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Development and Application of the Statistically Similar Representative Volume Element for Numerical Modelling of Multiphase Materials

ABSTRACT: Modern aerospace, automotive and construction industries rely on materials with non-homogeneous properties like composites or multiphase structures. Such materials offer a lot of advantages, but they also require application of advanced numerical models of exploitation condition, which are of high importance for designers, architects and engineers. However, computational cost is one of the most important problems in this approach, being very high and sometimes unacceptable. In this paper we propose approach based on Statistically Similar Representative Volume Element (SSRVE), which is generated by combination of isogeometric analysis and optimization methods. The proposed solution significantly decreases computational cost of complex multiscale simulations and simultaneously maintains high reliability of solvers. At first, the motivation of the work is described in introduction, which is followed by general idea of the SSRVE as a modelling technique. Afterwards, examples of generated SSRVEs based on two different cases are given and passed further to numerical simulations of exploitation conditions. The results obtained from these calculations are used in the model predicting gradients of material properties, which are crucial results for discussion on uniqueness of the proposed solution. Additionally, some aspects of computational cost reduction are discussed, as well.

SUBMITTER: Krzhizhanovskaya V

PROVIDER: S-EPMC7304715 | biostudies-literature | 2020 May

REPOSITORIES: biostudies-literature

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Project description:Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar's work [J. Comput.-Aided Mol. Des. 9, 149 (1995)], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that the methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online as supplemental material.

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Development and Application of the Statistically Similar Representative Volume Element for Numerical Modelling of Multiphase Materials

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