Micromorphic theory: a gateway to nano world

Micromorphic theory (MMT) envisions a material body as a continuous collection of deformable particles; each possesses finite size and inner structure. It is considered as the most successful top-down formulation of a two-level continuum model, in which the deformation is expressed as a sum of macroscopic continuous deformation and internal microscopic deformation of the inner structure. In this work, the kinematics including the objective Eringen tensors is introduced. Balance laws are derived by requiring the energy equation to be form-invariant under the generalized Galilean transformation. The concept of material force and the balance law of pseudomomentum are generalized for MMT. An axiomatic approach is demonstrated in the formulation of constitutive equations for a generalized micromorphic thermoviscoelastic solid, generalized micromorphic fluid, micromorphic plasticity, and micromorphic electromagnetic–thermoelastic solid. Applications of MMT in micro/nanoscale are discussed.