Documents published in Scipedia

• The Picard-Newton iteration for the Boussinesq equations

  L. Rebholz, E. Hawkins

  WCCM2024.

  
  

  Abstract

  We consider the Picard-Newton and Anderson accelerated Picard-Newton solvers applied to the Boussinesq equations, nonlinear Helmholtz equations and Liouville equation, for the purpose of accelerating convergence and improving robustness with respect to problem parameters. In all cases, we show the proposed solvers improve efficiency over the commonly used solvers and are able to find solutions for a much larger set of problem parameters.

  Abstract
  We consider the Picard-Newton and Anderson accelerated Picard-Newton solvers applied to the Boussinesq equations, nonlinear Helmholtz equations and Liouville equation, for [...]

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• A new concept for embedding sub-structures via level-sets

  T. Fries, J. Neumeyer, M. Kaiser

  WCCM2024.

  
  

  Abstract

  A framework is presented to continuously embed sub-structures such as fibres and membranes into otherwise homogeneous, isotropic bulk materials. The bulk material is modeled with classical finite strain theory. The sub-structures are geometrically defined via all level sets of a scalar function over the bulk domain. A mechanical model that is simultaneously applicable to all level sets is given and coupled to the bulk material. This results in a new concept for anisotropic materials with possible applications in biological tissues, layered rocks, composites, and textiles. For the numerical analysis, the bulk domain is discretized possibly using higher-order finite elements which do not conform to the level sets implying the shapes of the embedded sub-structures. Numerical results confirm the success of the proposed embedded sub-structure models in different contexts

  Abstract
  A framework is presented to continuously embed sub-structures such as fibres and membranes into otherwise homogeneous, isotropic bulk materials. The bulk material is modeled [...]

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• On triangular self-stabilized virtual elements for Kirchhoff-Love shells

  T. Park Wu, P. de Mattos Pimenta, P. Wriggers

  WCCM2024.

  
  

  Abstract

  This work presents a self-stabilized triangular virtual element for linear Kirchhoff–Love shells. The domain decomposition by flat triangles directly approximates the shell geometry without resorting to a curvilinear coordinate system or an initial mapping approach. The problem is discretized by the lowest-order conventional virtual element method for the membrane, in which stabilization is needless, and by a stabilization-free virtual element procedure for the plate. Numerical examples of static problems show the potential of the formulation as a prelude for the evolution of self-stabilized Kirchhoff–Love shell virtual elements.

  Abstract
  This work presents a self-stabilized triangular virtual element for linear Kirchhoff–Love shells. The domain decomposition by flat triangles directly approximates the shell [...]

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• Projector assembly: bridging Poisson and elasticity formulations

  T. Moherdaui, A. Gay Neto, P. Wriggers

  WCCM2024.

  
  

  Abstract

  Virtual element methods define their shape functions implicitly (tailored to each element’s geometry), foregoing the typical reference element and transformation scheme usually employed by the finite element method. The formulation leverages the use of polynomial projections supplied by heuristic stabilizations when necessary. These projections are represented by projector matrices, which require the solution of a local system. Elasticity formulations usually employ an 𝐿 2 -projection from a displacement multifield onto a strain multifield, requiring the solution of a considerably larger system than a typical Poisson problem would require, with dense matrices and lots of zeroes. This work presents a way to obtain the projections for elasticity formulation by assembling from the 𝐿 2 -projection for each derivative of the one-field a Poisson formulation, resulting in smaller local systems being solved and more efficient storage. This approach is based on the linearity of both projections and derivatives, and is shown in the examples to preserve the convergence rate of the method.

  Abstract
  Virtual element methods define their shape functions implicitly (tailored to each element’s geometry), foregoing the typical reference element and transformation scheme [...]

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• Mixed partition of unity methods and stochastic Gillespie algorithms for Transport-Reaction equations

  M. Kirkilionis

  WCCM2024.

