Final answer:
To find the locations of the two points after deformation, we substitute the coordinates into the displacement equations. The change of distance between these two points can be estimated using the definition of strain εxx. Comparing the result with the displacement field, both methods give a consistent value of 0.02.
Step-by-step explanation:
To find the locations of the two points (0,0,0) and (5,0,0) after deformation, we need to apply the displacement field to the initial positions. Substituting the coordinates into the displacement equations, we have:
Point (0,0,0) after deformation: u = 0.02(0) + 0.02(0) - 0.01(0) = 0cm, v = 0.01(0) - 0.02(0) = 0cm, w = -0.01(0) + 0.01(0) = 0cm
Point (5,0,0) after deformation: u = 0.02(5) + 0.02(0) - 0.01(0) = 0.1cm, v = 0.01(0) - 0.02(0) = 0cm, w = -0.01(5) + 0.01(0) = -0.05cm
The change of distance between these two points after deformation can be estimated using the definition of strain εxx. The strain component εxx is given by the change in length in the x-direction (Δx) divided by the initial length (x). In this case, since the points are on the x-axis, the initial length is 5cm and the change in length is 0.1cm. Therefore, εxx = Δx / x = 0.1/5 = 0.02.
Comparing this with the displacement field, we can see that the change of distance is consistent with the strain component. Both methods give a value of 0.02, which means that the change in distance between the two points is 2% of the initial distance.