Simplified Numerical Homogenization Method for the Plasticity Problem with Isotropic Hardening

The development of concrete buildings is related with the complex reinforcement of initial material. A way to improve concrete’s strength is to include metallic or polymer fibers. The numerical modelling of such composite materials is a computational challenge. Calculating deformations of single fib...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2023-10, Vol.44 (10), p.4157-4169
Main Author: Sivtsev, P. V.
Format: Article
Language:English
Subjects:
Accuracy
Algebra
Algorithms
Analysis
Composite materials
Concrete blocks
Deformation
Fiber reinforced concretes
Finite element method
Geometry
Hardening
Homogenization
Inclusions
Isotropic material
Mathematical Logic and Foundations
Mathematical models
Mathematics
Mathematics and Statistics
Numerical models
Plastic properties
Probability Theory and Stochastic Processes
Reinforced concrete
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Summary:The development of concrete buildings is related with the complex reinforcement of initial material. A way to improve concrete’s strength is to include metallic or polymer fibers. The numerical modelling of such composite materials is a computational challenge. Calculating deformations of single fiber-reinforced concrete block using a grid with the resolution of all inclusions is a very large-scale computational problem. To solve these problems, one can use numerical homogenization method. When plastic deformations are taken into account, the numerical homogenization becomes complicated due to nonlinearity. In this work, we present a simplified computational algorithm to describe the anisotropic nature of the composite material with isotropic hardening using numerical homogenization. As a model problem, a deformation of a composite material with a periodic arrangement of inclusions in the form of fibers is considered. Numerical homogenization of the elasticity and plasticity tangent is performed on the representative element. The calculated effective parameters are used to solve the problem on a coarse mesh. The accuracy of using the computational algorithm is checked in comparison with the original solution using a fine mesh with fiber resolution. The numerical results show good accuracy for the cases of interest.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080223100384