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A refinement indicator for adaptive quasicontinuum approaches for structural lattices Chen, Li ; ; et al in International Journal for Numerical Methods in Engineering (in press) The quasicontinuum method is a concurrent multiscale approach in which lattice models are fully resolved in small regions of interest and coarse-grained elsewhere. Since the method was originally proposed ... [more ▼] The quasicontinuum method is a concurrent multiscale approach in which lattice models are fully resolved in small regions of interest and coarse-grained elsewhere. Since the method was originally proposed to accelerate atomistic lattice simulations, its refinement criteria – that drive refining coarse-grained regions and/or increasing fully-resolved regions – are generally associated with quantities relevant to the atomistic scale. In this contribution, a new refinement indicator is presented, based on the energies of dedicated cells at coarse-grained domain surfaces. This indicator is incorporated in an adaptive scheme of a generalization of the quasicontinuum method able to consider periodic representative volume elements, like the ones employed in most computational homogenization approaches. However, this indicator can also be used for conventional quasicontinuum frameworks. Illustrative numerical examples of elastic indentation and scratch of different lattices demonstrate the capabilities of the refinement indicator and its impact on adaptive quasicontinuum simulations. [less ▲] Detailed reference viewed: 214 (22 UL)A mechanical model for compaction of strands in wire ropes Chen, Li ; ; Beex, Lars in International Journal of Solids and Structures (2023), 269 Steel wire ropes are used for numerous industrial applications such as ships, elevators, cranes and bridges. A wire rope consists of numerous thin, steel wires and its geometrical construction can be ... [more ▼] Steel wire ropes are used for numerous industrial applications such as ships, elevators, cranes and bridges. A wire rope consists of numerous thin, steel wires and its geometrical construction can be explained in two steps. First, several wires are wrapped together in a helical shape called a strand. Second, several strands are wrapped together in a helical shape to form the final wire rope. In most cases, each strand is compacted before they are wrapped together to form the final wire rope. Compaction generally reduces contact stresses and thereby, extends ropes’ service life. Not many models have been proposed to predict the compaction process and its influence on the strand’s mechanical behavior during service. This contribution proposes a computationally efficient approach that consists of two elastoplastic mechanical models. The first model, describing the compaction process, is of a 2D plane strain nature and is therefore fast. Subsequently, the 2D geometry and plastic variables predicted by the compaction model are used to generate the initial geometry and initial plastic state of a 3D model, that is subsequently used to describe the strand’s mechanical behavior during service (we limit ourselves to tension). The results of the approach, with and without the mapping of the plastic variables, are compared to experimental measurements and the results without compaction. This is investigated for two real world strands. [less ▲] Detailed reference viewed: 69 (0 UL)An adaptive multiscale quasicontinuum approach for mechanical simulations of elastoplastic periodic lattices Chen, Li ; ; et al in Mechanics Research Communications (2022), 126 The quasicontinuum method is a multiscale method that combines locally supported coarse-grained domains, with small regions in which the microstructural model is fully resolved. This contribution proposes ... [more ▼] The quasicontinuum method is a multiscale method that combines locally supported coarse-grained domains, with small regions in which the microstructural model is fully resolved. This contribution proposes the first adaptive formulation of the method for microstructural elastoplasticity. The microstructural model uses an elastoplastic beam description. The indicator for refinement is the occurrence of plastic deformation, such that plasticity can only occur in fully resolved regions. An illustrative numerical example of a scratch test of an elastoplastic Kelvin lattice demonstrates the capabilities of the resulting framework. [less ▲] Detailed reference viewed: 60 (0 UL)A quasicontinuum approach towards mechanical simulations of periodic lattice structures Chen, Li Doctoral thesis (2021) Thanks to the advancement of additive manufacturing, periodic metallic lattice structures are gaining more and more attention. A major attraction of them is that their design can be tailored to specific ... [more ▼] Thanks to the advancement of additive manufacturing, periodic metallic lattice structures are gaining more and more attention. A major attraction of them is that their design can be tailored to specific applications by changing the basic repetitive pattern of the lattice, called the unit cell. This may involve the selection of optimal strut diameters and orientations, as well as the connectivity and strut lengths. Numerical simulation plays a vital role in understanding the mechanical behavior of metallic lattices and it enables the optimization of design parameters. However, conventional numerical modeling strategies in which each strut is represented by one or more beam finite elements yield prohibitively timeconsuming simulations for metallic lattices in engineeringscale applications. The reasons are that millions of struts are involved, as well as that geometrical and material nonlinearities at the strut level need to be incorporated. The aim of this thesis is the development of multiscale quasicontinuum (QC) frameworks to substantially reduce the simulation time of nonlinear mechanical models of metallic lattices. For this purpose, this thesis generalizes the QC method by a multifield interpolation enabling amongst others the representation of varying diameters in the struts’ axial directions (as a consequence of the manufacturing process). The efficiency is further increased by a new adaptive scheme that automatically adjusts the model reduction whilst controlling the (elastic or elastoplastic) model’s accuracy. The capabilities of the proposed methodology are demonstrated using numerical examples, such as indentation tests and scratch tests, in which the lattice is modeled using geometrically nonlinear elastic and elastoplastic beam finite elements. They show that the multiscale framework combines a high accuracy with substantial model reduction that are out of reach of direct numerical simulations. [less ▲] Detailed reference viewed: 121 (13 UL)Generalized quasicontinuum modeling of metallic lattices