Strain gradient modelling and simulation for severe loading conditions, development of a new finite element.


The global aim of ESR5 is the formulation of a viscoplastic strain gradient continuum theory applicable to multi-coupled modelling.

Host institution

Universidad del País Vasco / Euskal Herriko Unibertsitatea (UPV/EHU) in Spain.

Job offer

The global aim of ESR5 is the formulation of a viscoplastic strain gradient continuum theory applicable to multi-coupled modelling.

Classical continuum solid mechanics theories, such as linear or nonlinear elasticity and plasticity, have been used in a wide range of fundamental problems and applications in mechanical and materials engineering. Although initially designed to describe deformation phenomena and processes at scales ranging from millimetres to meters, and therefore observable by the naked eye, these theories were applied in the last century to model phenomena at the atomic scale (elastic theory of dislocations).

However, recent experimental observations at the micrometre or nanometre scale with newly probes such as nano-indenters and atomic force microscopes have suggested that classical continuum theories are no longer sufficient for a precise and detailed description of the corresponding deformation phenomena. These drawbacks have led to the recent development of theories that attempt to capture such phenomena via dependencies on plastic strain gradients.

The purpose of strain gradient modelling is twofold. First, it provides a continuum model that can account for size effects observed during deformation, machining processes or material processing. Second, it is well-known that severe deformation leads to strain localization, e.g. adiabatic shear banding. Finite element simulations of localization phenomena usually exhibit spurious mesh-dependence (dependence of the results on finite element size and orientation) that can be regularized by means of strain gradient models. Coupling with thermal diffusion can lead to regularization but associated length scales are generally too small. Material length scales, related to microstructural features like grain size or dislocation structures, then play an essential role for the understanding and simulation of localisation processes.

The different steps of the PhD work in close cooperation with other ERS contributions will be as follows:

  • formulate the macroscopic strain gradient model
  • identify material parameters from experimental results obtained in ENABLE (ESR1, 2, 3)
  • identify characteristic length scales using in particular from the results of the multiscale polycrystalline approach of ESR4
  • simulate regularized strain localization phenomena including thermal coupling
  • extend the work to more severe loading conditions (including remeshing techniques) and relate to the experiments and simulations of ESR7 (Machining high strain rates), ESR 8 (FSW, high strain), ESR (Additive Manufacturing, high temperatures).
  • transfer of the result to ESR6 (High Performance Computing).

Model and element development will be performed following an implicit scheme. Reaching severe deformations and simulation of realistic processes may require the extension to an explicit solver.



10 months across Europe
  • 4 months MAT (Fr) (05/2019-08/2019)
  • 2 months SAF (Fr) (09/2020-10/2020)
  • 2 months ESI (Fr) (12/2020-01/2021)
  • 2 months UBx (Fr) (02/2021-03/2021)



Pr. Franck Girot
Research Director Samuel Forest
Dr. Arjen Roos
Dr. Raynald Laheurt
Dr. Didier Croizet
Dr. Dimitri Jacquin
Dr. Hyung-Jun CHANG
Pr. Frédéric Feyel


  • Excellent master degree in mechanical engineering, material science, computer science or related disciplines.
  • Strong interest in material science and working knowledge in the field of metallic alloys.
  • Significant laboratory experience in finite element computing and coding (C++)
  • Strong background in plasticity theory and computation.
  • Familiarity with lab equipment, including chemical handling procedures and attention to detail as well as environmental, health and safety (EHS) requirements.
  • Excellent communication skills and willingness to work in collaborative projects with multiple partners.
  • Very good English language skills
  • Self-motivation and the ability to achieve goals independently as well as to contribute effectively to the team.

apply for this job

  • Send your CV and a cover letter to the following address:
  • Please put in the object of your email that your are applying for the ESR5 position.
  • Please check that you meet all eligibility criteria.
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