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Information for Researchers No. 32 | 11 June 2013
Priority Programme “Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretisation Methods, Mechanical and Mathematical Analysis” (SPP 1748)

The Senate of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) has announced the establishment of a new Priority Programme entitled “Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretisation Methods, Mechanical and Mathematical Analysis” (SPP 1748). The programme is scheduled to run for six years; the present call invites proposals for the first three-year funding period.

Numerical simulation techniques are an essential component for the construction, design and optimisation of cutting-edge technologies as e.g. innovative products, new materials, medical-technical applications and production processes. These important developments pose great demands on quality, reliability and capability of numerical methods, which are used for the solution of the arising, mainly non-linear and/or discontinuous problems.

Despite of many joint efforts by engineers and mathematicians, still open problems (as for example stress oscillations, bad influence of mesh distortion, artificial stiffening effects and numerical instabilities) exist when these methods are applied in the framework of geometrical and/or material non-linearities. In addition, the discretisation and the quantitative resolution of secondary variables are affected by enormous difficulties. For instance the necessary detailed resolution of the stress fields is often hindered by highly oscillating coefficients. Moreover, established inelastic material laws for finite strains which are successfully used within structural problems with nearly homogeneous material properties, fail partly e.g. in the field of complex multiple-scale simulations even if moderate deformations are applied. Similar problems arise in crack or contact problems, where the local resolution of discontinuities as well as their evolution plays a major role in many application fields.

Since it is known that existing simulation tools cannot provide the necessary solutions, the main objective of this Priority Programme is the development of modern non-conventional discretisation methods, based on e.g. mixed (Galerkin or least-squares) finite element or discontinuous Galerkin formulations, including the mathematical analysis for geometrically as well as physically non-linear problems in the fields of e.g. incompressibility, anisotropies and discontinuities (cracks, contact).

It is the aim to pool the expertise of mechanics and mathematics in Germany and to create new and strengthen existing networks. In the framework of this cooperation the experiences should be exchanged in between the different working groups to create synergies, save time and costs and raise the efficiency. Furthermore, it is intended to lead this newborn research union to international excellence in the field of non-conventional discretisation techniques.

In detail the Priority Programme will drive research towards the following directions concerning non-conventional finite element formulations and discontinuities:

Non-conventional finite element formulations:

  • deep mathematical understanding of the structural requirements of reliable non-conforming finite element method (FEM) approaches for finite deformations,

  • mathematically sound variational formulations,

  • robust and stiffening-free discretisations at finite deformations,

    • with (quasi-) incompressible, (an-) isotropic material behaviour,

    • domains with oscillating coefficients,

  • accurate approximation of all process variables in the latter mentioned extremal cases,

  • insensitive behaviour concerning significant mesh deformation,

  • convergence of adaptive mesh refinement,

  • numerically stable formulations.


  • creation of a variational basis as well as suitable discretisation techniques for discontinuities: convergence, stability and approximation properties,

  • resolution of discontinuities based on isogeometric formulations,

  • novel crack growth and crack branching models,

  • contact formulations based on non-conventional discretisation techniques exceeding Mortar-methods.

The specification of benchmark problems by the coordinators in the early stages of the Priority Programme will ensure an extensive basis for test- and comparative calculations and is mandatory for all participants as well as the attendance of periodical workshops, SPP-meetings and conferences. The benchmark problems will guarantee a suitable foundation for detailed in-depth discussions on the topics related to the different research fields as for instance incompressibility, anisotropy, plasticity, crack propagation and contact.

The projects must be alliances of researchers (typically two or three) optimally representing different scientific fields as e.g. mathematics and mechanics. All proposed applications should clearly include concepts for a new quality of non-standard FEMs in combination with the essential mathematical analysis in the fields of geometrically and/or physically non-linear problems. Proposals that are restricted only to either methodological/material modelling or solver technologies are excluded. It is expected that the proposals provide clear visionary aims.

Proposals for the initial three-year funding period are now invited. All proposals must be written in English and submitted by 14 October 2013 through the DFG’s electronic proposal processing system ”elan”. In this system please select ”SPP 1748” when submitting your proposal. Please include a title page with your name, your address, and the title of your project in your application. When writing the proposal, please consult the current guidelines for Priority Programmes (DFG form 50.05en) and follow the instructions for the preparation of project proposals including the naming protocol for proposal documents (DFG form 54.01en). Proposals by one applicant must not exceed 20 pages. Joint proposals may comprise five additional pages for each additional applicant.

You are further asked to send a PDF file of the application to the coordinator of the Priority Programme. The review will take place in Bonn in the first quarter of 2014 and may include a proposal colloquium.

Further information

The DFG’s electronic portal “elan” can be found at:

Proposal guidelines and preparation instructions are outlined in the DFG forms 50.05en and 54.01en, which can be downloaded on the DFG website at:

Questions related to the scientific objectives and strategic intentions of this Priority Programme including the requirements for funding should be directed to the scientific coordinator:

  • Prof. Dr.-Ing. habil. Jörg Schröder,
    Universität Duisburg-Essen,
    Institut für Mechanik,
    Universitätsstraße 15,
    45141 Essen,
    phone: +49 201 183-2682,
    Link auf E-Mailj.schroeder@uni-due.de

Administrative questions, notably regarding the formal eligibility for participation and the submission of the proposals, should be directed to: