Author
Reza Zabihyan
Bio: Reza Zabihyan is an academic researcher from University of Erlangen-Nuremberg. The author has contributed to research in topics: Boundary value problem & Homogenization (chemistry). The author has an hindex of 4, co-authored 6 publications receiving 62 citations.
Papers
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TL;DR: Reduced-order modelling (ROM) for the geometrically nonlinear case using hyperelastic materials is applied and three methods for hyper-reduction, differing in how the nonlinearity is approximated and the subsequent projection, are compared in terms of accuracy and robustness.
Abstract: 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.
30 citations
TL;DR: In this article, the behavior of heterogeneous magnetorheological composites subjected to large deformations and external magnetic fields is studied and 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.
25 citations
TL;DR: In this article, 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.
25 citations
TL;DR: In this paper, the authors compare large-scale non-simplified and non-ergodic models with simplified, parametric, ergodic, and sometimes periodic models and demonstrate that for a stochastic problem there are more than three classical types of boundary conditions.
16 citations
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01 Jan 2016
TL;DR: Kindly say, the nonlinear finite elements for continua and structures is universally compatible with any devices to read.
Abstract: nonlinear finite elements for continua and structures is available in our book collection an online access to it is set as public so you can get it instantly. Our books collection saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the nonlinear finite elements for continua and structures is universally compatible with any devices to read.
445 citations
TL;DR: It is shown that a similar accuracy as with a FE 2 multi-scale simulation can be reached with the RNN-based surrogate model as long as the local strain state remains in the training range, while the computational time is reduced by four orders of magnitude.
90 citations
TL;DR: Hard-magnetic soft composites consist of magneto-active polymers (MAPs) where the fillers are composed of hardmagnetic (magnetically polarised) particles as mentioned in this paper.
70 citations
TL;DR: Twoscale simulations involving more than 10 6 DOF on the structural level are solved using the RNEXP and the influence of the microstructure on theStructural behavior is quantified.
Abstract: The nonlinear behavior of materials with three-dimensional microstructure is investigated using a data-driven approach. The key innovation is the combination of two hierarchies of precomputations with sensibly chosen sampling sites and adapted interpolation functions : First, finite element (FE) simulations are performed on the microstructural level. A sophisticated sampling strategy is developed in order to keep the number of costly FE computations low. Second, the generated simulation data serves as input for a reduced order model (ROM). The ROM allows for considerable speed-ups on the order of 10–100. Still, its performance is below the demands for actual twoscale simulations. In order to attain the needed speed-ups, in a third step, the use of radial numerically explicit potentials (RNEXP) is proposed. The latter combine uni-directional cubic interpolation functions with radial basis functions operating on geodesic distances. The evaluation of the RNEXP approximation is realized almost in real-time. It benefits from the computational efficiency of the ROM since a higher number of sampling points can be realized than if direct FE simulations were used. By virtue of the dedicated sampling strategy less samples and, thus, precomputations (both FE and ROM) are needed than in competing techniques from literature. These measures render the offline cost of the RNEXP manageable on workstation computers. Additionally, the chosen sampling directions show favorable for the employed kernel interpolation. Numerical examples for highly nonlinear hyperelastic (pseudo-plastic) composite materials with isotropic and anisotropic microstructure are investigated. Twoscale simulations involving more than 10 6 DOF on the structural level are solved using the RNEXP and the influence of the microstructure on the structural behavior is quantified.
63 citations
TL;DR: Hard-magnetic soft composites consist of magneto-active polymers (MAPs) where the fillers are composed of hardmagnetic (magnetically polarised) particles as mentioned in this paper .
58 citations