PhD: Bridging CAD, Image Data and Mechanics for Digital Twins of Additively Manufactured TPMS Lattice Metamaterials

PhD: Bridging CAD, Image Data and Mechanics for Digital Twins of Additively Manufactured TPMS Lattice Metamaterials

Project Assessment

How can CT images of a printed lattice become a compact, CAD-compatible model that predicts its mechanics and uncertainty? This INSA Toulouse/ICA thesis connects geometric modelling, inverse imaging, mechanical simulation and experiments, rather than simply applying AI to an existing dataset. BEST offers a 36-month salaried doctoral route with BCAM co-supervision. The application turns on holding a Master's by the 2026 call deadline, the France mobility rule and a conflicting closing clock. The guide, individual payroll terms and Spanish degree arrangement still need confirmation.

Research Problem and Doctoral Work

A printed lattice can have the intended topology yet the wrong local wall thickness and stiffness. This project asks how to predict the mechanics of the manufactured object while keeping an explicit connection to its original CAD design. The official individual project targets shell-based triply periodic minimal-surface (TPMS) lattices and combines computational mechanics, geometric design, image assimilation and actual specimen manufacture. It is a particular proposed thesis in BEST, not a separate entitlement to the programme's nineteen first-cohort places.

The geometry task uses multi-sided Generalized Bézier patches to describe a smooth shell midsurface and thickness, then fits manufacturing deviations to X-ray CT volumes using virtual image correlation. Unlike simply segmenting an image into an enormous mesh, the intended output remains compact and CAD-compatible. The uncertainty task exploits repeated cells to learn low-dimensional defect descriptors, potentially beginning with variational autoencoders. A 10×10×10 specimen contains one thousand nominal cells, but usefulness as statistical evidence depends on the stated similarity assumption: correlated spatial defects or common process drift must not be treated as one thousand independent specimens.

The mechanical task develops an efficient Kirchhoff–Love-type isogeometric shell formulation and propagates the inferred defect variability to effective response. These are planned contributions, not a delivered uncertainty certificate. A later perspective is to invert the process for CAD pre-compensation. That should remain a longer-term possibility rather than an additional guaranteed thesis outcome. The candidate also participates in printing and CT imaging at ICA, so the work is not a purely machine-learning project using an already assured public dataset.

A useful analyst-proposed sequence is to establish synthetic geometry/CT tests with known defects, distinguish registration error from physical shape variation, compare reconstruction and mechanical errors separately, and test predictions against manufactured specimens. Validate a defect model on independent builds where possible, rather than splitting neighbouring cells from a single build without considering dependence. Check when a thin-shell approximation remains adequate at junctions and highly variable walls. These are questions to discuss with the supervisors, not extra advertised requirements or a fixed work-package timetable.

The Clean Aviation mission provides a real industrial context for lightweight structures. Its target of at least 30% lower net greenhouse-gas emissions relative to 2020 technology is a programme objective, not an achieved benefit of this doctorate. The project description also cites nTop's lattice guide for a general shell-and-infill mass-reduction claim of 50% or more and a Blueflite case study reporting a 25% fuselage mass reduction. These guide and case-study figures are contextual examples, not results of this PhD or its specimens. Numerical accuracy, experimentally identifiable defects and defensible uncertainty are the immediate scientific contributions. Aerospace certification, fatigue life or production deployment would require additional evidence and agreed scope.

School, Field and Doctoral Training

Institutional roles. INSA Toulouse is the advertised employer and establishment of doctoral preparation; ICA, CNRS UMR 5312, is the research laboratory, with the MS2M team. The project names MEGEP and the mechanical-engineering/materials-mechanics specialty. The current Toulouse registration framework includes INSA in the establishments jointly delivering the Toulouse doctorate. This supports a national doctoral route through INSA and the Toulouse framework, rather than a degree awarded by the funding programme, CNRS laboratory or BCAM alone. Ask the doctoral office to confirm the exact diploma wording for the 2027 cohort.

Academic signal. The relevant strength is a direct match between image-based computational mechanics at ICA and geometric modelling at BCAM, supported by original team papers. The QS INSA profile exposes 2026 subject-ranking bands but the accessible extract does not identify which subject each band represents. No verified 2027 INSA-specific overall or TPMS ranking was established. Do not transfer Toulouse INP's separate ranking or a broader Toulouse institution's rank to this appointment. A missing precise rank is not evidence of weak supervision; laboratory output and the actual training arrangement are more useful here.

