The kinematics and dynamics of 3-D displacement fields

In the last few decades Experimental Mechanics, helped by advanced technologies to gather 3-D spatial information in non-transparent media, has evolved into a very general tool. It has become possible to observe the internal volume of engineering materials and in the area of biomechanics living internal tissues. This paper contains a brief review of Continuum Mechanics mathematical models that are available to formulate problems in 3-D including large deformations. The extension of the experimental methods that measure displacements in 2-D to 3-D is presented. Two important cases are considered: a) use of deterministic signals, b) use of random signals. In order to separate the complexity of the subject of 3-D analysis from the difficulties that arise from the use of random signals, the connection between mathematical models and their experimental determination is presented utilizing deterministic signals. The extension of the use of random signals to the determination of displacements in 2-D to 3-D is outlined. A new method to extract displacement information from random signals is developed and an example of application is provided. Two methods to extract displacement information in 3-D, the classical method based on displacement projections and discrete image correlation (DIC) based on following gradients of intensities are compared. There are many complex steps involved in data processing aside the basic approach, this circumstance makes difficult a comparison between the two methods, however it is possible to conclude that the results are in fair agreement