Problem 2.

This problem is based on Lecture 24 (L24) where the prosthesis geometry was created, and the

simulation was started. Please refer back to that lecture as needed to complete this homework. Part

D also ties back to Norton Chapter 6 on Fatigue Failure Theories - so please read that chapter in

preparation. Many of the dimensions are also listed in the L24 Notes. The goal here is to explore

the many modeling and design decisions that need to be made in realistic applications.

• Material:

Cup

Outer

Cup

Liner

Lip

Stem

• Cup Liner- Locate under Plastics,then choose PA Type6

• Stem - Locate under Titanium Alloys then choose Commercially Pure CP-TI UNS

R50700 Grade4(SS)

Cup Outer - Same material as Stem

Mesh: Use system default size Curvature based mesh, tetrahedral elements.

Fixture:

• To be specified by the user based on experience gained in previous exercises and an

understanding of the hip replacement process described above.

• Carefully consider how and where restraints are applied to the model relative to how and

where external loads are applied.

• External Load:

• Person's weight =145 lb. You may decide to use a different external load. If so, include

the reason for your decision in part(a)of the exercise listed below./nProblem 2, continued.

Determine the following:

• Develop a finite element model that includes material specification, realistic fixtures, external

load(s), mesh generation, and solution.

a.

On the upper half of one page, create a plot showing all fixtures and loads applied to

the stem and to the cup assembly. Manually label vectors representing Fixtures to

differentiate them from vectors representing External Loads. This image represents

the finite element equivalent of a free-body diagram. Do not show stresses or a mesh

on this plot. On the lower half of the page, provide:

• good reason(s) and justification for fixtures and/or external load(s) applied to

the cup outer. Discuss items such as magnitude(s), direction(s), and point(s)

of application.

good reason(s) and justification for fixtures and/or external load(s) applied to

the stem. Discuss items such as magnitude(s), direction(s), and point(s) of

application.

If an external load other than the person's given weight is used, provide

insight into the reasoning used to determine and recommend an alternate

load.

b. Create a plot of von Mises stress contours displayed on a deformed image of the

stem and cup assembly. Also, incorporate automatic labeling of the maximum von

Mises stress.

c. Create a plot showing Contact Pressure between the "ball" (located at top of the

Stem) and the Cup Liner (located between the ball and Cup Outer). Enlarge contact

vector size to make vectors easily visible, but in reasonable proportion to the overall

image. Select a view that clearly shows the three-dimensional nature of contact

pressure variation.

d. Question: Based on your understanding of fatigue in metals, does the maximum von

Mises stress determined in part (b) place this Stem and Cup Assembly in danger of

fatigue failure (again refer back to Norton Chapter 6 as needed)? Discuss practical

reasons for your answer in terms of stress repetitions expected for the assembly.

Also discuss the engineering reasons for your answer. Consider topics such as stress

magnitude, type of stress (tensile versus compressive), and material characteristics of

the general class of titanium steels.