This document summarizes a course project on the maximum stiffness to weight ratio of an auxetic material model. The project involves designing a 3D model, fabricating it using PLA plastic, and testing it to failure. The model is then analyzed using mechanics of materials calculations and Solidworks simulation. The results from MOM analysis, Solidworks and experimental testing are then compared, showing errors potentially due to coarse meshing and material property approximations. The experimental stiffness coefficient is 176.6 kN/m and experimental stiffness to weight ratio is 4647 kN/kg.m.

1. COURSE PROJECT
MECHANICS OF MATERIALS
BY
DINESHY ,
NAVAHARSHA,
AJAYRAJ BALLA

2. AIM : MAXIMUM STIFFNESS TO WEIGHT RATIO AND
ANALYSIS OF MODEL
CONTENTS
1.TOPOLOGY
2.SOLIDWORKS MODEL
3.ACTUAL MODEL
4.EXPERIMENT RESULTS
5.ANALYSIS
6.COMPARISION

3. INTRODUCTION
(+) POISSION RATIO : LATERAL AND AXIAL STAINS HAVE DIFFERENT SIGNS
(-) POISSION RATIO : BOTH WILL HAVE SAME SIGN
Auxetic structures will have NEGATIVE POISSION RATIO
Chiral structures are one of Auxetic structures
DIMENSIONS OF MODEL 160*19*20 (L*B*H)
LIGAMENT
NODE

4. SOLIDWORKS MODEL
THICKNESS 1 mm
NODE OUTER RADIUS 2mm
INNER RADIUS 1mm

5. ACTUAL MODEL
•
PLA MATERIAL IS USED FOR MAKING
WEIGHT OF BEAM 38 grams

6. MAXIMUM LOAD :700N
MAXIMUM DEFLECTION :4.59mm
F/DELTA = 0.1766
EXPERIMENTAL DATA

7. ANALYSIS

8. CALCULATIONS
MOM STIFFNESS COEFFICIENT k(F/DELTA) = 700N/(3.15*0.001)= 222.222 kN/m
STIFFNESS TO WEIGHT RATIO(k/w) = 222.222/(38*0.001) = 5847.94 kN/Kgm
•EXPERIMENTAL (FROM SLOPE OF GRAPH) : 176.600 kN/m
•EXPERIMENTAL STIFFNESS TO WEIGHT : 4647 kN/kg.m

9. `
MOM
ANALYSIS EXPERIMENTAL
DATA
SOLIDWORKS
SIMULATION
DEFLECTION 3.15 4.59 3.86
K 222.222 KN/m 176.600 KN/m 181.3KN/m
K/W 5847.94 KN/Kg.m 4647 KN/Kg.m 4771.05 KN/Kg.m
ERROR FOR
DEFLECTION
WITH
EXPERIMENTAL
DATA
28.9% 15.9%
COMPARISON

10. WHY ERROR?
•
CALCULATING INERTIA WE HAVE TAKEN 5mm INTERVAL SPACING WHICH BECAME
LARGE.
SMALLER INTERVALS CAN REDUCE ERROR PERCENT
MOM ANALYSIS ERROR DUE TO :
SOLIDWORKS SIMULATION ERROR DUE TO:
1.COARSE MESHING IS TAKEN FOR MODEL
2.ACTUAL YOUNGS MODULUS OF FABRICATED MODEL IS DIFFERENT FROM THE
ABS MATERIAL YOUNGS MODULUS

11. THANK YOU
•