Applications are open for one post-doctoral research fellowship at IDMEC, Instituto Superior Técnico, University of Lisbon, within the project DEEPFRAC (Deep fracture), FCT 2024.14907.PEX, supervised by Pedro Areias.
Reference of the call: BI 30.PL750.2026.IDMEC.
The project. Phase-field and gradient-enhanced damage predict nucleation, branching and coalescence of cracks without prescribing the crack path, at two costs: the regularization introduces a length scale that is hard
to identify from experiments, and the computation is expensive, since the mesh must resolve that length scale and, in three dimensions, the integration of the constitutive laws at the quadrature points dominates the running time. DEEPFRAC tests how far physics-informed neural networks
can be taken against both. A network trained on the constitutive response replaces the integration algorithm; a network trained on the variational structure of the phase-field problem replaces or preconditions the
solver; an inverse network identifies the length scale from
representative volume elements; and the same networks supply the sensitivities that optimization needs. The aim is not to replace the finite element method, but to put learned components where the classical algorithms are weakest and to measure the trade, in iso-error maps and in
running time, against them.
The work is done in SimPlas, the group's finite-element code, with a PyTorch and DeepXDE toolchain, and the large three-dimensional runs on the Deucalion supercomputer. Code, benchmark database and papers are public. The team is the supervisor and the fellow. The first task of the
project is complete, so the fellow starts with the state of the art already written, a monograph on phase-field fracture and its relation to gradient-enhanced damage, a benchmark suite running in SimPlas, and the constitutive and cohesive laws already implemented.
The tasks of the fellowship:
- months 1-3, constitutive PINN algorithms: neural-network surrogates of the integration algorithms of continuum-damage and cohesive constitutive laws, with iso-error maps and efficiency compared against the classical return-mapping algorithms, and crack-branching cases that
the classical algorithms do not resolve. Outputs: public code, a paper, a conference presentation;
- months 4-7, phase-field PINN: length-scale identification by inverse PINN on representative volume elements, formulations for brittle (Francfort-Marigo, AT1 and AT2) and quasi-brittle fracture with cohesive laws imposed as constraints, ductile damage with calibrated dissipation, and a public benchmark database;
- on renewal: large-scale three-dimensional fracture with crack branching and coalescence, computed on Deucalion and compared with tests on additively manufactured cellular structures; and topology and fibre-orientation optimization with sensitivities obtained from the networks, under manufacturing constraints.
Conditions. Seven months from 1 November 2026, renewable within the limits of the applicable regulations and of the project execution period.
Monthly allowance of 1901,00 EUR (no added taxes) according to the FCT table, paid by bank transfer, with personal-accident insurance, in exclusive-dedication
regime. The work is done in Lisbon.
Profile. Computational solid mechanics and finite elements, with work in fracture or damage; programming in Fortran and in Python (PyTorch or JAX); availability to take up duties in Lisbon on 1 November 2026.
Admission requirements, as set by the call:
a) PhD obtained in the three years prior to the application;
b) doctoral work carried out at an entity other than the host
institution, IDMEC;
c) not exceeding, with this contract and its renewals, three accumulated years in this type of fellowship;
d) no previous post-doctoral fellowship contract with IDMEC.
Application. By email to pedro.areias [at] tecnico.ulisboa.pt until 18:00 Lisbon time of 30 September 2026, with: curriculum vitae; PhD certificate (an applicant who does not yet hold it may send a declaration on honor and deliver the certificate before the contract is signed); a motivation
letter stating the date from which the applicant can take up duties in Lisbon and, where applicable, the status of any visa or residence-permit process for Portugal; and the declaration on honour required by requirements b) and c).
Selection is by curriculum evaluation (70%) and interview (30%), in person or by videoconference. The jury is Pedro Areias, Nuno Silvestre and Aurélio Araújo. All applicants are notified of the result by email and have 10 working days for a rebuttal. A reserve list is drawn up and remains usable for the whole execution period of the project.
The full call, in Portuguese and English, is published at
https://www.idmec.tecnico.ulisboa.pt/about/job-openings/ and on EURAXESS.
Questions before applying are welcome at pedro.areias [at] tecnico.ulisboa.pt.
Funded by national funds through FCT, project
https://doi.org/10.54499/2024.14907.PEX
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