Automatic differentiation based formulation of coupled problems

Our work will show that complex transient coupled problems can be formulated and solved effectively with AceGen and AceFEM using an automatic differentiation based formulation (ADB-formulation). From scalar pseudo-potential function consistent tangent matrix for strongly coupled problems can be derived, leading to quadratically convergent Newton-Raphson type procedure. Another problem considered is the implementation of finite element. Typically, all equations are written inside a single finite element and a single pseudo-potential is defined. Such implementation is efficient but rigid, therefore, a different implementation was considered. Within the second approach we wrote a separate finite element for each field, but in a way that quadratic convergent Newton-Raphson procedure is preserved. The paper presents examples where unified and field-by-field implementations are compared according to computational efficiency. The results show that with increasing ratio between the complexity of constitutive equations and discretization, generated code size and evaluation time of implementations become comparable

On two simple virtual Kirchhoff-Love plate elements for isotropic and anisotropic materials

The virtual element method allows to revisit the construction of Kirchhoff-Love elements because the C1-continuity condition is much easier to handle in the VEM framework than in the traditional Finite Elements methodology. Here we study the two most simple VEM elements suitable for Kirchhoff-Love plates as stated in Brezzi and Marini (Comput Methods Appl Mech Eng 253:455–462, 2013). The formulation contains new ideas and different approaches for the stabilisation needed in a virtual element, including classic and energy stabilisations. An efficient stabilisation is crucial in the case of C1-continuous elements because the rank deficiency of the stiffness matrix associated to the projected part of the ansatz function is larger than for C-continuous elements. This paper aims at providing engineering inside in how to construct simple and efficient virtual plate elements for isotropic and anisotropic materials and at comparing different possibilities for the stabilisation. Different examples and convergence studies discuss and demonstrate the accuracy of the resulting VEM elements. Finally, reduction of virtual plate elements to triangular and quadrilateral elements with 3 and 4 nodes, respectively, yields finite element like plate elements. It will be shown that these C1-continuous elements can be easily incorporated in legacy codes and demonstrate an efficiency and accuracy that is much higher than provided by traditional finite elements for thin plates. © 2021, The Author(s)

Virtual Element Formulation For Finite Strain Elastodynamics

This work provides an efficient virtual element scheme for the modeling of nonlinear elastodynamics undergoing large deformations. The virtual element method (VEM) has been applied to various engineering problems such as elasto-plasticity, multiphysics, damage and fracture mechanics. This work focuses on the extension of VEM towards dynamic applications. Within this framework, we employ low-order ansatz functions in one, two and three dimensions that having arbitrary convex or concave polygonal elements. The formulations considered in this contribution are based on minimization of potential function for both the static and the dynamic behavior. While the stiffness-matrix needs a suitable stabilization, the mass-matrix can be calculated using only the projection part. For the implicit time integration scheme, Newmark-Method is used. To show the performance of the method, various numerical examples in 1D, 2D and 3D are presented

Harmonized human biomonitoring in European children, teenagers and adults: EU-wide exposure data of 11 chemical substance groups from the HBM4EU Aligned Studies (2014-2021)

