Multiscale resolution continuum theory for elastic plastic material with damage, an implicit 3D implementation

The multiscale resolution continuum theory (MRCT) [1] is a higher order continuum theory in which additional kinematic variables are added to account for the size effect at several distinct length scales. This remedies the deficiency of the conventional continuum approach when predicting both strain softening and strain hardening materials and resolves the microstructure details without extremely fine mesh in the localization zone, however additional nodal degrees of freedom are needed and the requirement of element size at the length scale somewhat adds to the computational burden. This paper is an extension of the simplified 1D multiscale implementation presented in Complas XI 2011 [14]. A 3D elastic-plastic multiscale element, with one additional subscale in which the damage is applied, is implemented implicitly in the general purpose finite element analysis program FEAP