Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
Optimization hinders evolution!
BE 205 Introduction to Biomechanics of Solids Jan.-May., 2016
Instructors: G. K. Ananthasuresh, Room 106, ME Building, suresh at mecheng.iisc.ernet.in
Teaching assistant: Varsha Vasudevan, varsha at cns.iisc.ernet.in
Lectures: Tu, Th: 02:o0 pm - 03:30 pm;
Venue: MRDG classroom, Ground floor, Biological Sciences Building

Homework #2
Assigned: Jan. 19th, 2016
Due: Jan. 26th, 2016
Points: 50
Additional points for work that is beyond instructor's expectation!

1. 15 points
   For sigmax = 100 MPa, sigmay = 60 MPa, and sigmaxy = 30 MPa in a chosen xyz coordinate system, do the following.
   (a) Plot the two normal stresses and the shear stress in a polar plot as we rotate the coordinate system about the z-axis from 0 to 360 degrees.
   (b) Find the principal stresses and principal planes and draw the Mohr's circle.
   (c) Assuming isotropy and using E = 5 GPa and nu = 0.45, repeat (a) and (b) for strains.
2. 15 points
   For ux = (X + 0.001*c*Y) - X, uy = Y*(1 + c*0.002) - Y, and uz = (Y*0.004*c + 1.002*c*Z) - Z, find linear engineering strain and Green's strain tensors, first for c = 1 and then for c = 50.
3. 20 points
   Using the data of the previous problem, use linear strains for c = 1 and plot 3D spherical (orbital like) plots of normal stress and shear stress components as the coordinate system is rotated about azimuthal and elevation angles from 0 to 360 degrees. Use the following material properties of bone which is treated as an orthotropic material.
   E1 = 6.9 GPa, E2 = 8.5 GPa, E3 = 18.4 GPa
   nu12 = 0.49, nu23 = 0.14, nu13 = 0.12,
   G12 = 2.41 GPa, G13 = 3.56 GPa, G23 = 4.91 GPa