As one of the core elements of the European Human Biomonitoring Initiative (HBM4EU) a human biomonitoring (HBM) survey was conducted in 23 countries to generate EU-wide comparable HBM data. This survey has built on existing HBM capacity in Europe by aligning national or regional HBM studies, referred to as the HBM4EU Aligned Studies. The HBM4EU Aligned Studies included a total of 10,795 participants of three age groups: (i) 3,576 children aged 6-12 years, (ii) 3,117 teenagers aged 12-18 years and (iii) 4,102 young adults aged 20-39 years. The participants were recruited between 2014 and 2021 in 11-12 countries per age group, geographically distributed across Europe. Depending on the age group, internal exposure to phthalates and the substitute DINCH, halogenated and organophosphorus flame retardants, per- and polyfluoroalkyl substances (PFASs), cadmium, bisphenols, polycyclic aromatic hydrocarbons (PAHs), arsenic species, acrylamide, mycotoxins (deoxynivalenol (total DON)), benzophenones and selected pesticides was assessed by measuring substance specific biomarkers subjected to stringent quality control programs for chemical analysis. For substance groups analyzed in different age groups higher average exposure levels were observed in the youngest age group, i.e., phthalates/DINCH in children versus teenagers, acrylamide and pesticides in children versus adults, benzophenones in teenagers versus adults. Many biomarkers in teenagers and adults varied significantly according to educational attainment, with higher exposure levels of bisphenols, phthalates, benzophenones, PAHs and acrylamide in participants (from households) with lower educational attainment, while teenagers from households with higher educational attainment have higher exposure levels for PFASs and arsenic. In children, a social gradient was only observed for the non-specific pyrethroid metabolite 3-PBA and di-isodecyl phthalate (DiDP), with higher levels in children from households with higher educational attainment. Geographical variations were seen for all exposure biomarkers. For 15 biomarkers, the available health-based HBM guidance values were exceeded with highest exceedance rates for toxicologically relevant arsenic in teenagers (40%), 3-PBA in children (36%), and between 11 and 14% for total DON, Sigma (PFOA + PFNA + PFHxS + PFOS), bisphenol S and cadmium. The infrastructure and harmonized approach succeeded in obtaining comparable European wide internal exposure data for a prioritized set of 11 chemical groups. These data serve as a reference for comparison at the global level, provide a baseline to compare the efficacy of the European Commission's chemical strategy for sustainability and will give leverage to national policy makers for the implementation of targeted measures

Harmonized human biomonitoring in European children, teenagers and adults: EU-wide exposure data of 11 chemical substance groups from the HBM4EU Aligned Studies (2014–2021)

As one of the core elements of the European Human Biomonitoring Initiative (HBM4EU) a human biomonitoring (HBM) survey was conducted in 23 countries to generate EU-wide comparable HBM data. This survey has built on existing HBM capacity in Europe by aligning national or regional HBM studies, referred to as the HBM4EU Aligned Studies. The HBM4EU Aligned Studies included a total of 10,795 participants of three age groups: (i) 3,576 children aged 6–12 years, (ii) 3,117 teenagers aged 12–18 years and (iii) 4,102 young adults aged 20–39 years. The participants were recruited between 2014 and 2021 in 11–12 countries per age group, geographically distributed across Europe. Depending on the age group, internal exposure to phthalates and the substitute DINCH, halogenated and organophosphorus flame retardants, per- and polyfluoroalkyl substances (PFASs), cadmium, bisphenols, polycyclic aromatic hydrocarbons (PAHs), arsenic species, acrylamide, mycotoxins (deoxynivalenol (total DON)), benzophenones and selected pesticides was assessed by measuring substance specific biomarkers subjected to stringent quality control programs for chemical analysis. For substance groups analyzed in different age groups higher average exposure levels were observed in the youngest age group, i.e., phthalates/DINCH in children versus teenagers, acrylamide and pesticides in children versus adults, benzophenones in teenagers versus adults. Many biomarkers in teenagers and adults varied significantly according to educational attainment, with higher exposure levels of bisphenols, phthalates, benzophenones, PAHs and acrylamide in participants (from households) with lower educational attainment, while teenagers from households with higher educational attainment have higher exposure levels for PFASs and arsenic. In children, a social gradient was only observed for the non-specific pyrethroid metabolite 3-PBA and di-isodecyl phthalate (DiDP), with higher levels in children from households with higher educational attainment. Geographical variations were seen for all exposure biomarkers. For 15 biomarkers, the available health-based HBM guidance values were exceeded with highest exceedance rates for toxicologically relevant arsenic in teenagers (40%), 3-PBA in children (36%), and between 11 and 14% for total DON, Σ (PFOA + PFNA + PFHxS + PFOS), bisphenol S and cadmium. The infrastructure and harmonized approach succeeded in obtaining comparable European wide internal exposure data for a prioritized set of 11 chemical groups. These data serve as a reference for comparison at the global level, provide a baseline to compare the efficacy of the European Commission's chemical strategy for sustainability and will give leverage to national policy makers for the implementation of targeted measures

