Documents published in Scipedia

• A primal hybrid finite element method to solve general compressible, quasi-incompressible and incompressible elasticity using stable H(div)-L2 spaces

  P. Devloo, G. Avancini, N. Shauer, H. Oliveira

  WCCM2024.

  
  

  Abstract

  Hybrid methods are usually derived from an extended variational principle, in which the interelement continuity of the functions subspace is removed and weakly enforced by means of a Lagrange multiplier. In this context, a new primal hybrid finite element formulation is presented, which uses H(div) conforming displacement functions and discontinuos L2 approximation for pressure together with shear traction functions to weakly enforce tangential displacement. This combination allows the simulation of compressible, quasi-incompressible and fully incompressible elastic solids, with convergence rates independent of its bulk modulus. The proposed approach benefits from the property that the divergence of the H(div) displacement functions is De Rham compatible with the (dual) pressure functions. The hybridization of the tangential displacements is weakly enforced through a lower order shear stress space. This leads to a saddle-point problem that is stable over the full range of poisson coefficient (large compressibility up to incompressible). Moreover, a boundary stress (normal and shear) can be recovered that satisfies elementwise equilibrium. Hybridizing the tangent stresses and condensing the internal degrees of freedom, a positive-definite matrix with improved spectral properties can be recovered. The stability, consistency and local conservation features are discussed in details. The formulation is tested and verified for different test cases.

  Abstract
  Hybrid methods are usually derived from an extended variational principle, in which the interelement continuity of the functions subspace is removed and weakly enforced by [...]

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• Complete variable kinematic cuf-based multilayered shell elements

  E. Carrera, D. Scano

  WCCM2024.

  
  

  Abstract

  The paper presents a methodology for formulating multi-layered composite shell theories with arbitrary kinematic fields. Each displacement variable is examined through an independent expansion function, allowing integration of equivalent single layer and layer-wise approaches within the Carrera Unified Formulation. Finite element method discretizes the structure in the reference plane of the plate using Lagrange-based elements. Governing equations are derived using the principle of virtual displacements. The study considers multilayered structures with different radius-to-thickness ratios and compares results with analytical solutions from the literature. Findings suggest the most appropriate model selection depends strongly on specific problem parameters

  Abstract
  The paper presents a methodology for formulating multi-layered composite shell theories with arbitrary kinematic fields. Each displacement variable is examined through an [...]

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• Band gap evolution in nonlinear dynamics of metamaterials made structures via gradually-changing mechanical properties

  R. Augello, E. Carrera

  WCCM2024.

  
  

  Abstract

  This paper explores the dynamic behavior of metamaterial-like structures by investigating the evolution of their band gap under the influence of geometrical nonlinearities in the large displacement/rotations field. The study employs a unified framework based on the Carrera Unified Formulation (CUF) and a total Lagrangian approach to develop higher-order onedimensional beam theories that account for geometric nonlinearities. The axis discretization is achieved through a finite element approximation. The equations of motion are solved around nonlinear static equilibrium states, which are determined using a Newton–Raphson algorithm combined with a path-following method of arc-length type. The CUF approach introduces two key innovations that are highly suitable for the evolution of the band gap: 1) Thin-walled structures can be effectively represented using a single one-dimensional beam model, overcoming the common limitations of standard finite elements. This is crucial as three-dimensional solid elements would result in significant computational costs, and twodimensional elements pose limitations for this type of investigation. Finally, employing onedimensional finite elements usually requires a combination of elements, leading to additional mathematical complexities in their connections and lacking geometric precision. 2) CUF enables the use of the full Green-Lagrange strain tensor without the need for assumptions, as is the case with von Karm´ an nonlinearities. ´ The paper specifically compares results obtained with linear and nonlinear stiffness matrices, highlighting the differences. Numerical investigations are conducted on thin-walled structures composed of repeatable cells, assessing mode changes under traction and compression loading. The findings emphasize that the band gap is an inherent property of the equilibrium state, underscoring the necessity of a proper nonlinear analysis for accurately evaluating frequency transitions

  Abstract
  This paper explores the dynamic behavior of metamaterial-like structures by investigating the evolution of their band gap under the influence of geometrical nonlinearities [...]

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• A compact sixth order finite difference scheme for the 3D Poisson equation

  C. Kavouklis

  WCCM2024.

  
  

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• Discretization error estimation for flow simulations using general hybrid grids

  Y. Kallinderis

  WCCM2024.

