Method of Variable Material Properties for Small Elastoplastic Deformations

Authors

  • Nives Brajčić Kurbaša Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Croatia
  • Blaž Gotovac Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Croatia
  • Vedrana Kozulić Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Croatia

DOI:

https://doi.org/10.13052/ejcm2642-2085.34347

Keywords:

MVMP, Fup4, atomic basis functions, collocation, material parameters, small elastoplastic deformations

Abstract

This work presents a mesh-free formulation that combines the method of variable material properties (MVMP) with a collocation method based on finite atomic basis functions (ABF) for the analysis of small elastoplastic deformations. Unlike existing approaches that update only the tangent modulus of material hardening, the presented method simultaneously updates the elastic modulus E and Poisson’s ratio ν (i.e., Lamé constants λ and μ) as smooth fields. This reduces the nonlinear problem to a sequence of linear elasticity problems. The algorithm is implemented using a strong formulation and the finite Fup4 basis functions from the class of algebraic ABFs. Fup4 is an infinitely differentiable function that exactly reproduces polynomials up to the fourth degree, maintains the continuity of higher derivatives, and thus ensures numerical stability and fast convergence of the collocation-based MVMP procedure. Due to the compact support of the basis functions and the choice of the positions of the collocation points, the matrix of the equations system retains its band form throughout all iterations, which improves the conditioning of the system and accelerates convergence. The accuracy of the proposed approach has been verified on two classical benchmark problems with analytical solutions: a one-dimensional bar under axial load and a thin cylindrical disc subjected to internal pressure.

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Author Biographies

Nives Brajčić Kurbaša, Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Croatia

Nives Brajčić Kurbaša received the master’s degree in civil engineering (mag.ing.aedif.) from the Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Croatia, in 2008, where she also obtained her PhD degree in civil engineering (technical sciences) in 2016. She is currently an Assistant Professor at the Department of Engineering Mechanics of the same faculty. Her research interests include numerical modeling of elastoplastic deformations, mesh-free methods, and atomic basis functions. She is an active member of the Croatian Society of Mechanics and serves as President of the Alumni Association of the Faculty (F-GAGA).

Blaž Gotovac, Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Croatia

Blaž Gotovac graduated from the Faculty of Civil Engineering of the University of Zagreb in 1975. At the same faculty, he obtained his PhD degree in civil engineering (technical sciences) in 1987. Since the fall of 1975, he has been continuously employed at the current Faculty of Civil Engineering, Architecture and Geodesy in Split. Now he is Professor Emeritus. His research interests include development of numerical models for the analysis of structures composed of shells, plates, walls, beams and columns; research of numerical models for the analysis of tunnels and underground structures; implementation of atomic basis functions and development of new numerical procedures in computational mechanics; reconstruction and renovation of historical buildings. He is certified construction project auditor for massive and masonry constructions. Of the large number of professional projects on which he worked as an associate, designer, responsible designer or project manager, the participation of Gotovac in the role of manager of the rebuilding of the Old Bridge in Mostar from 2002 to 2004 should be singled out in particular. He is a member of the Croatian Chamber of Civil Engineers, Croatian Society of Mechanics and Croatian Society of Civil Engineers.

Vedrana Kozulić, Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Croatia

Vedrana Kozulić is employed at the University of Split, Faculty of Civil Engineering, Architecture and Geodesy, as a Full Professor (permanent title). She is the head of the Department of Technical Mechanics. She obtained her PhD degree in technical sciences in 1999. Her research subjects are numerical modelling of linear and nonlinear problems in technical mechanics; problems of continuum discretization; modeling of engineering structures and development of new numerical procedures in order to improve the quality of approximate solutions; development of numerical algorithms for meshless modeling of engineering problems on irregular areas. She is a member of a number of scientific societies: Croatian Society of Mechanics, Central European Association for Computational Mechanics (CEACM), European Mechanics Society (EUROMECH).

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Published

2026-02-26

How to Cite

Kurbaša, N. B. ., Gotovac, B. ., & Kozulić, V. . (2026). Method of Variable Material Properties for Small Elastoplastic Deformations. European Journal of Computational Mechanics, 34(3&4), 363–386. https://doi.org/10.13052/ejcm2642-2085.34347

Issue

2025: Vol 34 Iss 3&4

Section

ECCOMAS-MSF 2025: Multi-scale modeling & computations in solid & fluid mechanics