A numerical study of different projection-based model reduction techniques applied to computational homogenisation - Soldner, Dominic; Brands, Benjamin; Zabihyan, Reza; Mergheim, Julia; Steinmann, Paul (Computational Mechanics, 2017)
Keywords: Computational homogenisation; Reduced-order modelling; Hyper-reduction

Aspects of computational homogenization in magneto-mechanics: Boundary conditions, RVE size and microstructure composition - Zabihyan, Reza; Mergheim, Julia; Javili, Ali; Steinmann, Paul (International Journal of Solids and Structures, 2018)
In the present work, the behavior of heterogeneous magnetorheological composites subjected to large deformations and external magnetic fields is studied. Computational homogenization is used to derive the macroscopic material response from the averaged response of the underlying microstructure. The microstructure consists of two materials and is far smaller than the characteristic length of the macroscopic problem. Different types of boundary conditions based on the primary variables of the magneto-elastic enthalpy and internal energy functionals are applied to solve the problem at the micro-scale. The overall responses of the RVEs with different sizes and particle distributions are studied under different loads and magnetic fields. The results indicate that the application of each set of boundary conditions presents different macroscopic responses. However, increasing the size of the RVE, solutions from different boundary conditions get closer to each other and converge to the response obtained from periodic boundary conditions.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Boundary condition; Homogenization; Magneto-mechanics

Computational Homogenisation using Reduced-Order Modelling applied to Hyperelasticity - Soldner, Dominic; Brands, Benjamin; Zabihyan, Reza; Steinmann, Paul; Mergheim, Julia (Proceedings in Applied Mathematics and Mechanics, 2016)
Within this study nonlinear reduced-order modelling for hyperelastic material is applied for the boundary value problem on the micro-scale which arises in the context of computational homogenisation. This involves the Proper Orthogonal Decomposition and the Discrete Empirical Interpolation Method for the nonlinear term. Considered error measures are the errors of the displacement field, the averaged stresses and the effective elasticity tensor.
Keywords: Model Reduction; Computational Homogenisation; Discrete Empirical Interpolation Method

Computational Homogenization in Magneto-Mechanical Composites - Zabihyan, Reza; Mergheim, Julia; Javili, Ali; Steinmann, Paul (Proceedings in Applied Mathematics and Mechanics, 2016)
In the present work, the behavior of heterogeneous magnetorheological elastomers undergoing large deformations under the action of magnetic fields is studied. First-order computational homogenization is used to derive the homogenized stresses and magnetic inductions of the macro-structure from the response of the underlying micro-structure. Different types of boundary conditions are applied to solve the micro problem where the constitutive law is assumed to be known.
Keywords: Magneto-elasticity; homogenization; boundary condition

FE2 simulations of magnetorheological elastomers: influence of microscopic boundary conditions, microstructures and free space on the macroscopic responses of MREs - Zabihyan, Reza; Mergheim, Julia; Pelteret, Jean-Paul; Brands, Benjamin; Steinmann, Paul (International Journal of Solids and Structures, 2020)
In the current work, the response of heterogeneous magnetorheological elastomers (MREs) which are loaded by external magnetic fields in the absence and also in the presence of free space is studied. A fully-coupled two-scale finite element computational homogenization procedure is used to derive the material response at the macro-scale from the averaged response of the underlying micro-scale problem. Different combinations of boundary conditions, that satisfy the Hill-Mandel condition and are based on the primary variables of the magneto-elastic enthalpy and energy functionals are applied to solve the micro-scale boundary value problem. Furthermore, the influences of various microstructures on the macroscopic response of the MREs are investigated. The results indicate that the choice of microscopic boundary conditions and microstructure types can significantly affect the macroscopic responses of MREs.
CRIS-Team Scopus Importer:2020-03-17
Keywords: Boundary conditions; FE; Homogenization; Magneto-elasticity; Magneto-mechanics; Magnetorheological elastomers (MREs)

On periodic boundary conditions and ergodicity in computational homogenization of heterogeneous materials with random microstructure - Pivovarov, Dmytro; Zabihyan, Reza; Mergheim, Julia; Willner, Kai; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2019)
Due to high computational costs associated with stochastic computational homogenization, a highly complex random material microstructure is often replaced by simplified, parametric, ergodic, and sometimes periodic models. This replacement is often criticized in the literature due to unclear error resulting from the periodicity and ergodicity assumptions. In the current contribution we perform a validation of both assumptions through various numerical examples. To this end we compare large-scale non-simplified and non-ergodic models with simplified, ergodic, and periodic solutions. In addition we analyze the Hill-Mandel condition for stochastic homogenization problems and demonstrate that for a stochastic problem there are more than three classical types of boundary conditions. As an example, we propose two novel stochastic periodic boundary conditions which possess a clear physical meaning. The effect of these novel periodic boundary conditions is also analyzed by comparing with non-ergodic simulation results. (C) 2019 Elsevier B.V. All rights reserved.
CRIS-Team WoS Importer:2019-10-25