  
  

  Abstract

  We introduce a new type of model framework which is part stochastic and part deterministic. The starting point is a finite size particle system within a single reaction volume, with type exchanges modelled by a contact process. Inside the reaction volume, each particle can interact with every other particle with the same probability. This is the setting of a classical reaction system simulated with a Gillespie algorithm. Such systems can be used to describe other than chemistry type exchanges, like an infection process, and therefore are already very versatile. Their advantage is that they are able to be used where small size effects can play a role, like extinction events, which are impossible to model with differential equations, including stochastic differential equations. However finite size and single reaction volume settings for reaction systems are too restrictive in other ways. We might like to add internal or external states to the particles. These states are coordinates in a position space. An example of an internal position/state space is age (since entering the system), an example for an external position/state space is geographical location. The particles then can also change their positions in these state spaces, according to some probability distribution which evolution is modelled deterministically. The classical example for a transport process is a partial differential equation like the heat equation, or more general parabolic advection-diffusion equations. We assume that the distribution of the particles in position space is not influencing the evolution of the probability distribution driving in turn the evolution of the particles’ positions. The model framework with its finite-size particle population approach can very accurately model situations where finite-size effects take place, however provides in addition detailed descriptions of both internal and external particle state spaces where needed. The framework can therefore be used in addition to traditional established models, like transport PDEs or internally structured population models, when the computation of the statistics of finite-size effects is important.

  Abstract
  We introduce a new type of model framework which is part stochastic and part deterministic. The starting point is a finite size particle system within a single reaction volume, [...]

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• Immersed-boundary approach based on integrated RBFs and smooth extension for solving PDEs in complex domains

  N. Mai-Duy, C. Tran, D. Strunin, W. Karunasena

  WCCM2024.

  
  

  Abstract

  We propose an immersed-boundary approach, based on point collocation, five-point integrated radial basis function stencils, rectangular Cartesian grids and smooth extension of the solution, for solving the two-dimensional elliptic partial differential equation in a geometrically complex domain.

  Abstract
  We propose an immersed-boundary approach, based on point collocation, five-point integrated radial basis function stencils, rectangular Cartesian grids and smooth extension [...]

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• pyMesoscale: A friendly python library for generating 3D concrete mesoscale models based on the local background grid method

  F. Muhammad, S. Kolawale Adekunle

  WCCM2024.

  
  

  Abstract

  Mesoscale modeling of concrete and its composites has attracted a lot of researchers over the years with the promise of establishing an accurate relationship between the mesoscopic model and the macroscopic mechanical properties of concrete. The primary constraints inhibiting the widespread application of mesoscale modeling include (i) achieving high packing density with control over aggregate shape and gradation, (ii) high computational cost, (iii) accomplishing realistic interfacial transition zone, and (iv) implementing efficient aggregate intrusion detection. Besides these constraints, one major challenge is the lack of open program codes for algorithms implemented in published research papers. For example, improving, upgrading, and repurposing an existing algorithm by other researchers requires the open availability of the codes. The unavailability of these codes and the common absence of subtle implementation details in published papers hinder research progress on mesoscale modeling of concrete composites. This paper presents pyMesoscale, a Python library for generating 3D mesoscale models for concrete like composites. pyMesoscale implements the local background method, a highly effective mesoscale generation algorithm that offers a much better aggregate intrusion detection system and a high aggregate volume fraction. Developed with Python due to its smoother learning curve and beginner friendliness, pyMesoscale reduces implementation complexity for ease of use by both new and experienced researchers in the field. This paper offers the mathematical formulars and the detailed steps required to implement the generation of mesoscale geometric model of concrete and its derived mesoscale finite element model covering aggregate gradation and shape, random aggregate translation and aggregate intrusion detection.

  Abstract
  Mesoscale modeling of concrete and its composites has attracted a lot of researchers over the years with the promise of establishing an accurate relationship between the mesoscopic [...]

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• Modeling the quasi-brittle fracture of structural materials using a mixed stabilized two-field finite element formulation

  C. Guzmán, W. Morocho, S. Cáceres, E. Castillo

  WCCM2024.

