Introduction:

Soft solid materials are the ones which have modulus upto ~10 MPa; they are elastic or viscoelastic and they deform easily when subjected to external forces. Engineering materials, such as rubbers and thermoplastic elastomers, and soft biological tissues, such as skin, cartilage, liver and brain tissue, fall into this category. Understanding the mechanical response of these materials is important in many engineering and biomedical applications. The goal of this course is to expose the students and researchers of these diverse research interests to the principles of mechanics, its rich mathematical structure and how these tools can be useful for analyzing variety of problems related to soft deformable materials.

Displacement:

Displacement occurs when particles in a body moves from initial state to a final state.

If the length of a line joining the two particles remains unaltered in the initial and the final state, then the displacement is called rigid body displacement.

If the displacement alters this length then the final state of the body is said to be in “strained state” and the initial state is called the “unstrained state”.

Let be the location of a point occupied by a particle which in the strained state occupies a location: , then are the projections of displacements of the particle. In simple uni-axial extension along the axis, displacement of a particle is given by , where is the extension.

In simple shear along the axis, the planes parallel to the axis slide past each other so that particles in plane parallel to remain in that plane. The displacement is then given by where .