K. Mikes and M. Jirasek
International Journal of Solids and Structures, 238, 111369 (2022).
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.