A finite element formulation for the doublet mechanics modeling of microstructural materials
The doublet mechanics (DM) theory was developed [7]and[8] for modeling the behavior of solids where the microstructure is important. Within the DM theory, solid bodies are discretized as an ensemble of particles, with each pair of neighboring particles forming a doublet. Microstructural strains and stresses are introduced through displacements and mutual interactions of the particles within the doublets. This description also includes a scale parameter, interpreted as the separation distance between two particles in a doublet. The DM theory is consistent with other microstructural approaches and reduces to continuum mechanics in the case of non-scale formulation. Several problems in solid mechanics have been treated analytically using DM [5]. In this work, DM is reformulated using a finite element approach with the aim of expanding even more the potential applications of such an approach. As a first step in our development we considered the microstructural elongation strains only, while the other two: shear and torsional are left for subsequent investigations. Two constitutive laws are considered: linear elastic and linear viscoelastic. A number of solved examples reveal the accuracy of the FE formulation developed for DM. The present numerical framework could be incorporated into various general numerical solution strategies, such as multiscale-multidomain modeling, and further extended to include other constitutive relationships.
doublet mechanics theory microstructural discrete models multiscale model finite element method flamant problem kelvin problem