with geometrical and material nonlinearity and variability Chen, Li ; Beex, Lars ; et al in Computer Methods in Applied Mechanics and Engineering (2020), 366(112878), We propose a generalized quasicontinuum method to model the mechanical response of 3D lattice structures. The method relies on the spatial coupling of fully-resolved domains and coarse-grained domains. In ... [more ▼] We propose a generalized quasicontinuum method to model the mechanical response of 3D lattice structures. The method relies on the spatial coupling of fully-resolved domains and coarse-grained domains. In the fully-resolved domain, the full micro-structure is taken into account. In the coarse-grained domain, the kinematics of the micro-structure are individually interpolated based on their connectivity. On top of that, the contributions of the microstructure to the governing equations in the coarse-grained domain are sampled using only a few unit cells. In both domains, geometrical and material variability along the strut can be naturally taken into account using a 3D co-rotational beam finite element with embedded plastic hinges. We verify the approach for BCC lattices, demonstrating that the new method can capture both material and geometrical non-linearities of single struts at a fraction of the cost of a direct numerical simulation. [less ▲] Detailed reference viewed: 111 (16 UL)Adaptive equation-free multiscale modeling of metallic lattices with geometrical nonlinearity and variability Chen, Li ; ; Beex, Lars et al Scientific Conference (2019, September 12) An equation-free concurrent multiscale framework is proposed to model 3D metallic lattice structures. The proposed equation-free multiscale method (EFMM) is effectively a generalization of the ... [more ▼] An equation-free concurrent multiscale framework is proposed to model 3D metallic lattice structures. The proposed equation-free multiscale method (EFMM) is effectively a generalization of the quasicontinuum method [2] and relies on the use of fully-resolved domains (FRD) in which all details of the lattice micro-structure are captured, and of coarse-grained domains (CGD) in which a model reduction is performed by interpolation and summation steps. The particularity of the lattice geometrical description is that cross section variations along the lattice struts (caused by the manufacturing process) are explicitly represented by their discretization in several beam finite elements, both in the FRDs and CGDs. The interpolation step of the EFMM refers to a kinematic approximation of the lattice deformation within CGDs based on the displacement of a reduced number of material points. One of the originalities of this work is the consideration of a separate interpolation of each type of kinematic variables within the CGDs, as a function of the connectivity of the lattice beam nodes (i.e. taking the location of different cross sections into account) and their kinematical pattern. This, together with accounting for geometric nonlinearity, by the development and implementation of a 3D co-rotational beam finite element [1], are innovative contributions. Choosing the appropriate sizes of the FRDs and the CGDs for a lattice to be simulated is a trade-off because larger FRDs prevail the accuracy but compromise the efficiency while larger CGDs do the opposite. Since the required sizes of the FRDs and CGDs are generally not known a priori for specific applications, an adaptive coarse-graining strategy is developed. To be specific, the whole lattice is initially considered as a CGD. Two kinds of error indicator are proposed (e.g. the Zienkiewicz-Zhu error indicator [4, 3] and the error indicator based on the discrepancy of strain energy). The error indicator guides on: 1) introducing more material points and rearranging the interpolation for the CGDs; 2) changing the localization-prone parts of the lattice into FRDs. The adaptive EFMM is applied to metallic BCC lattices with various sizes and loading conditions. By comparing to the results of those of the direct numerical simulation (DNS), it is shown that geometrical non-linearities can be captured at a fraction of the DNS cost. [less ▲] Detailed reference viewed: 54 (2 UL)Equation-free multiscale modeling of metallic lattices with geometrical and material nonlinearity and variability Chen, Li ; ; Beex, Lars et al Scientific Conference (2019, September 05) An nonlinear equation-free concurrent multiscale numerical framework, being the generalization of the quasicontinuum method [2] is proposed in this contribution to model 3D metallic lattice structures ... [more ▼] An nonlinear equation-free concurrent multiscale numerical framework, being the generalization of the quasicontinuum method [2] is proposed in this contribution to model 3D metallic lattice structures. The proposed equation-free multiscale method (EFMM) relies on the use of fully-resolved domains (FRD) in which all of the details of the lattice micro-structure are captured, and of coarse-grained domains (CGD) in which a model reduction is performed by interpolation and summation steps. The particularity of the lattice geometry description is that cross section variations along the lattice struts (that are experimentally observed as a result of the manufacturing process) are explicitly represented by their discretization in several beam finite elements, both in the FRDs and CGDs. The interpolation step of the EFMM refers to a kinematic approximation of the lattice deformation within CGDs based on the movement of a reduced number of material points at the CGD corners. One of the originalities of this work is the consideration of a separate interpolation of each type of degrees of freedom within the CGDs, as a function of the connectivity of the lattice beam nodes (i.e. taking the location of different cross sections into account) and their kinematical pattern. This, together with accounting for plasticity, by the development and implementation of a 3D co-rotational beam finite element [1] with embedded plastic hinges [3], are unprecedented and original contributions. The EFMM is applied to metallic BCC lattices with various sizes and loading conditions. By comparing to direct numerical simulation (DNS), it is shown that both material and geometrical non-linearities can be captured at a fraction of the DNS cost (the computational time is reduced by 97.27% while introducing an error of only 3.76%). [less ▲] Detailed reference viewed: 72 (7 UL)Multiscale fracture: a natural connection between reduced order models and homogenisation Bordas, Stéphane ; Beex, Lars ; Chen, Li et al Scientific Conference (2019, May 13) Detailed reference viewed: 171 (16 UL)Observation of room-temperature polar skyrmions ; ; et al in NATURE (2019), 568(7752), 368- Detailed reference viewed: 95 (4 UL) |
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