Molecular statics simulation of dislocation pileup using quasicontinuum method

In this contribution, accuracy of the QuasiContinuum (QC) methodology is studied for the case of dislocation pileup against an impenetrable obstacle in two-dimensional hexagonal lattices. To this end, a simplified shear test with a predetermined horizontal glide plane and next-to-nearest interactions described by the Lennard-Jones potential is adopted. The full molecular statics solution is computed, which is compared to two different QC simulations in terms of spatial positioning of individual dislocations along the glide plane, corresponding disregistry profiles, and dislocation core structures

Molecular statics simulation of nanoindentation using adaptive quasicontinuum method

In this work, molecular statics is used to model a nanoindentation test on a two-dimensional hexagonal lattice. To this end, the QuasiContinuum (QC) method with adaptive propagation of the fully resolved domain is used to reduce the computational cost required by the full atomistic model. Three different adaptive mesh refinement criteria are introduced and tested, based on: (i) the Zienkiewicz-Zhu criterion (used for the deformation gradient), (ii) local atoms’ site energy, and (iii) local lattice disregistry. Accuracy and efficiency of individual refinement schemes are compared against the full atomistic model and obtained results are discussed

eXtended variational quasicontinuum methodology for lattice networks with damage and crack propagation

Lattice networks with dissipative interactions are often employed to analyze materials with discrete micro- or meso-structures, or for a description of heterogeneous materials which can be modelled discretely. They are, however, computationally prohibitive for engineering-scale applications. The (variational) QuasiContinuum (QC) method is a concurrent multiscale approach that reduces their computational cost by fully resolving the (dissipative) lattice network in small regions of interest while coarsening elsewhere. When applied to damageable lattices, moving crack tips can be captured by adaptive mesh refinement schemes, whereas fully-resolved trails in crack wakes can be removed by mesh coarsening. In order to address crack propagation efficiently and accurately, we develop in this contribution the necessary generalizations of the variational QC methodology. First, a suitable definition of crack paths in discrete systems is introduced, which allows for their geometrical representation in terms of the signed distance function. Second, special function enrichments based on the partition of unity concept are adopted, in order to capture kinematics in the wakes of crack tips. Third, a summation rule that reflects the adopted enrichment functions with sufficient degree of accuracy is developed. Finally, as our standpoint is variational, we discuss implications of the mesh refinement and coarsening from an energy-consistency point of view. All theoretical considerations are demonstrated using two numerical examples for which the resulting reaction forces, energy evolutions, and crack paths are compared to those of the direct numerical simulations

Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials

\u3cp\u3eExotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a transformation, effective properties of a metamaterial may change significantly. To capture this phenomenon accurately and efficiently, homogenization schemes are required that reflect microstructural as well as macro-structural instabilities, large deformations, and non-local effects. To this end, a micromorphic computational homogenization scheme has recently been developed, which employs the particular microstructural transformation as a non-local mechanism, magnitude of which is governed by an additional coupled partial differential equation. Upon discretizing the resulting problem it turns out that the macroscopic stiffness matrix requires integration of macro-element basis functions as well as their derivatives, thus calling for higher-order integration rules. Because evaluation of a constitutive law in multiscale schemes involves an expensive solution of a non-linear boundary value problem, computational efficiency of the micromorphic scheme can be improved by reducing the number of integration points. Therefore, the goal of this paper is to investigate reduced-order schemes in computational homogenization, with emphasis on the stability of the resulting elements. In particular, arguments for lowering the order of integration from expensive mass-matrix to a cheaper stiffness-matrix equivalent are outlined first. An efficient one-point integration quadrilateral element is then introduced and a proper hourglass stabilization is discussed. Performance of the resulting set of elements is finally tested on a benchmark bending example, showing that we achieve accuracy comparable to the full quadrature rules, whereas computational cost decreases proportionally to the reduction in the number of quadrature points used.\u3c/p\u3

Modelling of crack propagation:Comparison of discrete lattice system and cohesive zone model

\u3cp\u3eLattice models are often used to analyze materials with discrete micro-structures mainly due to their ability to accurately reflect behaviour of individual fibres or struts and capture macroscopic phenomena such as crack initiation, propagation, or branching. Due to the excessive number of discrete interactions, however, such models are often computationally expensive or even intractable for realistic problem dimensions. Simplifications therefore need to be adopted, which allow for efficient yet accurate modelling of engineering applications. For crack propagation modelling, the underlying discrete microstructure is typically replaced with an effective continuum, whereas the crack is inserted as an infinitely thin cohesive zone with a specific traction-separation law. In this work, the accuracy and efficiency of such an effective cohesive zone model is evaluated against the full lattice representation for an example of crack propagation in a three-point bending test. The variational formulation of both models is provided, and obtained results are compared for brittle and ductile behaviour of the underlying lattice in terms of force-displacement curves, crack opening diagrams, and crack length evolutions. The influence of the thickness of the process zone, which is present in the full lattice model but neglected in the effective cohesive zone model, is studied in detail.\u3c/p\u3

An adaptive variational quasicontinuum methodology for lattice networks with localized damage

Lattice networks with dissipative interactions can be used to describe the mechanics of discrete meso-structures of materials such as 3D-printed structures and foams. This contribution deals with the crack initiation and propagation in such materials and focuses on an adaptive multiscale approach that captures the spatially evolving fracture. Lattice networks naturally incorporate non-locality, large deformations, and dissipative mechanisms taking place inside fracture zones. Because the physically relevant length scales are significantly larger than those of individual interactions, discrete models are computationally expensive. The Quasicontinuum (QC) method is a multiscale approach specifically constructed for discrete models. This method reduces the computational cost by fully resolving the underlying lattice only in regions of interest, while coarsening elsewhere. In this contribution, the (variational) QC is applied to damageable lattices for engineering-scale predictions. To deal with the spatially evolving fracture zone, an adaptive scheme is proposed. Implications induced by the adaptive procedure are discussed from the energy-consistency point of view, and theoretical considerations are demonstrated on two examples. The first one serves as a proof of concept, illustrates the consistency of the adaptive schemes, and presents errors in energies. The second one demonstrates the performance of the adaptive QC scheme for a more complex problem

The role of kinematic boundary conditions and their (in)accuracy in micromechanical parameter identification

part of S07b - Advanced numerical methods (discretization

On micromechanical parameter identification and the role of kinematic boundary conditions

Integrated Digital Image Correlation (IDIC) necessitates a mechanical model with appropriate boundary conditions, geometry, and constitutive laws. Because boundary conditions are applied on the entire specimen, they by definition lie outside the employed field of view in micromechanical parameter identification. To avoid excessive computational cost by modelling the entire specimen, Microstructural Volume Element (MVE) is used instead in IDIC, which requires micromechanical kinematic boundary conditions. The aim of this contribution is to examine the influence of errors in boundary conditions prescribed to MVE on the accuracy of micromechanical parameter identification in IDIC. It is shown that relatively small errors in micromechanical boundary conditions may yield significant inaccuracies in the identified material parameters, and that all microstructural features need to be captured