  
  

  Abstract

  A primary area of the author’s work with his students is outlined in the present article. It regards the estimation of the discretization error with mixed-element and adaptive meshes. Use of general hybrid meshes for computational flow simulations is of importance due to the complexity of both the geometry and the fields. The meshes can consist of a mix of hexahedra, prisms and tetrahedra with pyramids being transitional elements. The discretization error is a primary component of the numerical error in flow simulations. Primary factors affecting it are the local density of the mesh, as well as its “distortions”, namely the variation in local size and orientation (stretching, skewness), the shape of the individual elements (shear, twist), and the local change in their type (grid interfaces). Two distinct approaches have been followed in order to estimate and control the discretization error. The grid-based (“a priori”) approach assesses mesh quality from the analytic expression of the truncation error. The solution-based (“a posteriori”) approach monitors approximations of the variation of flow quantities (“sensors”). Those are then applied to guide adaptation of the grid to the simulated flow field

  Abstract
  A primary area of the author’s work with his students is outlined in the present article. It regards the estimation of the discretization error with mixed-element and adaptive [...]

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• 3D-ACA for the time domain boundary element method: Comparison of FMM and H-matrix based approaches

  M. Schanz

  WCCM2024.

  
  

  Abstract

  The time domain Boundary Element Method (BEM) for the homogeneous wave equation with vanishing initial conditions is considered. The generalized convolution quadrature method (gCQ) developed by Lopez-Fernandez and Sauter is used for the temporal discretisation. The spatial discretisation is done classically using low order shape functions. A collocation approach is applied. Essentially, the gCQ requires to establish boundary element matrices of the corresponding elliptic problem in Laplace domain at several complex frequencies. Consequently, an array of system matrices is obtained. This array of system matrices can be interpreted as a threedimensional array of data which should be approximated by a data-sparse representation. The generalised Adaptive Cross Approximation (3D-ACA) can be applied to get a data sparse representation of these three-dimensional data arrays. Adaptively, the rank of the three-dimensional data array is increased until a prescribed accuracy is obtained. On a pure algebraic level it is decided whether a low-rank approximation of the three-dimensional data array is close enough to the original matrix. Within the data slices corresponding to the BEM calculations at each frequency either the standard H-matrices approach with ACA or a fast multipole (FMM) approach can be used. The third dimension of the data array represents the complex frequencies. Hence, the algorithm makes not only a data sparse approximation in the two spatial dimensions but detects adaptively how much frequencies are necessary for which matrix block. Numerical studies show the performance of these methods

  Abstract
  The time domain Boundary Element Method (BEM) for the homogeneous wave equation with vanishing initial conditions is considered. The generalized convolution quadrature method [...]

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• Random Dense Packing of Continuous Distributions of Spherical Particles - Use of Particle Packing Model and Discrete-Particle-Method to predict Particle Spacing Factors

  T. Stengel, F. Wiese, N. Obermeier

  particles2023.

  
  

  Abstract

  Portland Cement (PC) is responsible for about 8% of global CO2 emissions and is mainly used as a binder in concrete, which is a basic material for all types of load-bearing structures. Due to its versatile usage (precast or ready-mix concrete) and availability almost all over the world, concrete is used in a wide range of applications. When looking at possible pathways to reduce the carbon footprint four measures emerge: 1. 2. 3. 4. Use of renewable energy for PC production (mainly clinker burning process) CO2 capture during PC production. Use of supplementary cementitious materials to reduce the amount of PC. Optimization of PC efficiency within the concrete to reduce the amount of PC needed. To optimize the efficiency of PC, particle packing methods can be used, see e.g. [1], [2]. A well-established geometrical particle packing model is the compressible packing model (CPM) [3], which was extended to the compressible interaction packing model (CIPM) to account for colloidal interactions [4]. Based on the CIPM a so-called cement-spacing-factor (CSF) is calculated [2], [4] by dividing the PC volume in concrete by the maximum packing density (PD). CSF is then used to optimize PC efficiency, i.e., strength of PC based materials. However, CSF calculated based on PD is only an auxiliary parameter (i.e., particle saturation on a volume base), which at best qualitatively describes PC spacing in a particle arrangement and does not take the spread of the PC spacing into account. In this paper, a DEM-based enriched particle packing algorithm is developed that accounts for particle type (i.e., inert particles or PC) and distribution of PC particle distance. The results are compared to strength tests on PC-based pastes and the correlation to the calculated distribution of PC particle distance is shown. Based on PD calculations and the enriched DEM particle packing algorithm an optimization of PC efficiency in concrete can be performed.

