. user image

    Organize your report according to the following general guidelines: Cover page: Giving title and dates, etc. Table of Contents: Listing the sections and figures. Abstract: Summarizing the report including important findings. Introduction: Describing the importance of the work done. Procedure and Results: Including figures and/or tables. Discussion of Results: Giving a thorough analysis and interpretation of results. Conclusions: Giving a summary of the findings. Appendix: Showing important calculations and formulas. Figures and tables should be numbered and must have captions explaining what the figures and tables are illustrating. You must always show units of axes for figures and the units for the numbers listed in the tables.

Ask Question & Get Answers from Experts
Browse some more (Mechanical Engineering) Materials
Assuming air to be an ideal gas, what would be the mass of air in a classroom of size 20 ft x 15 ft x 9 ft assuming the pressure inside the classroom is 1 atm and the classroo
(a) Sketch the cycle on a p V diagram. (b) Calculate the net work for the cycle, in kJ. (c) Calculate the heat transfer for process 2 3, in kJ. (d) Calculate the heat transf
An ideal diesel cycle has a compression ratio of 16.8 and a cut off ratio of 1.63. Determine the maximum air temperature and the rate of heat addition to this cycle when it pr
A double strap butt joint had to carry a load of 17kN. the ultimate shear strength of the rivets used is 260MPa and a factor of safety of 8 is to apply. if the rivet diamete
The transfer function between the elevator input and the pitch attitude of a plane is given by: Design an autopilot controller (using a lead compensator) for the system so tha
A section of Magnesium alloy is being tested .It is subjected to 12 kN compression force.The length is 50 mm.The cross section is 10 mm by 10 mm.The longitudinal strain is 1.5
This means that V is invariant under the simultaneous operations (i) a rotation through any angle α about the axis Oz, and (ii) a translation cα in the z-direction. What con
The analysis of a mass basis of an ideal gas mixture at 50 F, 25 lbf/in2. is 60% CO2, 25% SO2, and 15% N2. The analysis in terms of mole fractions. Determine: The apparent mol