PhD Position

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Development of necking instabilities in anisotropic ductile plates subjected to dynamic loading

Supervisor: Professor José A. Rodríguez-Martínez

Thin plates of lightweight alloys are commonly used in the manufacture of aircraft and spacecraft structures. Likewise, assemblies used for the protection of critical systems are frequently made of metal sheets. These structures may be submitted to impact or blast loads and their aptitude to absorb the energy of the dynamic load is strongly related to their ability to delay the onset of plastic instabilities which trigger failure in ductile metals. Since strain rate affects both plastic flow and failure, its influence has been studied in the last decades both theoretically and experimentally. In particular, the 3 academic partners of OUTCOME have strongly contributed to this field through the development of original theoretical and experimental methodologies, leading to a deeper knowledge on the effect that individually inertia, strain rate, loading path and anisotropy have on the localization of plastic instabilities and failure. In particular, the systematic confrontation of results obtained from linear perturbation analysis and finite element calculations has allowed to the academic members of OUTCOME to provide new insights into the specific localization patterns that emerge under dynamic biaxial loading. This investigation settled a theoretical framework that can be used in the design of structures for energy absorption, with the ultimate aim of predicting the limits in material ductility which imposes important restrictions to this type of applications. However, the coupled influence of all these material and loading effects, needed for a higher reliability in design, deserves further analysis.

Research outputs:

Development of a linear perturbation model to assess the joint effect that inertia, strain rate, loading path, porosity and anisotropy have on the onset and development of necking instabilities in ductile plates subjected to dynamic loading.

Multidisciplinary/ intersectoral research approach:

The ESR will develop at the University Carlos III of Madrid the core of a linear perturbation analysis to assess the interplay between inertia, strain rate, loading path and anisotropy in the formation of necks in ductile plates subjected to dynamic loading. Moreover she/he will carry out a research period at the TECHNION where she/he will perform Split Hopkinson Tensile Bar tests in ductile sheets in order to have our own experimental validation of the linear perturbation model. Additionally the ESR will carry out a research period in France during which the ESR will stay both at the University of Lorraine and at CIMULEC. At the University of Lorraine she/he will develop the comparison between the linear stability analysis and the experimental results. At CIMULEC where she/he will identify and model real cases in which aerospace components fail due to plastic localization.

Training activities:

The successful candidate will have access to the PhD program of the University Carlos III of Madrid as well as to the training activities organized within the OUTCOME consortium (see here for more information).


The successful candidate will be employed for 3 years and receive a financial package plus an additional mobility and family allowance according to the rules for Early Stage Researchers (ESRs) in an EU Marie Skłodowska-Curie Actions Innovative Training Networks (ITN):

  • Living allowance – 3035.36€ (per month).
  • Mobility allowance – 600€ (per month).
  • Family allowance – 500€ (per month – if applicable).

This amount is a gross contribution to the salary costs. Net salary will result from deducting all compulsory social security/direct taxes from the gross salary according to the law applicable to the agreement concluded with the ESR.

Additional information about the funding provided by the ITN  projects can be found here.

Key publications:

Dudzinski D., Molinari, A. Instability of visco-plastic deformation in biaxial loading. Comptes Rendues Academie Science Paris. 1988; 307: 1315–1321.
Dudzinski D., Molinari A. Perturbation analysis of thermoviscoplastic instabilities in biaxial loading. International Journal of Solids and Structures. 1991; 27: 601–628.
Rodríguez-Martínez J. A., Vadillo G., Fernandez-Sáez J., Molinari A. Identification of the critical wavelength responsible for the fragmentation of ductile rings expanding at very high strain rates. Journal of the Mechanics and Physics of Solids. 2013; 61: 1357–1376.
Rodríguez-Martínez J. A., Vadillo G., Zaera R., Fernandez-Sáez J. On the complete extinction of selected imperfection wavelengths in dynamically expanded ductile rings. Mechanics of Materials. 2013; 60: 107–120.
Zaera, R., Rodríguez-Martínez, J. A., Vadillo, G., Fernandez-Sáez J., Molinari, A. Collective behaviour and spacing of necks in ductile plates subjected to dynamic biaxial loading. Journal of the Mechanics and Physics of Solids. 2015; 85: 245-269.


We are looking for highly motivated early-stage researchers with the following profile:

  • Hands-on mentality, good organizational and communication skills.
  • Proactive attitude and ability to work both independently/autonomously and within a team.
  • Excellent communication skills in English.

In order to meet the specific requirements of the Marie Skłodowska-Curie funded PhDs, you must not have resided or carried out your main activity (work, studies, etc.) in Spain for more than 12 months in the last 3 years. You may be of any Nationality.

Required educational level:

Degree: Master degree or equivalent
Degree field: Engineering: civil, mechanical, aerospace
Degree: Master degree or equivalent
Degree field: Physics

Career stage:

Early stage researcher or 0-4 years (Post graduate).

Professional and/or research experience:

We will particularly consider those candidates with proven experience in technological and/or research activities. Publication/s in journals indexed in the Journal of Citation Reports will be especially welcomed.

Letter of motivation:

The candidates must provide a letter of motivation where they clearly state why, under their point of view, they should be enrolled in OUTCOME.


At least, one recommendation letter from the scientist/s who mentored the candidate during her/his master studies is required. The letter must clearly expose the profile of the candidate with emphasis in the qualities which make her/him suitable for being recruited in OUTCOME. Additional recommendation letters from any other professor/professional will be most welcomed.

Specific qualifications:

Candidates should have a solid background in Solid Mechanics, Experimental Mechanics, Fracture Mechanics and Numerical Modeling.

Flexible working conditions:

We are committed to provide flexible hours and home working conditions for researchers having family obligations. The following web-site contains relevant information related to the EU equal opportunities policy.

Moreover, the web-site  facilitates geographic mobility by providing help to find a job for an accompanying partner.

The application period is closed.
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