Modeling and simulation of inelastic materials and structures

PhD Topic: Modeling and simulation of inelastic materials and structures

Supervisor: Milan Jirásek (Milan.Jirasek@cvut.cz), possibly in collaboration with Jan Zeman, Martin Horák, Petr Havlásek or Martin Doškář

Doctoral programs:

• Physical and Materials Engineering / Fyzikální a materiálové inženýrství
• Structural and Transportation Engineering / Konstrukce a dopravní stavby

Summary: The proposed PhD dissertation will focus on mathematical modeling and numerical simulation of inelastic materials and structures, aiming to develop sound theoretical formulations and robust computational frameworks for analyzing materials that exhibit irreversible changes under load. The student will develop and test a suitable constitutive model that extends existing formulations within the theories of plasticity, viscoelasticity or damage mechanics and reflects the complex behavior of materials beyond their elastic limits. Powerful numerical methods, such as the nonlinear version of the finite element method (FEM), will be employed to solve the governing equations at the structural level. Applications of this work include structural analysis in engineering, failure prediction, and optimization of material design or manufacturing processes. They will contribute to improved efficiency, reliability and safety in civil engineering, with possible extensions to mechanical or aerospace engineering.

International collaboration: The student is expected to participate in externally funded research projects related to the main theme and to collaborate with international partners, e.g., with the research teams at TU Eindhoven, Université Paris-Saclay, University of Oxford, University of Glasgow or Northwestern University.

Specific projects:

Advanced models for quasibrittle failure

Quasibrittle materials encompass a wide range of natural and man-made materials, such as concrete, rock, masonry, wood, tough ceramics, various types of composites, bone, or sea ice. The characteristic feature of their mechanical behavior is a gradual development of large inelastic process zones, which often evolve into localized patterns. Depending on the type of loading and on the specific material microstructure, dissipative processes in quasibrittle materials may involve initiation and propagation of cracks or other defects, delamination, fiber rupture or pullout, aggregate interlock, frictional sliding, or crushing. Realistic mathematical modeling of the effect of propagating defects requires either stress-strain laws with softening (smeared approach), or incorporation of displacement discontinuities that correspond to cohesive cracks or cohesive- frictional slip lines (discrete approach). Furthermore, sliding along rough surfaces leads to dilatancy, which can be accurately described by elastoplastic models only if non-associative flow rules are adopted. Softening as well as non-associative flow are destabilizing factors that may lead to localization of dissipative processes into narrow bands. Traditional constitutive models formulated within the standard continuum framework cannot provide an objective description of localized failure patterns, and their enhancement by suitable regularization techniques acting as localization limiters is needed.

Improvements to an existing damage-plastic model for concrete will allow more reliable predictions of the ultimate load-carrying capacity of concrete structures under general monotonic loading scenarios. In addition to the maximum load, the post-peak structural response will be captured in an objective manner, which is important for the evaluation of structural ductility and of the total energy dissipated during failure.

Potential funding: A research proposal has been submitted to the Czech Science Foundation. If the proposal is accepted, a funded PhD position will become available from 2025.