Registration and training. The INSA first-year procedure separates doctoral-school approval in ADUM from administrative registration in Coriandre. Its published 2026/27 dates are not the 2027/28 admission calendar. The shared training catalogue covers scientific methods, thesis practice, publishing, international/language work, teaching and careers. MEGEP's exact individual hours, courses, progress criteria and thesis-language agreement were not verified. They should be set alongside a plan for geometry, inverse problems, uncertainty and experimental practice, not inferred from the availability of generic courses.

International arrangement. The individual page labels a Spain cotutelle and proposes up to 12 months at BCAM. However, formal Toulouse cotutelle rules require an agreement between degree-awarding higher-education institutions, registration in both, defined fees and individual monitoring; they normally require at least 12 months abroad for a three-year thesis. The project wording 'up to 12' and that minimum need reconciliation. BCAM's research supervision does not by itself identify the Spanish university issuing a diploma. Two degrees should only be claimed after the actual agreement establishes them. The normal funded 36 months does not guarantee completion or support for an extension.

Supervisors, Resources and Recent Original Papers

Robin Bouclier's academic page confirms a full professorship at INSA, ICA/MS2M and an associated IMT role, with isogeometric direct/inverse methods, data assimilation and scientific computing. The IUF profile confirms Junior 2024 status; his 2024–2029 research period is not a five-year student contract. An older directory calling him MCF should not override the current professor profiles. Research time and grants support the environment but do not establish a new student's meeting schedule.

Michael Barton's current BCAM profile lists him as Group Leader and Ikerbasque Research Associate Professor in Mathematical Design, Modelling and Simulations. His CAD/manufacturing/IGA work and co-authorship of the GB study support the geometric component. The project also names IRT Saint Exupéry research engineer Ludovic Barrière for industrial co-supervision. Individual availability, day-to-day responsibility and the division of experimental versus numerical support remain interview questions. The recruitment contact includes Thibaut Hirschler, but a contact entry alone does not make him a formal doctoral supervisor.

The ICA equipment table lists tomography in Toulouse, a selective-laser-melting machine in Albi and metal additive manufacturing at an ISAE site. The project promises fabrication/imaging resources, but the campus-specific table makes booking, specimen manufacture, operator training and travel worth clarifying. It does not establish unlimited personal access or a guaranteed material budget.

Generalized Bézier geometry (2026): compact smooth models

2026 GB geometry paper. Pareja-Corcho, Hirschler, Bouclier, Elber and Bartoň develop smooth geometry-conforming lattices, DOI 10.1111/cgf.70490. The author-shared original main text was read in selected geometry, IGA conversion, numerical-example and limitations sections. It constructs continuity-preserving patches and compares smoother stress fields; one representation comparison uses 384 rather than 768 control points. That is a particular geometry comparison, not a universal speedup. The shape/sizing examples are explicitly prospective, not a solved topology-optimization problem. Smooth global mapping and compatible interfaces matter; this is not validation on uncertain manufactured TPMS shells. Supplementary archives were not audited.

Nonlinear solver (2026 preprint): scope of the numerical evidence

2026 nonlinear solver paper. Guillet, Hirschler, Jolivet, Antolin and Bouclier's March 2026 original preprint was read in selected formulation, solver, numerical-results and conclusions sections. Principal-cell reduced bases accelerate tangent assembly and an inexact FETI-DP solver. The two-/three-dimensional demonstrations use a neo-Hookean model and serial laptop calculations, reaching roughly 30–40% deformation before contact; selected comparisons report about threefold memory savings. Elastoplasticity and self-contact remain future work. This is a volumetric deterministic solver, not the proposed uncertain-geometry shell pipeline; do not transfer timings or constitutive validity to metal TPMS specimens. The later journal citation does not prove every final-version detail matches the preprint.

CT fitting (2025): abstract-level evidence

2025 CT-fitting paper. Bichet, Passieux, Périé and Bouclier, CMA 436:117729, publisher record, reports multipatch B-spline fitting using virtual image correlation, image learning, membrane regularisation, pose estimation and continuity control, with sub-voxel accuracy in its tests. Only the primary indexed abstract was available for this review; full methods, numerical tables and discussion were not read. It establishes a directly related approach and useful questions about image resolution and regularisation, but the reported accuracy cannot be treated as independently audited or as demonstrated performance for this future thesis.

