Microscopic density-functional approach to nonlinear elasticity theory

Starting from a general classical model of many interacting particles we present well defined step by procedure to derive the continuum-mechanics equations nonlinear elasticity theory with fluctuations which describe macroscopic phenomena solid crystal. As relevant variables specify coarse-grained densities conserved quantities and properly displacement field describes local translations, rotations, deformations. In order stay within framework conventional density-functional first mainly consider isothermal case omit effects heat transport warming friction where later extend our include these effects. We proceed in two steps. First, apply concept thermodynamic equilibrium minimize free energy functional under constraints that are fixed. results obtain density explicit formulas for elastic constants exact theory. Second, methods nonequilibrium statistical mechanics projection-operator techniques. projection operators coarse-graining field. result time-evolution three kinds terms on right-hand sides: reversible, dissipative, fluctuating terms. find coefficients limit continuum if defined. By construction allows diffusion point defects where, however, normal crystal this is suppressed.