Development of SBFem finite elements approximations to model multi scale problems

• Grant number: 17/08683-0
• Support Opportunities: Scholarships abroad - Research
• Start date: November 01, 2017
• End date: January 31, 2018
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Principal Investigator: Philippe Remy Bernard Devloo
• Grantee: Philippe Remy Bernard Devloo
• Host Investigator: Chongmin Song
• Host Institution: Faculdade de Engenharia Civil, Arquitetura e Urbanismo (FEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: University of New South Wales (UNSW), Australia

Abstract

In a first period of 2 1/2 months (1st August till 15th October) tensor approximation spaces applied to hyper elastic problems will be developed and implemented in colaboration with Profs Chensong Zhang and Long Chen at the Chinese Academy of Science. Tensor approximation spaces lead to numerical approximations where each element in in local equilibrium. Tensor approximation spaces also form the basis of efficient error estimators for high order continuous finite element approximations.In a second period (1st November till 31st January) the SBFem (Scaled Boundary Finite Element) approximations will be incorporated in the NeoPZ library in collaboration with Prof. Chongmin Song of the University of New South Wales (UNSW). The SBFem approximations will be applied to the simulation of multi scale problems combining MHM (multi scale hybrid) approximations with the SBFem method to model heterogeneous material properties. Such problems are representative of many multi scale problems. The combination of MHM with SBFem can be viewed as a two three level simulation. The global fluxes represent the global scale, the fine mesh represent the tension state in grains and SBFem represents the intergranular tensions.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DEVLOO, PHILIPPE R. B.; GOMES, SONIA M.; QUINELATO, THIAGO O.; TIAN, SHUDAN. Enriched two dimensional mixed finite element models for linear elasticity with weak stress symmetry. COMPUTERS & MATHEMATICS WITH APPLICATIONS, v. 79, n. 9, p. 2678-2700, MAY 1 2020. (17/08683-0)

COELHO, KAROLINNE O.; DEVLOO, PHILIPPE R. B.; GOMES, SONIA M.. Error estimates for the Scaled Boundary Finite Element Method. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, v. 379, JUN 1 2021. (16/05155-0, 17/08683-0)