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• Fatigue crack propagation behavior analysis of 15MnTi steel based on cyclic cohesion model

  J. Guo, J. He, X. Sun

  WCCM2024.

  
  

  Abstract

  15MnTi steel is widely used in high load structures such as bridges, pressure vessels, ships, and vehicles due to its excellent mechanical properties. In the course of service, the failure of steel structure is mostly caused by fatigue fracture. In order to investigate the crack growth of 15MnTi steel under fatigue load, the cohesive zone model (CZM) was used to simulate the crack growth. The CZM can simulate brittle and plastic fracture behavior by using the function of crack interface opening force and opening displacement to avoid the stress singularity of crack tip. On this basis, a cyclic cohesive zone model (CCZM) was established to study the fatigue crack propagation behavior. This model effectively links damage, tractive force, and cumulative displacement while incorporating the process of fatigue crack growth to accurately simulate material damage evolution under fatigue load. Experimental studies on crack growth in 15MnTi steel at three stress ratios reveal a linear relationship between crack growth rate and stress intensity factor range for different stress ratios. The parameters of Paris formula were calculated using crack growth rate and stress intensity factor range, which provided reference for the selection of model parameters. By utilizing the user element subroutine (UEL) in Abaqus and compiling the CCZM using Fortran language specifically for 15MnTi steel, simulations were conducted to analyze the evolution of crack tip state under various stress ratios and discuss the corresponding crack growth behavior based on experimental observations. The results demonstrate that the fatigue crack propagation rate varies linearly with both stress ratio range and stress intensity factor range, consistent with experimental findings. The results of the opening and closing evolution of the crack tip are consistent with the law of crack propagation, which indicates that the plastic behavior of the crack tip can be effectively characterized by the CCZM. Furthermore, parameters obtained from the cyclic cohesive zone model's Paris formula closely match experimental data, thus validating its accuracy and feasibility in simulating fatigue crack propagation behavior.

  Abstract
  15MnTi steel is widely used in high load structures such as bridges, pressure vessels, ships, and vehicles due to its excellent mechanical properties. In the course of service, [...]

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• Numerical simulation of the swelling and deswelling process of gel

  I. Riku, K. Mimura

  WCCM2024.

  
  

  Abstract

  It is well known that the entropy elasticity of rubberlike materials and Brownian motion are described by formally analogous equations as both originated from thermal fluctuations. In rubberlike materials, the shear modulus is conventionally considered to be proportional to the absolute temperature and the proportionality factor is the number density of polymer chains for an affine polymer chains’ network model. On the other hand, the self-diffusion coefficient of Brownian motion is described as the product of the mobility and the absolute temperature. However, for the polymer chains’ network in a solvent, the interaction between the polymer chains and the solvent molecules occurs and the collective diffusion coefficient of the solvent molecules should be different to the self-diffusion coefficient of Brownian motion. Moreover, the shear modulus of the resultant polymer gel should be dependent on the swelling ratio due to the nonaffine movement of polymer chains. Therefore, to verify the analogy of the equations for the shear modulus of the nonaffine polymer chains’ network model and the collective diffusion coefficient of the solvent molecules, in this study, the swelling and deswelling process of the polymer gel is investigated by the numerical simulations.

  Abstract
  It is well known that the entropy elasticity of rubberlike materials and Brownian motion are described by formally analogous equations as both originated from thermal fluctuations. [...]

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• Numerical studies of compression failure in triply periodic minimal surface-based ceramic foams

  T. Tran, R. Piat

  WCCM2024.

  
  

  Abstract

  Microstructures with minimal surfaces can be often found in natural porous architectures, where the surface tension minimizes the area. The triply periodic minimal surfaces (TPMS) [1] are an example of such microstructures. Compared with other porous structures, TPMS have three significant features: firstly, their geometries can be completely expressed via analytical functions; secondly, TPMS are periodic in three independent directions and thirdly, the mean curvature of TPMS is zero [2]. Transforming the TPMS-based unit cell into a lattice structure has particular usage in aerospace, nuclear energy, and biomedical applications where light weight, high stiffness, and temperature resistance are of critical importance. In the presented studies, the failure behavior of four typical TPMS structures (Primitive, Gyroid, Neovius, and IWP) under compression was studied using finite element analysis. Numerical modeling of the damage propagation and strength prediction was performed by removing the finite elements in which the appropriate damage criterion is reached. Utilizing the equations of the generated TPMS structures, the wall thickness of unit cell was considered the main parameter that defined the ceramics volume fraction and should be taken into consideration. Therefore, various unit cell models for different wall thicknesses were generated and used to investigate the impact of the cell geometry on the damage initiation, propagation, and overall compression strength. The results of compression strength and damage development were compared with those of other TPMS structures for the same wall thickness and volume fraction. Finally, the grade TPMS porous structure was provided to verify the effect of wall thickness variation on damage evolution on the macroscale.

  Abstract
  Microstructures with minimal surfaces can be often found in natural porous architectures, where the surface tension minimizes the area. The triply periodic minimal surfaces [...]

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• Penetration resistance of graphene coated ceramic materials under projectile impacts

  M. Talebi Bidhendi, K. Behdinan

  WCCM2024.

  
  

  Abstract

  Extreme conditions including impact can result in material degradation, permanent damages, and occasionally property/life loss. Therefore, investigation of materials and structures under projectile impact has been a canonical field of research over the past decades. Such studies have led to the development of hybrid materials with high performance and durability under the aforementioned loading. As an emerging hybrid material, graphene oxide (GO) - silicon carbide (SiC) provides promising thermo-chemo-mechanical properties with various applications in defense, energy, and aerospace engineering. Nevertheless, penetration resistance of such composites under impact received less attention due to experimental and computational difficulties. Here, ReaxFF molecular dynamics is leveraged to address the aforesaid problem around room temperature. In that regard, the response of 4H-SiC thin films coated by GO samples under indentation and high-velocity projectile impact is studied. It is observed that (a) ceramic substrates coated by GO samples with higher functional groups concentration (oxidation degree) demonstrate softer behavior under indentation, and (b) fracture and penetration resistance under high-velocity impact are altered based on the oxidation degree of the coating layers. In essence, impact-induced complete perforation becomes more localized to the impacted region by increasing the oxidation content of the coating layers. The influence of oxygen functional groups on the adhesion energy between GO and SiC layers is also investigated. It is observed that adhesion energy between SiC and the coating can be ameliorated by the oxidation degree of the graphene samples. Eventually, the above-mentioned findings provide some insights into the bottom-up design pathways for developing ceramic-based protective barriers in which GO is used as a coating layer or reinforcement

  Abstract
  Extreme conditions including impact can result in material degradation, permanent damages, and occasionally property/life loss. Therefore, investigation of materials and structures [...]

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• 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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