The papers support a coherent methods chain. They do not remove the new research problem: a compact representation must still capture actual defects, identify their statistics and predict mechanics with validated uncertainty. Two papers were examined beyond abstracts; the third remains an explicit limited reading, with no claim to exhaustive supplementary review.

Funding, Application and Living Costs

The individual page identifies BEST funding from 1 September 2027 to 31 August 2030 and INSA as employer. A separate recruitment card lists Université de Technologie de Belfort-Montbéliard (UTBM), so the contracting institution needs confirmation. The BEST recruitment notice describes a full-time 36-month French doctoral employment contract. It quotes approximately €2,800 net monthly before income tax, plus a €350 monthly travel/mobility allowance. This terminology is not gross salary and not final take-home pay after income tax. The detailed official guide was not read, so whether the allowance is additional in every payroll case, its tax treatment, personal deductions, teaching duties and exact INSA offer must be confirmed. A generic MSCA label does not establish an additional living or family allowance under these COFUND BEST terms.

The official programme page confirms a 23 November 2026 closing date and 1 September 2027 start. There is a material clock conflict: the individual doctoral page says 23:59; the individual advertisement says 00:00; the programme-issued call says 12:00 Paris and prints an inconsistent UTC offset, while one metadata field even shows 2027. No single definitive clock has been established. A prudent personal plan is to submit before 23 November and ask best-helpdesk@utoulouse.fr for the controlling time; this is planning advice, not a newly asserted official deadline. The nineteen places belong to the whole first cohort, with competition across projects. The second cohort is a later call, not an extension of this one.

Apply through the BEST portal, not merely by emailing a researcher or registering an ADUM account. The official programme allows either a listed topic or a personal project. Its page links a call, applicant guide and doctoral-school letter template, but the full attachment body and exact compulsory upload checklist were not obtained. The available application materials do not establish whether the application form is currently accessible or whether the call is still accepting applications. Confirm portal access and obtain the guide before relying on a submission plan. Prepare qualification evidence, research motivation and a credible technical discussion; label this as preparation until the actual guide specifies documents, reference letters, language proof and evaluation criteria. The programme-level indicative schedule gives eligibility checking in late November, written evaluation during December/January, oral evaluation around late March/early April and results from April 2027; final instructions should govern.

The current INSA fee table gives a 2026/27 doctoral registration fee of €398. The registration procedure gives €105 CVEC and a cotutelle-dependent exception when registration fees are paid at the partner university. That procedure also contains an older 2025/26 fee, so use the dated current table for context. Neither source fixes 2027/28 charges or promises BEST reimbursement. Non-EU engineering/master differentiated fees should not be substituted for the doctoral line.

INSA's practical international guide advises an undated student budget of €800–900/month. This is a local institutional baseline, not a 2027 doctoral private-lease quotation. For planning, an explicitly assumed €1,000–1,400/month Toulouse scenario can reserve €550–800 for housing/utilities, €250–350 for food and €200–250 for transport, communications, insurance and ordinary costs. It excludes deposits, relocation, registration and temporary accommodation. No defensible guaranteed surplus follows from comparing that scenario with a before-income-tax salary. Up to 12 months in Bilbao requires a separate actual housing and travel plan, including possible double rent; no verified 2027 Bilbao budget was established.

Qualifications, Preparation and Chinese-Applicant Pathway

The individual subject welcomes computational mechanics, applied mathematics, mechanical/aerospace engineering, computer science and closely related training. Numerical methods/finite elements, scientific programming such as Python/MATLAB/C++, and interest in CAD, IGA, imaging or experiments are desirable; the call does not require mastery of every field. The key hard condition is that the candidate must hold a Master's or equivalent by the call deadline and must not hold a doctorate. The broader subject wording 'about to obtain' does not waive the programme's explicit deadline rule. A 2027 Master's completion cannot be assumed acceptable for this 2026 selection.

The official BEST page repeats the France mobility requirement: no more than 12 months of residence or main activity in the 36 months before the call deadline, with the stated tourism/refugee/national-service exceptions. This is not a rule measured from the eventual September recruitment date. English is described as Excellent in the individual advertisement and upper-intermediate on the doctoral page; the programme advertisement uses Good. No verified harmonised examination threshold was found. Obtain the accepted evidence and the working language for experiments, administration and the Spanish stay, without inventing a French or Spanish hard requirement.

