Finite element technology for solid mechanics at finite deformations

Mahmood Jabareen and Pedro Areias

Technion - Israel Institute of Technology; Universidade de Lisboa

Relevance to WCCM–ECCOMAS

The objective of this one-day intensive course is to provide a rigorous and implementation-oriented understanding of advanced finite element technologies for solid mechanics at finite deformations.

Course description

The objective of this one-day intensive course is to provide a rigorous and implementation-oriented understanding of advanced finite element technologies for solid mechanics at finite deformations. The course establishes the theoretical and element-technology foundations, covering nonlinear continuum mechanics, hyperelastic constitutive modeling, and advanced element formulations that overcome well-known limitations of standard displacement-based methods.

The course is designed to: Establish a consistent theoretical foundation linking nonlinear continuum mechanics to finite element discretization; Cover advanced constitutive modeling for hyperelastic and inelastic materials; Present advanced finite element technologies; Provide a critical comparison of element technologies in terms of accuracy, robustness, and computational efficiency; Highlight practical implementation aspects.

The course establishes the theoretical and element-technology foundations, covering nonlinear continuum mechanics, hyperelastic constitutive modeling, and advanced element formulations that overcome well-known limitations of standard displacement-based methods.

Objectives and target groups

Learning Outcomes:

  • Formulate finite deformation problems using appropriate kinematic descriptions and stress/strain measures
  • Select and implement hyperelastic and inelastic constitutive models for finite-strain applications
  • Derive and interpret weak forms based on the Bubnov–Galerkin approach for nonlinear problems
  • Distinguish between Total Lagrangian and Updated Lagrangian formulations and select the appropriate framework for a given application
  • Analyze numerical pathologies (e.g., volumetric locking, shear locking, hourglass instability)
  • Evaluate and compare advanced formulations, including: three-field mixed methods; Enhanced Assumed Strain (EAS) methods; reduced integration with stabilization techniques; Cosserat-point theory

Target groups: Graduate students in mechanical, civil, and aerospace engineering; Researchers in computational and applied mechanics; Practicing engineers performing nonlinear finite element simulations.

Scientific and technical areas covered

  • Nonlinear continuum mechanics (kinematics, stress and strain measures)
  • Hyperelastic and inelastic constitutive modeling
  • Variational formulations and the Bubnov–Galerkin method
  • Total and Updated Lagrangian finite element frameworks
  • Mixed finite element methods (three-field formulations)
  • Enhanced Assumed Strain (EAS) techniques
  • Reduced integration method with hourglass stabilization
  • Cosserat point theory
  • Numerical implementation aspects

Bio-sketch

Mahmood Jabareen is an Associate Professor at the Faculty of Civil and Environmental Engineering, Technion - Israel Institute of Technology. He received his Ph.D. degree in 2005 from the Technion – Israel Institute of Technology, and joined the Technion as an Assistant Professor in 2009 after two successively held postdoctoral positions at Technion and the Swiss Federal Institute of Technology – ETH. Mahmood is currently serving as the President of the Israel Association for Computational Methods in Mechanics (IACMM).
His main research interest is developing advanced finite element formulations and computational methods for modeling solids and structures at different scales. Specifically, Mahmood is working on a variety of topics in computational mechanics, including Cosserat point element, modeling of electroactive polymers, biomechanics, failure modeling and crack propagation in soft materials. His research has been funded by grants from the Israel Science Foundation, The Ministry of Housing and Construction, and other resources.

Pedro M. A. Areias is Associate Professor in the Department of Mechanical Engineering at Instituto Superior Técnico, Universidade de Lisboa. He received his PhD in Engineering from the University of Porto in 2003. His research focuses on computational mechanics, finite element methods, nonlinear solid mechanics, fracture, remeshing, and finite-strain plasticity.
He has held research positions at Northwestern University, UIUC-CSAR, CERIS/IST, and the University of Évora, where he was Assistant Professor. He has authored work on XFEM, constitutive modelling, sparse numerical algorithms, and high-performance scientific software. His current interests include robust computational methods for solids, advanced discretisation techniques, and efficient C++/C#/Fortran implementations for large-scale mechanics problems.