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ARTICLE

Integrated Discrete Cell Complexes and Finite Element Analysis for Microstructure Topology Evolution during Severe Plastic Deformation

Siying Zhu^1,#, Weijian Gao^2,#, Min Yi^1,2,*, Zhuhua Zhang^1,2,*

1 Institute for Frontier Science & Key Lab for Intelligent Nano Materials and Devices of the Ministry of Education, Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, 210016, China
2 State Key Lab of Mechanics and Control for Aerospace Structures & College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, 210016, China

* Corresponding Authors: Min Yi. Email: ; Zhuhua Zhang. Email:
# Equal Contribution

(This article belongs to the Special Issue: Computational Analysis of Micro-Nano Material Mechanics and Manufacturing)

Computers, Materials & Continua 2025, 85(1), 657-679. https://doi.org/10.32604/cmc.2025.068242

Received 23 May 2025; Accepted 03 July 2025; Issue published 29 August 2025

Abstract

Microstructure topology evolution during severe plastic deformation (SPD) is crucial for understanding and optimising the mechanical properties of metallic materials, though its prediction remains challenging. Herein, we combine discrete cell complexes (DCC), a fully discrete algebraic topology model—with finite element analysis (FEA) to simulate and analyse the microstructure topology of pure copper under SPD. Using DCC, we model the evolution of microstructure topology characterised by Betti numbers (, , ) and Euler characteristic (). This captures key changes in GBNs and topological features within representative volume elements (RVEs) containing several hundred grains during SPD-induced recrystallisation. As SPD cycles increase, high-angle grain boundaries (HAGBs) progressively form. Topological analysis reveals an overall decrease in values, indicating fewer isolated HAGB substructures, while values show a steady upward trend, highlighting new grain formation. Leveraging DCC-derived RVE topology and FEA-generated plastic strain data, we directly simulate the evolution and spatial distribution of microstructure topology and HAGB fraction in a copper tube undergoing cyclic parallel tube channel angular pressing (PTCAP), a representative SPD technique. Within the tube, the HAGB fraction continuously increases with PTCAP cycles, reflecting the microstructure’s gradual transition from subgrains to fully-formed grains. Analysis of Betti number distribution and evolution reveals the microstructural reconstruction mechanism underpinning this subgrain to grain transition during PTCAP. We further demonstrate the significant influence of spatially non-uniform plastic strain distribution on microstructure reconstruction kinetics. This study demonstrates a feasible approach for simulating microstructure topology evolution of metals processed by cyclic SPD via the integration of DCC and FEA.

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Keywords

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