26 C. A. Sciammarella et al. Fig. 3.6 Schematic representation of the determination process of iso-derivatives fringes at different load levels for u(x,P). A similar scheme is utilized for displacements v(x,P) Fig. 3.7 Schematic of a tensile specimen subject to axial force and to bending stresses Fig. 3.6, the image corresponding to a given frame and a following frame are subtracted: Eqs. (3.17) and (3.18) are obtained, thus generating iso-derivative fringes. The specklegrams contrast depends on the correlation between the two interacting speckle patterns. Acquisition times and loading times are such that good contrast fringes are obtained. For example, in the case of the V displacements, isothetic lines in the direction of the vertical axis of the specimen are functions V(y,P,t) where t is the time corresponding to a frame number of the recorded images, by the chain rule of differentiation, ∂v(y, P) ∂t = ∂v ∂y ∂y ∂t + ∂y ∂P ∂P ∂t (3.19) Equation (3.19) indicates that if we have a film recording of displacements and times for these displacements, and at the same time recordings of the loads corresponding to the film frames, we can get also the time derivatives of the projected velocities of deformation. A similar equation can be written for the U(x,P) component.
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