Robust Multiscale Modelling Of Two-Phase Steels On Heterogeneous Hardware Infrastructures By Using Statistically Similar Representative Volume Element

Abstract

Robust multiscale modelling of two-phase steels on heteRogeneous haRdwaRe infRastRuctuRes by using statistically similaR RepResentative volume element efektywne modelowanie wieloskalowe stali dwufazowych na heteRogenicznych architekturach sprzętowych z wykorzystaniem statystycznie podobnych reprezentatywnych elementów objętościowychThe coupled finite element multiscale simulations (FE 2 ) require costly numerical procedures in both macro and micro scales. Attempts to improve numerical efficiency are focused mainly on two areas of development, i.e. parallelization/ distribution of numerical procedures and simplification of virtual material representation. One of the representatives of both mentioned areas is the idea of Statistically Similar Representative Volume Element (SSRVE). It aims at the reduction of the number of finite elements in micro scale as well as at parallelization of the calculations in micro scale which can be performed without barriers. The simplification of computational domain is realized by transformation of sophisticated images of material microstructure into artificially created simple objects being characterized by similar features as their original equivalents. In existing solutions for two-phase steels SSRVE is created on the basis of the analysis of shape coefficients of hard phase in real microstructure and searching for a representative simple structure with similar shape coefficients. Optimization techniques were used to solve this task. In the present paper local strains and stresses are added to the cost function in optimization. Various forms of the objective function composed of different elements were investigated and used in the optimization procedure for the creation of the final SSRVE. The results are compared as far as the efficiency of the procedure and uniqueness of the solution are considered. The best objective function composed of shape coefficients, as well as of strains and stresses, was proposed. Examples of SSRVEs determined for the investigated two-phase steel using that objective function are demonstrated in the paper. Each step of SSRVE creation is investigated from computational efficiency point of view. the proposition of implementation of the whole computational procedure on modern high Performance computing (hPc) infrastructures is described. it includes software architecture of the solution as well as presentation of the middleware applied for data farming purposes.