Tensor Complementarity and Q-Tensor Stability Analysis for Nonlinear Contact Systems with Applications to Additive Manufacturing

Authors

  • Rakib Efendiev Department of Mathematics and Computer Science, Baku Engineering University, Baku, AZ 0101, Azerbaijan. Author
  • Murkur Rajesh Department of Mechanical Engineering, JNTUA College of Engineering Pulivendula, Pulivendula 516 390, YSR Kadapa Dt, India. Author
  • Sayapogu Prateepkumar Department of Mechanical Engineering, JNTUA College of Engineering Pulivendula, Pulivendula 516 390, YSR Kadapa Dt, India. Author
  • Sunil Kumar Department of Mathematics, School of Sciences, National Institute of Technology Andhra Pradesh, Tadepalligudem, 534 101, India. , Department of Mathematics, SRM University Andhra Pradesh, Mangalagiri- 522 502, Andhra Pradesh, India. Author
  • Fatmir Basholli Department of Engineering; Faculty of Engineering, Informatics and Architecture; European University of Tirana, Tirana, Albania. Author

DOI:

https://doi.org/10.71426/jasm.v2.i1.pp101-105

Keywords:

Tensor complementarity, Q-tensors, Nonlinear contact, Additive manufacturing, Copositive tensors, Stability analysis.

Abstract

Nonlinear contact interactions in additive manufacturing involve multi-layer coupling, thermo-mechanical nonlinearity, and evolving material interfaces. Classical matrix-based complementarity models cannot fully represent higher-order interaction structures. This paper formulates nonlinear contact equilibrium as a tensor complementarity problem (TCP) and establishes solvability and stability using Q-tensor and copositivity conditions. A stability margin based on tensor energy and game-theoretic interpretation is introduced. Numerical simulations of layered deposition demonstrate improved prediction of contact forces, stress localization, and structural stability.

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Published

2026-06-24

Issue

Vol. 2 No. 1 (2026): Volume 2, Issue 1, Jan - Jun 2026

Section

Research Article

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Copyright (c) 2026 Rakib Efendiev, Murkur Rajesh, Sayapogu Prateepkumar, Sunil Kumar (Author)

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How to Cite

[1]
R. Efendiev, M. Rajesh, S. Prateepkumar, S. Kumar, and F. Basholli, “Tensor Complementarity and Q-Tensor Stability Analysis for Nonlinear Contact Systems with Applications to Additive Manufacturing”, Journal of Applied Sciences and Modelling, vol. 2, no. 1, pp. 101–105, Jun. 2026, doi: 10.71426/jasm.v2.i1.pp101-105.