There is affirmative eligibility evidence for a China-educated, non-EU applicant: the Commission's COFUND rules permit doctoral researchers of any nationality, and the actual BEST call accepts Master-equivalent qualifications subject to mobility and academic assessment. The national equivalent-study mechanism explains the statutory doctoral recognition route, but it is not an INSA individual admission decision or a BEST deadline exemption. A domestic Chinese Master's can be assessed; no automatic recognition or award is promised.

France's researcher residence route requires Master-equivalent study, research and an approved hosting agreement. HR must confirm the arrangement for this salaried contract and the separate practical requirements for a stay in Spain. Permission to work on one French appointment does not automatically settle every cross-border registration or mobility document. If actual activities require restricted-zone access, the PPST framework requires the relevant individual authorization. This project's ZRR scope is unknown; neither a categorical Chinese ban nor individual clearance follows from the aerospace context.

Useful preparation would be a reproducible small finite-element/IGA or image-registration example with error analysis, clear code and an explanation of boundary conditions. A mechanics applicant can show how to learn geometric modelling; a computing applicant should demonstrate the physical assumptions underlying a simulation. These are analyst suggestions, not added mandatory attachments. Sensitive industrial datasets or existing equipment certification are not prerequisites stated in the advert.

Career Implications and Next Decisions

The strongest transferable capabilities are CAD-to-analysis geometry, inverse identification from CT, numerical solver development, uncertainty modelling and experimental validation. These are relevant to computational-mechanics research, CAE/software development, additive-manufacturing process assessment and materials/structural R&D. Clean Aviation establishes a research-and-industry audience, not a count of available jobs, a graduate salary premium or an exemption from a future employer's access rules. No programme-specific placement or completion-rate dataset was verified.

Before applying, ask the BEST helpdesk to resolve the deadline clock, obtain the current guide/upload checklist and establish that the Master's will be formally awarded in time. Ask the supervisor to confirm the exact topic/project reference and accepted English evidence. Read the three technical approaches as different contributions: smooth design geometry, deterministic nonlinear solving and image fitting. None is an already complete uncertain-geometry TPMS shell solution.

At interview, request a realistic first-year scope, available CT/build data and experimental support. How will dependence between cells and build-to-build variability be tested? Which errors belong to imaging, geometric approximation, shell assumptions or material response? Who supervises geometry, mechanics and experiments day to day, and what is the fallback if a common CAD support fails for complex junctions? These questions assess readiness without presuming deficiencies.

Before accepting, obtain the INSA payroll/allowance statement, fees and mobility budget, 36-month employment dates, intellectual-property/open-output conditions and any extension arrangements. Resolve whether this is formal cotutelle or international co-supervision, the Spanish degree institution and the up-to 12 versus at-least 12 month mobility wording. Confirm doctoral training/monitoring and foreign-degree, hosting, visa and any actual access permissions. The opportunity is promising with material conditions: a closely matched team and concrete research chain, with administrative and financial details that still require a responsible institutional answer.

Evidence and Sources

The evidence distinguishes the individual project and recruitment notice from programme-level BEST information. Two original papers were read in selected substantive sections; one paper remains primary-abstract-only. The full applicant guide and supplementary archives were not read. These sources do not establish current availability, portal access or personal 2027 employment terms.

Recruitment, training and institutions

• Official doctoral project 76526
• Official BEST programme current call
• European Commission COFUND rules
• INSA first-year doctoral registration
• INSA exact current fee table
• Toulouse joint doctorate registration framework
• Toulouse formal international cotutelle rules
• Toulouse doctoral training catalogue
• Bouclier academic homepage
• IUF official Bouclier appointment
• Barton BCAM current profile
• ICA equipment and booking
• QS INSA Toulouse institution profile

Original research

• GB geometry-conforming lattices 2026 original author manuscript
• 2026 nonlinear hyperelastic lattice solver original preprint
• 2025 multipatch CT fitting original paper

Practical conditions and field context

• INSA international practical budget
• France non-EU researcher residence route
• National equivalent qualification admission explained by doctoral school
• PPST official restricted-zone FAQ
• Clean Aviation public-private programme mission
• nTop lattice structures in additive manufacturing guide
• Blueflite lattice-infill fuselage case study