66 research outputs found

    Continuum modeling of paperboard for the mechanical response of converting processes

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    Paperboard is a thin and lightweight material made of cellulose fibers and it is an important component in packaging material where it provides stiffness and rigidity. The scope of this work is the development of continuum models, and its numerical treatments, for simulating the processes of converting paperboard into packages. The thesis begins with a general introduction to paperboard and a review of modeling approaches are presented. Important continuum modeling concepts used in the papers are presented and key paperboard converting processes are discussed. The main part of the thesis consists of four papers denoted A, B, C and D and they are briefly outlined below.To reduce the computational effort during large scale paperboard forming simulations, a numerical technique which combines a state-of-the-art continuum model for paperboard with state-of-the-art finite element modeling is investigated in Paper A. The model is built up by solid-shell elements where the thickness direction is naturally included in the framework such that the out-of-plane response can be modeled. The approach is validated by numerical studies where the results are compared against fully integrated brick elements. Furthermore, a large-scale forming example for paperboard is explored. Since the loading rate varies during industrial processes and the aim is to maximize the operational velocity, a rate-dependent continuum model for paperboard is developed in Paper B. The new rate-dependent model is based on the static material model in Paper A which is enhanced with a viscoelastic and viscoplastic framework. The developed model is calibrated using uniaxial experiments and evaluated against line-creasing and line-folding measurements. In Paper C, the continuum model in Paper A is enhanced to include continuum damage. Damage is needed to adequately capture the mechanical response during sequential loading of creasing and folding. A scalar isotropic damage variable is introduced and the damage evolution is calibrated for a reference mesh during folding. A simple scaling strategy is introduced to reduce the mesh dependence due to damage evolution. To showcase the proposed model, an illustrative 33D example is presented where a paperboard sheet is creased and folded to mimic the corner folding process. In Paper D, an experimental device and a protocol is developed for cyclic uniaxial out-of-plane compression and tension measurements. This load case is important since it is present during creasing and subsequent folding where the material is subject to large out-of-plane compressive stresses followed by out-of-plane tension and delamination. The soft initial load-displacement response during compression is shown to stem from the surface roughness and not a material property. In addition, the experiments show that the transition from compression to tension is smooth. Consequently, a switch function, previously introduced in literature that separates the elastic behavior between compression and tension, is deemed as questionable for continuum modeling

    Discrete-to-Continuum Limits of Long-Range Electrical Interactions in Nanostructures

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    We consider electrostatic interactions in two classes of nanostructures embedded in a three dimensional space: (1) helical nanotubes, and (2) thin films with uniform bending (i.e., constant mean curvature). Starting from the atomic scale with a discrete distribution of dipoles, we obtain the continuum limit of the electrostatic energy; the continuum energy depends on the geometric parameters that define the nanostructure, such as the pitch and twist of the helical nanotubes and the curvature of the thin film. We find that the limiting energy is local in nature. This can be rationalized by noticing that the decay of the dipole kernel is sufficiently fast when the lattice sums run over one and two dimensions, and is also consistent with prior work on dimension reduction of continuum micromagnetic bodies to the thin film limit. However, an interesting contrast between the discrete-to-continuum approach and the continuum dimension reduction approaches is that the limit energy in the latter depends only on the normal component of the dipole field, whereas in the discrete-to-continuum approach, both tangential and normal components of the dipole field contribute to the limit energy.Comment: 31 pages, 5 figure

    Numerical Computation, Data Analysis and Software in Mathematics and Engineering

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    The present book contains 14 articles that were accepted for publication in the Special Issue “Numerical Computation, Data Analysis and Software in Mathematics and Engineering” of the MDPI journal Mathematics. The topics of these articles include the aspects of the meshless method, numerical simulation, mathematical models, deep learning and data analysis. Meshless methods, such as the improved element-free Galerkin method, the dimension-splitting, interpolating, moving, least-squares method, the dimension-splitting, generalized, interpolating, element-free Galerkin method and the improved interpolating, complex variable, element-free Galerkin method, are presented. Some complicated problems, such as tge cold roll-forming process, ceramsite compound insulation block, crack propagation and heavy-haul railway tunnel with defects, are numerically analyzed. Mathematical models, such as the lattice hydrodynamic model, extended car-following model and smart helmet-based PLS-BPNN error compensation model, are proposed. The use of the deep learning approach to predict the mechanical properties of single-network hydrogel is presented, and data analysis for land leasing is discussed. This book will be interesting and useful for those working in the meshless method, numerical simulation, mathematical model, deep learning and data analysis fields

    On the role of topology and micro-structure on the adhesion and fracture of soft materials

