ABSTRACT

In this paper, we show how certain ideas of the microplane theory can be used in the quasicontinuum method for an irregular structural lattice with axial interactions representing a heterogeneous material. The paper first analyzes the microplane material model, and then the relation between the lattice model and the microplane model is described. Based on this analogy, a microplane-based summation rule for the quasicontinuum method is proposed. Five simplified approaches adopting various levels of simplification are introduced using interpolation, global or local microplane-based homogenization, and an isotropic or anisotropic microplane model. For an adaptive quasicontinuum method, a new refinement criterion based on strain at individual microplanes is proposed and investigated. All presented approaches have been implemented in OOFEM (Patzak, 2012) an open-source object-oriented code. Accuracy, efficiency and specific properties of all simplified models based on the quasicontinuum idea are evaluated by comparing the results with the fully resolved lattice model for a number of examples in 2D and 3D. The presented results show that using the proposed microplane-based quasicontinuum approaches, a significant simplification of the problem can be reached while keeping the error acceptable.