Browsing by Author "Keshav, Sanath"

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Open Access
FFT-based homogenization at finite strains using composite boxels (ComBo)
(2022) Keshav, Sanath; Fritzen, Felix; Kabel, Matthias
Computational homogenization is the gold standard for concurrent multi-scale simulations (e.g., FE2) in scale-bridging applications. Often the simulations are based on experimental and synthetic material microstructures represented by high-resolution 3D image data. The computational complexity of simulations operating on such voxel data is distinct. The inability of voxelized 3D geometries to capture smooth material interfaces accurately, along with the necessity for complexity reduction, has motivated a special local coarse-graining technique called composite voxels (Kabel et al. Comput Methods Appl Mech Eng 294: 168-188, 2015). They condense multiple fine-scale voxels into a single voxel, whose constitutive model is derived from the laminate theory. Our contribution generalizes composite voxels towards composite boxels (ComBo) that are non-equiaxed, a feature that can pay off for materials with a preferred direction such as pseudo-uni-directional fiber composites. A novel image-based normal detection algorithm is devised which (i) allows for boxels in the firsts place and (ii) reduces the error in the phase-averaged stresses by around 30% against the orientation cf. Kabel et al. (Comput Methods Appl Mech Eng 294: 168-188, 2015) even for equiaxed voxels. Further, the use of ComBo for finite strain simulations is studied in detail. An efficient and robust implementation is proposed, featuring an essential selective back-projection algorithm preventing physically inadmissible states. Various examples show the efficiency of ComBo against the original proposal by Kabel et al. (Comput Methods Appl Mech Eng 294: 168-188, 2015) and the proposed algorithmic enhancements for nonlinear mechanical problems. The general usability is emphasized by examining various Fast Fourier Transform (FFT) based solvers, including a detailed description of the Doubly-Fine Material Grid (DFMG) for finite strains. All of the studied schemes benefit from the ComBo discretization.
Open Access
Spectral normalization and Voigt-Reuss net : a universal approach to microstructure‐property forecasting with physical guarantees
(2025) Keshav, Sanath; Herb, Julius; Fritzen, Felix
Heterogeneous materials are crucial to producing lightweight components, functional components, and structures composed of them. A crucial step in the design process is the rapid evaluation of their effective mechanical, thermal, or, in general, constitutive properties. The established procedure is to use forward models that accept microstructure geometry and local constitutive properties as inputs. The classical simulation‐based approach, which uses, for example, finite elements and FFT‐based solvers, can require substantial computational resources. At the same time, simulation‐based models struggle to provide gradients with respect to the microstructure and the constitutive parameters. Such gradients are, however, of paramount importance for microstructure design and for inverting the microstructure‐property mapping. Machine learning surrogates can excel in these situations. However, they can lead to unphysical predictions that violate essential bounds on the constitutive response, such as the upper (Voigt‐like) or the lower (Reuss‐like) bound in linear elasticity. Therefore, we propose a novel spectral normalization scheme that a priori enforces these bounds. The approach is fully agnostic with respect to the chosen microstructural features and the utilized surrogate model: It can be linked to neural networks, kernel methods, or combined schemes. All of these will automatically and strictly predict outputs that obey the upper and lower bounds by construction. The technique can be used for any constitutive tensor that is symmetric and where upper and lower bounds (in the Löwner sense) exist, that is, for permeability, thermal conductivity, linear elasticity, and many more. We demonstrate the use of spectral normalization in the Voigt–Reuss net using a simple neural network. Numerical examples on truly extensive datasets illustrate the improved accuracy, robustness, and independence of the type of input features in comparison to much‐used neural networks.