Quasicontinuum method combined with microplane model. (1st March 2022)

• Record Type: Journal Article
• Authors: Mikeš, Karel; Jirásek, Milan
• Is Part Of: International journal of solids and structures. Volume 238(2022)
• Publication Date: 2022-03-01
• Subjects: Quasicontinuum -- Microplane model -- Irregular lattice -- Plasticity; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2021.111369
• Languages: English
• ISSNs: 0020-7683

Abstract

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 (Patzák, 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.