  
  

  Abstract

  The fracture process zone (FPZ) is typically characterized as a small region around a crack where non-linear phenomena occur, such as plasticity. In brittle materials, this zone is small and can be safely neglected. However, in quasi-brittle materials, which exhibit a combination of brittle and ductile behavior rather than a clear manifestation of either, the material within the FPZ tends to damage and displays a softening curve after reaching peak load. This behavior is frequently observed in structural materials like concrete and timber, and it can be challenging to model. Traditionally, displacement-based irreducible finite element (FE) formulations have been widely used for simulating structural materials. However, this approach comes with significant drawbacks, such as mesh dependence and convergence problems, when applied to certain phenomena like softening, localization, and fracture. To address these challenges, various techniques have been employed, including extended FE methods and phase-field modeling. In this work, the utilization of a mixed FE formulation in which both displacement and strain serve as primary unknowns within the system, is proposed. To ensure satisfaction of the inf-sup condition, which is associated with saddle point stability in mixed formulations, we employ the variational multiscale method to introduce stabilizing terms into the system. The implementation is conducted using FEniCS, an open-source FE software that offers a high-level programming interface written in Python. The implementation is validated by comparing the obtained results with those reported in the literature for bending test in notched specimens. The results demonstrate remarkably good performance in terms of maximum load, softening curve, and structural size effect in various specimens, exhibiting minimal mesh dependence even when using low-order interpolation elements

  Abstract
  The fracture process zone (FPZ) is typically characterized as a small region around a crack where non-linear phenomena occur, such as plasticity. In brittle materials, this [...]

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• Calibration of damage parameters of super high-rise frame-core structural subsystem under torsional ground motion

  Z. Guo, Y. Ma, Z. He

  WCCM2024.

  
  

  Abstract

  To clarify the dynamic characteristics of the structure under torsional seismic excitation, a macroscopic dynamic model of the structure and simplified hysteretic models of each sub-system were established through theoretical derivation, and the accuracy of the models was verified using finite element models. To determine the design parameters of the hysteretic models for each sub-system, a multi-objective seismic optimization approach considering both structural cost and overall torsional damage was proposed. Through multi-objective optimization based on torsional overturning analysis, the design parameters of each sub-system were successfully determined. The results indicate that the outrigger truss sub-system plays a significant role in controlling the overall torsional behavior of the structure.

  Abstract
  To clarify the dynamic characteristics of the structure under torsional seismic excitation, a macroscopic dynamic model of the structure and simplified hysteretic models of [...]

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• Synergistic effects of environmental deterioration on fatigue and flexure properties of glass fiber reinforced polymeric (GFRP) composites : a multiscale and multiphysics model.

  Z. Li, M. Lepech

  WCCM2024.

  
  

  Abstract

  This study aims to simulate synergistic UV & moisture deterioration and demonstrate its role in changing the residual fatigue and flexure strength in architectural GFRP composite material. This study develops an experimentally validated 3D Multiphysics model at a structural level and gets this homogenization-based model to identify the degradation mechanisms observed in the experimental data. Sensitivity analyses are conducted to investigate the effect of mesh density on the accuracy of functions homogenized from micromechanical models. In addition, this macroscale model also quantifies how these degradation mechanisms weaken the strength and durability of environmentally aged composite materials. The aging-fatigue-bend macroscale model assumes that the degradation-induced damage field is concentrated within a depth to the plate surface. According to the computational results, the degradation process caused by the combined effect of UV and moisture exposure involves the removal of polymeric matter from the exposed surface. In other words, the degradation mechanism of UV exposure involves both the chemical alteration and mechanical damage of polymeric matter, primarily located at the exposed surface. This model can be incorporated into many commercial finite element codes for a sustainability study of composite structures/systems. In future work, the models developed in this study will be combined with life cycle assessment (LCA) tools to support better sustainability-focused new material design, thus reducing costs and environmental impacts in the built environment.

  Abstract
  This study aims to simulate synergistic UV & moisture deterioration and demonstrate its role in changing the residual fatigue and flexure strength in architectural GFRP composite [...]

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