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Item type:Publication, Access status: with files , A short note on minor and major symmetries in linear elasticitySimply applying the directional derivative either twice to the strain-energy density function (hyperelasticity) or once to the stress–strain state (Cauchy elasticity) does not lead to the symmetries of the fourth-order elasticity tensor specified in the literature. Moreover, there are many justifications and arguments for the desired symmetries, which are summarized in this contribution. Thus, a symmetrization operator has to be introduced to guarantee minor symmetry, since the symmetry of the strain tensor is frequently neglected but is needed to obtain results required for particular elasticity relations. A thorough investigation is provided for both Cauchy elasticity and hyperelasticity, and what conclusion can be drawn on by various assumptions.Publicationtype: Journal Article15 20 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Full-field validation of finite cell method computations on wire arc additive manufactured components(Springer, 2024-06-05); ; ; Wire arc additive manufacturing enables the production of components with high deposition rates and the incorporation of multiple materials. However, the manufactured components possess a wavy surface, which is a major difficulty when it comes to simulating the mechanical behavior of wire arc additively manufactured components and evaluation of experimental full-field measurements. In this work, the wavy surface of a thick-walled tube is measured with a portable 3D scanning technique first. Then, the surface contour is considered numerically using the finite cell method. There, hierarchic shape functions based on integrated Legendre polynomials are combined with a fictitious domain approach to simplify the discretization process. This enables a hierarchic p-refinement process to study the convergence of the reaction quantities and the surface strains under tension–torsion load. Throughout all considerations, uncertainties arising from multiple sources are assessed. This includes the material parameter identification, the geometry measurement, and the experimental analysis. When comparing experiment and numerical simulation, the in-plane surface strains are computed based on displacement data using radial basis functions as ansatz for global surface interpolation. It turns out that the finite cell method is a suitable numerical technique to consider the wavy surface encountered for additively manufactured components. The numerical results of the mechanical response of thick-walled tubes subjected to tension–torsion load demonstrate good agreement with real experimental data, particularly when employing higher-order polynomials. This agreement persists even under the consideration of the inherent uncertainties stemming from multiple sources, which are determined by Gaussian error propagation.Publicationtype: Journal Article47 24 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Monolithic and partitioned coupling schemes for thermo-viscoplasticity(2015-08-05); ; ; In this article we investigate a fully, thermo-mechanically coupled viscoplasticity model in view of various numerical aspects. First, we develop the entire system of differential-algebraic equations resulting from the spatially discretized principle of virtual displacements, the principle of virtual temperatures, and the evolution equations of the internal variables provided by the constitutive model. In the time-integration step this system is solved both using a fully monolithic approach based on a Backward-Euler scheme in combination with the Multilevel-Newton algorithm as well as a partitioned approach solving the fully coupled system. The latter is treated by means of a combination of a Backward-Euler method and an accelerated Gauss-Seidel/Multilevel-Newton scheme to solve the resulting system of algebraic equations within each time-integration step. Additionally, we consider a specific treatment of the interpolation between different meshes within the partitioned approach. This is shown for p-version finite elements based on hierarchical shape functions. Finally, it turns out that the specific constitutive model of small-strain thermo-viscoplasticity, which is based on the decomposition into kinematic hardening and energy storing strains, yields a problem-adapted stress algorithm. This allows to reduce the stress algorithm on Gauss-point level to the solution of one scalar equation. Numerical examples serve to elucidate the behavior and properties of the proposed methods.Publicationtype: Journal Article98 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A partitioned solution approach for electro-thermo-mechanical problemsThe purposes of this article are to present new aspects of modeling multi-physically coupled fields, focusing particularly on the partitioned treatment of electro-thermo-mechanical problems. Coupled problems of this kind occur in many industrial applications, such as micro-electrical devices, field-assisted sintering processes or electrical fuses. In this paper, we restrict ourselves to the case of nonlinear thermo-elasticity at finite strains and a heat source resulting from the electrical field. Plasticity effects are not taken into consideration. The objective is to ascertain the coupling of the algorithm relating to the fields involved individually and to demonstrate a global partitioned solution strategy. We also introduce several methods that increase algorithmic stability and accelerate the iterative coupling process. This article aims to present an efficient partitioned coupling strategy for different coupling levels between the fields. To this end, we study the proposed algorithm with the help of several numerical examples ranging from linear to highly nonlinear problems, involving substantial geometric changes and finite strains.Publicationtype: Journal Article138 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , High-order finite elements compared to low-order mixed element formulationsHigh-order finite elements are commonly compared with linear element formulations showing that, in terms of the relation between computational time and achievable accuracy, linear element formulations are inferior to high-order elements. On the other hthe finite element community follows the h-version approach due to its simplicity in implementation. This article compares high-order finite elements based on hierarchic shape functions with low-order mixed element formulations using finite strain hyperelasticity. These comparisons are conducted from the point of view of both accuracy and efficiency as well as highly deformed structures. It also investigates improvements to minimize the overall computational effort such as parallelizing the element assemblage procedure, choosing a starting vector estimator for Newton's method, and investigating the Newton-Chord method. The advantages and disadvantages of both finite element approaches are also discussed. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.Publicationtype: Journal Article71