FINITE ELEMENT METHOD
Although the Finite Element Method (FEM) approach seems simple, its implementation is much more complicated especially when a 3D model is used for viscoelastic material. For simplicity it is assumed that the compressive force is applied only in z direction and strain in both x and y directions is zero. Hence, elastic strain is considered only in z direction while velocity of viscous fluid is also considered only in x and y direction. The proposed simplifications are based on the nature of the force applied and deformation produced in tactile sensing applications. The 3D model of viscoelastic material before and after deformation is depicted in figure below.
For tactile sensing application, the objects are manipulated by touch. More precisely, they are manipulated with applying force in compressive manner or contact force in sliding manner. The latter one is namely considered for texture/roughness detection. For softness analysis, vertical compressive load need to be applied. Therefore, the attention is concentrated on compressive force. The force boundary condition in the manner of compressive force requires distributed force or pressure on the surface of the object. To apply a compressive force or pressure, two parallel surfaces are required: one the supporting surface and the other for applying the pressure. A Compressive force is naturally applied to an object via a probe or similar apparatus which should have a limited contact area with the material. The contact surface is always considered flat that means there is no irregularity within the shape of model. Consequently, triangular element is not required to deal with shape of the object. On the other hand rectangular element provides the flat contact surface naturally. Regarding what was mentioned for the consideration of strain and manner of applying force, the model should consist of rectangular quadratic element(s).
There is one more consideration that is required to be taken into account and that is the order of the element. The model of viscoelastic material consists of a viscous media as well as a hyperelastic material. The element of the model should comply with fluid properties. Regarding to deformation of the model, the viscous media flows through the model under the pressure of external applied force.
Regarding to what was mentioned for solid in the previous section; the same procedure is used for fluid with the difference that in fluid, velocity, which is a field vector, is the independent variable. Therefore, rate of deformation is used with respect to time.
For more information refer to “Method and system for real time characterization of soft materials and biological tissues based on nonlinear properties, Patent No. 10126219”.