  Abstract
  Portland Cement (PC) is responsible for about 8% of global CO2 emissions and is mainly used as a binder in concrete, which is a basic material for all types of load-bearing [...]

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• Particle- based Simulation of Crack Propagation in Structural Connections Produced with Direct Energy Deposition 3D- Printing

  J. Olsson, M. Ander, S. Larsson, O. Borgström, E. Tibuzzi, P. Barden, C. Williams

  particles2023.

  
  

  Abstract

  This paper explores how Force Flux Peridynamics (FFPD) can support the design of lightweight metal components in building structures produced with Direct Energy Deposition (DED) Additive Manufacturing (AM). DED is a relatively new technology that deposit metal layer-by-layer to create three-dimensional structures without the need for support structures. This process has the potential to significantly reduce the embodied carbon in building structures by reducing the weight of the structural connections and hence the weight of all other structural components [4]. However, the process applied in AM for metals can make the printed objects susceptible to defects which may compromise their structural integrity and may even lead to fracture [5]. In this paper we describe a design process for the creation of lightweight structural components while including modelling of anisotropy, yielding and brittle fracture. The central core of the process is the application of a particle method called Force Flux Peridynamics (FFPD) which is used to predict yielding and fracture. The paper thus builds upon strategies developed and defined in other publications including; the derivation of the FFPD particle method [2], a strategy for calibration of materials in paper [1], a motivation to apply this concept in the context of nodal connections for spatial structures as described in paper [3]. The specific nodal connection that is analysed in this paper is designed for rotational DED printing which creates a component with radial anisotropic mechanical properties. The node is analysed using an axial tensile and an axial compression load case where the load is applied by imposing incremental translations to the attachments where the structural members would be connected. The susceptibility to fracture in relation to the anisotropy of the printed metal is discussed.

  Abstract
  This paper explores how Force Flux Peridynamics (FFPD) can support the design of lightweight metal components in building structures produced with Direct Energy Deposition [...]

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• Numerical Investigation of the Installation of Suction Caisson in Sand Using Material Point Method

  M. Alturki, L. Zambrano-Cruzatty, A. Faramarzi, M. Mehravar

  particles2023.

  
  

  Abstract

  Suction caisson has gained interest in recent years as an alternative foundation for offshore wind turbines due to its cost-effectiveness and easy installation compared to conventional foundations such as monopile. After initial penetration due to its self-weight, suction is applied until the caisson reaches the desired depth. Applying suction provides additional driving force due to the pressure difference between inside and outside the caisson and induces seepage that degrades friction and tip resistance, which further facilitates the installation. The seepage plays a vital role in installing suction caisson in sand; however, it might change the soil state which affects the ultimate bearing capacity of the caisson. Several research works have been conducted to study the suction caisson installation in sand. However, the complexities of the problem including large deformation, solid-fluid and soil-structure interaction, inhibited these studies from fully understanding the installation mechanism. This paper proposes a large deformation modeling framework by using the material point method (MPM). MPM is a hybrid Lagrangian-Eulerian particle-based method that uses material points over a fixed computational mesh where governing equations are solved. During the convection of the particles, the background mesh is kept fixed, making it suitable for large deformation problems. The model considers soil-structure interaction by adopting a Coulomb contact algorithm between the caisson and surrounding soil. In this paper, the stability of the contact algorithm is ensured by correcting material point velocities in the vicinity of the caisson interface using a limiting velocity based on the element size and time step. The framework is validated by comparing a simulation of caisson installation under constant velocity with results published in the literature. Our proposed framework’s results agree with previous published results, demonstrating that the simplified stabilization procedure does not affect the simulation results. This is a promising result that will enable the incorporation of fully coupled analysis to better understand the effects of induced seepage on the installation mechanism of suction caissons.

  Abstract
  Suction caisson has gained interest in recent years as an alternative foundation for offshore wind turbines due to its cost-effectiveness and easy installation compared to [...]

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• Final open-door industrial day

  F. Rechsteiner, V. Mathes

  Fibregy OA (2024). Vol. Public Deliverables, 34

  
  

  Abstract

  The final open-door industrial day forms the final milestone of the project (MS 20) and thus the project completion. The event will take place again at one of the partners sites. During the meeting the project results are presented comprehensively. The prototypes should also be shown again. In terms of content, the following points are in the foreground: Results of life cycle assessment and waste management, global business plan, standardization recommendations, final conclusions. (D7.12)

  Abstract
  The final open-door industrial day forms the final milestone of the project (MS 20) and thus the project completion. The event will take place again at one of the partners [...]

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