Computational homogenization of polycrystalline materials with the Virtual Element Method

Homogenized properties of polycrystalline materials are needed in many engineering applications. The present work investigates the effectiveness of computational homogenization approaches based on the Virtual Element Method (VEM). Advantages and/or disadvantages of the VEM formulation with respect to traditional FEM approaches are explored by means of a number of numerical examples. Representative volume elements with different geometrical and material properties are investigated. Both two-and three-dimensional applications, as well as both linear and nonlinear homogenization schemes, are presented. The results show the accuracy of a VEM-based approach. On the contrary, traditional FEM-based homogenization schemes suffer with increasing grains anisotropy, requiring a high number of degree of freedoms for maintaining an acceptable accuracy. In conclusion, VEM is a promising methodology for the homogenization of polycrystalline materials. The advantage of VEM when compared to FEM is of engineering relevance for facing the challenging case of materials with strong and heterogeneous anisotropies. In fact, it is shown that VEM formulations are free from anisotropic locking. (C) 2019 Elsevier B.V. All rights reserved

On two simple virtual Kirchhoff-Love plate elements for isotropic and anisotropic materials

International audienceAbstract The virtual element method allows to revisit the construction of Kirchhoff-Love elements because the $$C^1$$ C 1 -continuity condition is much easier to handle in the VEM framework than in the traditional Finite Elements methodology. Here we study the two most simple VEM elements suitable for Kirchhoff-Love plates as stated in Brezzi and Marini (Comput Methods Appl Mech Eng 253:455–462, 2013). The formulation contains new ideas and different approaches for the stabilisation needed in a virtual element, including classic and energy stabilisations. An efficient stabilisation is crucial in the case of $$C^1$$ C 1 -continuous elements because the rank deficiency of the stiffness matrix associated to the projected part of the ansatz function is larger than for $$C^0$$ C 0 -continuous elements. This paper aims at providing engineering inside in how to construct simple and efficient virtual plate elements for isotropic and anisotropic materials and at comparing different possibilities for the stabilisation. Different examples and convergence studies discuss and demonstrate the accuracy of the resulting VEM elements. Finally, reduction of virtual plate elements to triangular and quadrilateral elements with 3 and 4 nodes, respectively, yields finite element like plate elements. It will be shown that these $$C^1$$ C 1 -continuous elements can be easily incorporated in legacy codes and demonstrate an efficiency and accuracy that is much higher than provided by traditional finite elements for thin plates

Electro-magneto-mechanically response of polycrystalline materials: Computational homogenization via the Virtual Element Method

This work presents a study on the computational homogenization of electro-magneto-mechanically coupled problems through the Virtual Element Method (VEM). VE-approaches have great potential for the homogenization of the physical properties of heterogeneous polycrystalline microstructures with anisotropic grains. The flexibility in element shapes can be exploited for creating VE-mesh with a significant lower number of degrees of freedom if compared to finite element (FE) meshes, while maintaining a high accuracy. Evidence that VE-approaches outperform FEM is available in the literature, but only addressing purely-mechanic problems (i.e. elastic properties) and transversely anisotropic materials. The aim of this work is twofold. On one hand, the study compares VE-and FE-based numerical homogenization schemes for electro-mechanically coupled problems for different crystal lattice structures and degrees of elastic anisotropy. Within all considered materials, the VEapproach outperforms the FE-approach for the same number of nodes. On the other hand, a hybrid microstructure made up by both electro-mechanical and magneto-mechanical grains is investigated resulting in an electro-magneto-mechanically coupled microstructure. Again, VEM provides a more accurate solution strategy. (C) 2021 Elsevier B.V. All rights reserved