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    With recent progress in characterization, synthesis and manufacturing techniques, soft materials are playing an increasingly important role in many emerging technologies in different fields, such as biomedical, industrial, and electric engineering fields. In many of these applications, the performance of soft materials is largely limited by their strength and toughness, either in the bulk or at the interface. Thus, the adhesion and fracture properties of soft materials have been the main focus of many experimental and theoretical studies. In this research, we focus on the effects of the macro and micro scale topology on the adhesion and fracture of soft materials. We start by investigating the possibility of manipulating interfacial adhesion by patterning geometric and structural features in the bulk. Inspired by the natural example of mussel adhesion, we show that even for planar homogeneous interfaces, topological design of the bulk may lead to enhancement of the interfacial adhesion properties. We demonstrate this by showing examples of bulk patterned voids and distributed sacrificial cuts. We also show that by manipulating the topology, it is possible to realize peeling adhesion asymmetry such that the force required to peel a strip is significantly dependent on the peeling direction. We then study the role of the microstructure of soft materials on their fracture properties. Most of the existing methodologies for investigating damage and fracture in soft materials adapt continuum approaches, which may lead to the negligence of essential microscale features in the vicinity of propagating cracks or may require information on the fracture energy or material length scales which are difficult to measure. On the other hand, it is computationally prohibitive to adopt fully discrete approaches to capture the local topology effects for large samples. To address this challenge, we develop a novel numerical approach for simulating fracture in polymer networks, the building blocks for many natural and artificial soft materials, using an extended version of the Quasicontinuum (QC) method. Explicit representation of the polymer chains is retained in regions of high interest, in the vicinity of cracks for example. Away from the imperfections, the network structure is computationally homogenized and only a fraction of the network nodes is solved. Dynamic mesh adaptivity enables transition between the two representations. The method enables accurate modeling of crack initiation and propagation without apriori constraint on the fracture energy. The accuracy and computational efficiency of the method are demonstrated by applying it to study the fracture of large-scale networks with and without rate dependent effects

    In-Silico Prediction of the Physical Performance of Pharmaceutical Crystals

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    Knowledge of the hardness of pharmaceutical crystals expedites the large-scale manufacturing of drug tablets. This research involved the development and testing of computational methods to simulate the various deformations of crystals that lead to the calculation of hardness. Both methods were applied to a range of materials and provided a consistent ranking of the slip systems with experiment, a detailed atomistic description of the deformation mechanisms, and the calculation of ideal shear strength

    Phase-field Modeling of Phase Changes and Mechanical Stresses in Electrode Particles of Secondary Batteries

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    Most storage materials exhibit phase changes, which cause stresses and, thus, lead to damage of the electrode particles. In this work, a phase-field model for the cathode material NaxFePO4 of Na-ion batteries is studied to understand phase changes and stress evolution. Furthermore, we study the particle size and SOC dependent miscibility gap of the nanoscale insertion materials. Finally, we introduce the nonlocal species concentration theory, and show how the nonlocality influences the results

    Computational modelling of microstructurally sensitive fatigue crack nucleation using discrete dislocation plasticity

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    Discrete Dislocation Plasticity (DDP) modelling is employed to investigate various mi- crostructural quantities that are believed to drive fatigue crack nucleation at the microscale. The exploration begins with the calculation of geometrically necessary dislocation (GND) density within the DDP framework and the study of its behaviour during cyclic loading. The observations from modelling are compared against reports from the literature and conclusions are drawn on the GND density calculations within DDP. A central quantity in this thesis is the dislocation configurational energy. This quantity is assigned to describe the elastically-stored energy associated with the interaction of disloca- tions and their structures. It is the energy which is over and above that from the summation of the dislocation line energies when considered isolated and non-interacting. The total geometrically necessary and statistically stored dislocation density mean free distance allows the configurational energy density to be determined, thus providing a length scale over which the configurational energy is stored. A higher length scale crystal plasticity stored energy density has recently been introduced which attempts to capture local dislocation configurational energy density as an indicator of fatigue crack nucleation and growth. The former is compared and assessed against the dislocation configurational energy density. The dislocation configurational energy and stored energy densities are determined in discrete dislocation and crystal plasticity modelling respectively and assessed with respect to experiments on single crystal nickel fatigue crack nucleation, reported in the literature. Direct comparisons between the three techniques are provided for two crystal orientation fatigue tests. These provide confirmation that both quantities correctly identify the sites of fatigue crack nucleation and that stored energy density is a reasonable approximation to the more rigorous dislocation configurational energy. GND density is shown to be important in locating crack nucleation sites because of its role in the local configurational energy density.Open Acces
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