TABLE OF CONTENTS / Summary and Scope of Continuum Mechanics / Evolution Equations for Fluids and Solids / Initial and Boundary Conditions / Constitutive Equations for Equilibrium and Nonequilibrium Fluids / Artificial Viscosity and Conductivity / Constitutive Equations for Elastic Solids / Constitutive Equations for Plastic Flow / Algorithm for Plastic Flow /
/ 10 Figures /
Example Problems :
[ Heat Conduction, Sound Propagation, Rayleigh-B nard Flow ]
Continuum mechanics, like particle mechanics, quantum mechanics, and other approximate physical descriptions of nature, is a mathematical "model". This model is a set of partial differential equations for the temporal evolution of mass, momentum, and energy flows in a spatial continuum with assumed constitutive relations, initial conditions, and boundary conditions. By generating approximate numerical solutions of these partial differential equations, we seek to approximate flows of "real matter" in space and time. A numerical implementation of continuum mechanics is a useful one to the extent that the agreement is good and that the effort required to program and execute the programs to obtain solutions is not excessive.
Because any physics model is intrinsically incomplete there is always the possibility that an implementation will produce faulty conclusions. There is always certainty too that a model can be applied outside its range of usefulness. Continuum mechanics is at its best in describing relatively simple materials which are homogeneous and isotropic on the scale of observation. Continuum mechanics is not able to deal well with the intrinsic complexity...
