
Theoretical and computational peridynamics for fracture of materials and structures Project Ref: NGCM0105 Available: Yes Supervisor: Georges Limbert, Faculty: FEE Academic Unit: Engineering Sciences Research Group: nCATS Cosupervisor: Ajit Shenoi Faculty: FEE Academic Unit: Ship Science Research Group: FSISMMI Research Area: Computational Engineering Project Description: Background: Predicting and simulating the fracture and failure of materials and structures remains one of the greatest challenges of computational engineering. This stems from the multiscale (and often multiphysics) nature of fracture mechanics and the inherent limitations of continuum mechanics (CM) theories and associated finite element techniques to capture and predict such phenomena. Local theories of matter assume that a material point only exchanges mass, momentum and energy with its closest neighbours. As a result, the stress state at a point depends on the deformation at that point only. In addition, within classical continuum mechanics a body remains continuous as it deforms and the mathematical formulation governed by PDEs breaks down when a discontinuity appears (e.g. a crack). In addition, limitations of current finite element (FE) methods for fracture mechanics include: (1) Cumbersome and complicated numerical implementation. (2) Assumption of preexisting cracks rather than the nucleation of new cracks. (3) Need for mesh adaptation. (4) Inefficient and/or simply infeasible methods for multiple cracks, crack branching and crack coalescence. (5) Need to provide a kinetic relation for crack growth: how a crack evolves based on local conditions.Although first enunciated in principle by Piola in the 19th century, peridynamics (PD) theory was practically formulated by Silling in 2000 [1]. This nonlocal theory of matter can address all the shortcomings mentioned above is ideally suited for fracture phenomena.The project: Although similar in principles to molecular dynamics (MD), peridynamics is not restricted to the very short length and time scales associated with MD. That means that practical engineering applications operating at the macroscopic scale can be practically simulated using PD. PD can be implemented in a MD code or, especially relevant to this project, within a FE code and benefits from the more reasonable computing times of FE methods prior to crack initiation.The overall aim of this project is to develop a novel finite elementbased peridynamics computational environment to study crack propagation and stability conditions in maritime engineering structures. A statebased PD will be used so that arbitrary constitutive models could be implemented. Departing from the original PD approach which goes from a PD continuum (theory) to its discretised version (computational implementation) we propose to follow the ideas of Gerstle [2] and introduce a PD lattice model which is a discretised version of matter a priori, where lattice spacing is dictated by the internal material length scale (i.e. characteristic size of microstructure). This avoids the problem of defining/storing mass density or other internal variable fields, continuous or discontinuous (e.g. plastic strain). Instead they are defined/stored at each particle of the lattice.Although PD address many shortcomings of traditional theories and numerical methods, one challenge where research efforts are urgently needed is concerned with the formulation of constitutive models and their calibration from experimental data which differ from CM approaches.In this project, an efficient and modular workflow to automatically generate optimised code for new material constitutive models as well as their calibration from experimental data will be devised: the mathematical models will be formulated in symbolic form in the mature symbolicnumeric environment AceGen/AceFEM integrated within Mathematica. From these formulations optimised numerical code (e.g. Fortran, C, Matlab or Mathematica) will be generated and integrated within a FE environment (e.g Abaqus/Implicit and /Explicit, AceFEM) for large scale simulations. The use of HPC capabilities will be essential.[1] Silling, S. A., 2000, Reformulation of elasticity theory for discontinuities and longrange forces, J. Mech. Phys. Sol., 48:175209.[2] Gerstle, W. H., Introduction to practical peridynamics, World Scientific, London, First edition, 2016, 410 pages. We are looking for an applicant with a background in physics, engineering mechanics, applied mathematics or computer science with strong interest and/or skills in programming, and an appetite to learn and research across conventional discipline boundaries.The stipend is at the standard EPSRC levels. More details on facilities and computing equipment are available http://ngcm.soton.ac.uk/facilities.htmlThe successful candidate will work in a stimulating research environment, supported by worldleading organisations such as Procter & Gamble, Rolls Royce, Lloyds Register, Shell and the US Air Force and will be encouraged to work with our international academic and industrial collaborators in Europe, Singapore, New Zealand and the USA. If you wish to discuss any details of the project informally, please contact Georges Limbert, Email: g.limbert@soton.ac.uk Tel: +44 (0) 2380 592381 Keywords: Applied Mathematics, Applied Physics, Civil and Structural Engineering, Computer Science, Materials Science, Mechanical Engineering, Structural Biology Support: All studentships provide access to our unique facilities and training and research support . Project Images

