arXiv subjects

Ajinkya Gote

Publications and source records attributed to Ajinkya Gote.

4 recordsLinked to original sources

arXiv2021

Computational Homogenization of Concrete in the Cyber Size-Resolution-Discretization (SRD) Parameter Space

Micro- and mesostructures of multiphase materials obtained from tomography and image acquisition are an ever more important database for simulation analyses. Huge data sets for reconstructed 3d volumes typically as voxel grids call for criteria and measures to find an affordable balance of accuracy and efficiency. The present work shows for a 3d mesostructure of concrete in the elastic deformation range, how the computational complexity in analyses of numerical homogenization can be reduced at controlled errors. Reduction is systematically applied to specimen size S, resolution R, and discretization D, which span the newly introduced SRD parameter space. Key indicators for accuracy are (i) the phase fractions, (ii) the homogenized elasticity tensor, (iii) its invariance with respect to the applied boundary conditions and (iv) the total error as well as spatial error distributions, which are computed and estimated. Pre-analyses in the 2d SRD parameter sub-space explore the transferability to the 3d case. Beyond the concrete specimen undergoing elastic deformations in the present work, the proposed concept enables accuracy-efficiency balances for various classes of heterogeneous materials in different deformation regimes and thus contributes to build comprehensive digital twins of materials with validated attributes.

cs.CE↗

arXiv2020

From image data towards microstructure information -- accuracy analysis at the digital core of materials

A cornerstone of computational solid mechanics in the context of digital transformation are databases for microstructures obtained from advanced tomography techniques. Uniform discretizations of pixelized images in 2D are the raw-data point of departure for simulation analyses. This paper proposes the concept of a unified error analysis for image-based microstructure representations in uniform resolution along with adaptively coarsened discretizations. The analysis distinguishes between a modeling error due to finite, possibly coarsened image resolution and a discretization error, investigates their quantitative relation, spatial distributions and their impacts on the simulation results both on the microscale and the macroscale in the context of computational homogenization. The assessment of accuracy and efficiency is carried out for an exemplary two-phase material. Beyond the example considered here the concept is a rational tool in the transformation of raw image data into microstructure information adapted to particular simulation needs and endows the digital twin of real microstructures with validated characteristics for reliable, predictive simulations.

math.NA↗

arXiv2019

A Nonlinear Finite Element Heterogeneous Multiscale Method for the Homogenization of Hyperelastic Solids and a Novel Staggered Two-Scale Solution Algorithm

In this paper we address three aspects of nonlinear computational homogenization of elastic solids by two-scale finite element methods. First, we present a nonlinear formulation of the finite element heterogeneous multiscale method FE-HMM in a Lagrangean formulation that covers geometrical nonlinearity and, more general, hyperelasticity. Second, a-priori estimates of FE-HMM, which exist so far only for the fully linear elastic case in solid mechanics, are assessed in the regime of nonlinear elasticity. The measured convergence rates agree fairly well with those of the fully linear regime. Third, we revise the standard solution algorithm of FE$^2$ which is a staggered scheme in terms of a nested loop embedding the full solution of the micro problem into one macro solution iteration step. We demonstrate that suchlike staggered scheme, which is typically realized by a nested two-level Newton algorithm, can safely and efficiently be replaced by direct alternations between micro and macro iterations. The novel algorithmic structure is exemplarily detailed for the proposed nonlinear FE-HMM, its efficiency is substantiated by a considerable speedup in numerical tests.

math.NA↗

arXiv2018

Estimating the Effective Elasticity Properties of a Diamond/$β$-SiC Composite Thin Film by 3D Reconstruction and Numerical Homogenization

The main aim of the present work is to estimate the effective elastic stiffnesses of a two-phase diamond/$β$-SiC composite thin film that is fabricated by chemical vapor deposition. The parameters of linear elasticity are determined by numerical homogenization. The database is sparse since for the 3D volume of interest only two micrographs displaying the phase distributions in perpendicular planes are available; micrographs each of a cross-section and the surface of the thin film. A representative volume element (RVE) is reconstructed by an optimization software and by means of identified material symmetries in 2D of the specimen. The elastic homogenization results indicate that the two-phase diamond/$β$-SiC composite exhibits the behavior of transverse isotropy, for which the set of six independent material parameters is identified.

cond-mat.mtrl-sci↗