Stress Analysis - Graphical Representation of The Stress Field

Graphical Representation of The Stress Field

The complete state of stress in a body at a particular deformed configuration, i.e., at a particular time during the motion of the body, implies knowing the six independent components of the stress tensor, or the three principal stresses, at each material point in the body at that time. However, numerical analysis and analytical methods allow only for the calculation of the stress tensor at a certain number of discrete material points. To graphically represent in two dimensions this partial picture of the stress field different sets of contour lines can be used:

• Isobars are curves along which the principal stress, e.g., is constant.
• Isochromatics are curves along which the maximum shear stress is constant. This curves are directly determined using photoelasticity methods.
• Isopachs are curves along which the mean normal stress is constant
• Isostatics or stress trajectories are a system of curves which are at each material point tangent to the principal axes of stress.
• Isoclinics are curves on which the principal axes make a constant angle with a given fixed reference direction. These curves can also be obtained directly by photoelasticity methods.
• Slip lines are curves on which the shear stress is a maximum.