Homogenization of heterogeneous, fibre structured materials

This contribution presents a multi-scale homogenization method to model fibre structured materials. On the macroscopic level textiles are characterized by a large area-to-thickness ratio, such that a discretization with shell elements is numerically efficient. The material behavior is strongly influenced by the heterogeneous micro structure. To capture the contact on the micro level, the RVE is explicitly modelled by means of a volumetric micro sample and a shell specific homogenization scheme is applied to transfer the microscopic response to the macro level. Theoretical aspects are discussed and a numerical example for contact behavior of a periodic knitted structure is give

Finite Element Simulation and Comparison of Piezoelectric Vibration-Based Energy Harvesters with Advanced Electric Circuits

[EN] A system simulation method based on the Finite-Element Method (FEM) is applied to simulate a bimorph piezoelectric vibration-based energy harvester (PVEH) with different electric circuits: The standard circuit, the synchronized switch harvesting on inductor (SSHI) circuit and the synchronized electric charge extraction (SECE) circuit are considered. Moreover, nonlinear elasticity of the piezoelectric material is taken into account and different magnitudes of base excitations are applied. The holistic FEM-based system simulation approach allows the detailed evaluation of the influences of the considered electric circuits on the vibrational behavior of the PVEH. Furthermore, the harvested energy of the different applied electric circuits with respect to the magnitude of base excitation is compared and results from literature regarding the efficiency of electric circuits are confirmed.The authors gratefully acknowledge financial support for this work by the Deutsche Forschungsgemeinschaft under GRK2495/C.Hegendörfer, A.; Mergheim, J. (2022). Finite Element Simulation and Comparison of Piezoelectric Vibration-Based Energy Harvesters with Advanced Electric Circuits. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 160-169. https://doi.org/10.4995/YIC2021.2021.12177OCS16016

Two-scale parameter identification for heterogeneous elastoplastic materials

The aim of this paper is to describe a method for identifying micro material parameters using only macroscopic experimental data. The FE2 method is used to model the behavior of the complex materials with heterogeneous micro-structure. The resulting least squares problem, with the difference of the simulated and the measured macroscopic data in the objective function, is minimized using gradient-based optimization algorithms with respect to the microscopic material parameters. The gradient information is derived analytically within the discretized scheme

Reduced-Order Modelling and Homogenisation in Magneto-Mechanics: A Numerical Comparison of Established Hyper-Reduction Methods

The simulation of complex engineering structures built from magneto-rheological elastomers is a computationally challenging task. Using the FE 2 method, which is based on computational homogenisation, leads to the repetitive solution of micro-scale FE problems, causing excessive computational effort. In this paper, the micro-scale FE problems are replaced by POD reduced models of comparable accuracy. As these models do not deliver the required reductions in computational effort, they are combined with hyper-reduction methods like the Discrete Empirical Interpolation Method (DEIM), Gappy POD, Gauss–Newton Approximated Tensors (GNAT), Empirical Cubature (EC) and Reduced Integration Domain (RID). The goal of this work is the comparison of the aforementioned hyper-reduction techniques focusing on accuracy and robustness. For the application in the FE 2 framework, EC and RID are favourable due to their robustness, whereas Gappy POD rendered both the most accurate and efficient reduced models. The well-known DEIM is discarded for this application as it suffers from serious robustness deficiencies

On optimization of heterogeneous materials for enhanced resistance to bulk fracture

We propose a novel approach to optimize the design of heterogeneous materials, with the goal of enhancing their effective fracture toughness under mode-I loading. The method employs a Gaussian processes-based Bayesian optimization framework to determine the optimal shapes and locations of stiff elliptical inclusions within a periodic microstructure in two dimensions. To model crack propagation, the phase-field fracture method with an efficient interior-point monolithic solver and adaptive mesh refinement, is used. To account for the high sensitivity of fracture properties to initial crack location with respect to heterogeneities, we consider multiple cases of initial crack and optimize the material for the worst-case scenario. We also impose a minimum clearance constraint between the inclusions to ensure design feasibility. Numerical experiments demonstrate that the method significantly improves the fracture toughness of the material compared to the homogeneous case

A numerical study of different projection-based model reduction techniques applied to computational homogenisation

Computing the macroscopic material response of a continuum body commonly involves the formulation of a phenomenological constitutive model. However, the response is mainly influenced by the heterogeneous microstructure. Computational homogenisation can be used to determine the constitutive behaviour on the macro-scale by solving a boundary value problem at the micro-scale for every so-called macroscopic material point within a nested solution scheme. Hence, this procedure requires the repeated solution of similar microscopic boundary value problems. To reduce the computational cost, model order reduction techniques can be applied. An important aspect thereby is the robustness of the obtained reduced model. Within this study reduced-order modelling (ROM) for the geometrically nonlinear case using hyperelastic materials is applied for the boundary value problem on the micro-scale. This involves the Proper Orthogonal Decomposition (POD) for the primary unknown and hyper-reduction methods for the arising nonlinearity. Therein three methods for hyper-reduction, differing in how the nonlinearity is approximated and the subsequent projection, are compared in terms of accuracy and robustness. Introducing interpolation or Gappy-POD based approximations may not preserve the symmetry of the system tangent, rendering the widely used Galerkin projection sub-optimal. Hence, a different projection related to a Gauss-Newton scheme (Gauss-Newton with Approximated Tensors- GNAT) is favoured to obtain an optimal projection and a robust reduced model

Macroscopic simulation and experimental measurement of melt pool characteristics in selective electron beam melting of Ti-6Al-4V

Selective electron beam melting of Ti-6Al-4V is a promising additive manufacturing process to produce complex parts layer-by-layer additively. The quality and dimensional accuracy of the produced parts depend on various process parameters and their interactions. In the present contribution, the lifetime, width and depth of the pools of molten powder material are analyzed for different beam powers, scan speeds and line energies in experiments and simulations. In the experiments, thin-walled structures are built with an ARCAM AB A2 selective electron beam melting machine and for the simulations a thermal finite element simulation tool is used, which is developed by the authors to simulate the temperature distribution in the selective electron beam melting process. The experimental and numerical results are compared and a good agreement is observed. The lifetime of the melt pool increases linearly with the line energy, whereby the melt pool dimensions show a nonlinear relation with the line energy

On the numerical integration of isogeometric interface elements

Zero-thickness interface elements are commonly used in computational mechanics to model material interfaces or to introduce discontinuities. The latter class requires the existence of a non-compliant interface prior to the onset of fracture initiation. This is accomplished by assigning a high dummy stiffness to the interface prior to cracking. This dummy stiffness is known to introduce oscillations in the traction profile when using Gauss quadrature for the interface elements, but these oscillations are removed when resorting to a Newton-Cotes integration scheme 1. The traction oscillations are aggravated for interface elements that use B-splines or non-uniform rational B-splines as basis functions (isogeometric interface elements), and worse, do not disappear when using Newton-Cotes quadrature. An analysis is presented of this phenomenon, including eigenvalue analyses, and it appears that the use of lumped integration (at the control points) is the only way to avoid the oscillations in isogeometric interface elements. New findings have also been obtained for standard interface elements, for example that oscillations occur in the relative displacements at the interface irrespective of the value of the dummy stiffness