A multiscale quasicontinuum method for lattice models with bond failure and fiber sliding

Abstract

Structural lattice models incorporating trusses and beams are frequently used to mechanically model fibrous materials, because they can capture (local) mesoscale phenomena. Physically relevant lattice computations are however computationally expensive. A suitable multiscale approach to reduce the computational cost of large-scale lattice computations is the quasicontinuum (QC) method. This method resolves local mesoscale phenomena in regions of interest and coarse grains elsewhere, using only the lattice model. In previous work, a virtual-power-based QC framework is proposed for lattice models that include local dissipative mechanisms. In this paper, the virtualpower-based QC method is adopted for lattice models in which bond failure and subsequent frictional fiber sliding are incorporated -which are of significant importance for fibrous materials such as paper, cardboard, textile and electronic textile. Bond failure and fiber sliding are nonlocal dissipative mechanisms and to deal with this nonlocality, the virtual-power-based QC method is equipped with a mixed formulation in which the kinematic variables as well as the internal history variables are interpolated. Previously defined summation rules can still be used to sample the governing equations in this QC framework. Illustrative examples are presented.

Higher‐order quasicontinuum methods for elastic and dissipative lattice models: uniaxial deformation and pure bending

“…Furthermore, conforming triangulations are generally used to achieve a smooth transition from fully resolved domains to coarse-grained domains (see e.g. [17,[19][20][21][22][23][24][25][26][31][32][33]). …”

“…those for fibrous materials, often include dissipation, QC approaches can now be applied to a wide variety of lattice models. This has for instance been shown for a lattice model that includes bond failure and subsequent fibre sliding [20] and an elastoplastic lattice model for an electronic textile [21]. In light of applying QC approaches to structural lattice models, recently a QC approach was also formulated for planar beam lattices undergoing in-plane and out-of-plane deformation [28].…”

“…Note that not all QC approaches are equation-free; see e.g. [19][20][21] for equation-free methods and e.g. [17,22] for non-equation-free formulations.…”

Quasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation

“…Interpolation of lattice variables (kinematic variables and sometimes also internal history variables (Beex et al, 2014b)) is employed in QC methodologies by selecting a small number of lattice points to represent the variables of the entire lattice. Therefore, these lattice points are often referred to as representative points or reppoints.…”

“…These variants depart from the virtual-power statement of the lattice and are therefore referred to as virtual-power-based QC approaches. Their applicability was demonstrated for structural lattice models with dissipative mechanisms in the lattice interactions (Beex et al, 2014a) and for lattice models with dissipative mechanisms in the lattice nodes (Beex et al, 2014b).…”