Matter is commonly found in the form of materials. Analytical mechanics turned its back upon this fact, creating the centrally useful but abstract concepts of the mass point and the rigid body, in which matter manifests itself only through its inertia, independent of its constitution; “modern” physics likewise turns its back, since it concerns solely the small particles of matter, declining to face the problem of how a specimen made up of such particles will behave in the typical circumstances in which we meet it. Materials, however, continue to furnish the masses of matter we see and use from day to day: air, water, earth, flesh, wood, stone, steel, concrete, glass, rubber, ... All are deformable. A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys.

The non-linear field theories of mechanics

http://link.springer.com/content/pdf/10.1007/978-3-642-69569-8_3.pdf

Growth and Decay of Waves in Solids

The particle-velocity histories associated with the compression waves produced by the planar impact of polymethyl methacrylate plates were observed by means of laser interferometry The impact velocity and the thickness of material through which the wave passed were varied from 006 to 064 mm μsec and from 6 to 37 mm respectively Over this range of impact velocities, the observations disclosed a shock followed by a smooth transition to the maximum particle-velocity; the speed and magnitude of the shock varied non-linearly with the impact stress For impact velocities below 03 mm μsec , the wave was steady A steady-wave analysis based on finite linear viscoelasticity theory has been shown to be in good agreement with the experimental observations

Propagation of steady shock waves in polymethyl methacrylate

This paper proves the non-existence of global smooth solutions to an equation for a viscoelastic fluid shearing flow. The non-existence of smooth solutions is interpreted physically as the formation of a vortex sheet and an instability in the fluid motion.

Instability of steady shearing flows in a non-linear viscoelastic fluid

Recent results in nonlinear viscoelastic wave propagation

/pdf/shock-structure-in-a-viscoelastic-fluid-2ysu52ak4h.pdf

A. C. Pipkin

Papers

Shock structure in a viscoelastic fluid