647 – Stability and bifurcation problems in nonlinear solid mechanics
23 April 2025 – 25 April 2025
James Watt School of Engineering
University of Glasgow
734, Rankine Building, Oakfield Avenue
Glasgow G12 8LT,
University of Galway
Extreme deformation of solids often leads to structural or material instabilities that can be mathematically modelled as a local or global bifurcation of the solution to the underlying partial differential equations. With recent advances in material science and additive manufacturing techniques, novel soft polymers with advanced microstructure have been developed that can undergo significantly large reversible deformations. Microstructural and macroscopic instabilities associated with these nonlinear deformation regimes can be coupled with multi-physics applications such as electromagnetic forces, thermal energy, residual stress, and growth. Subsequently, new engineering design mechanisms are made possible by employing recent developments in inverse design approaches. In the natural world, the mechanical instability mechanisms observed in residually stressed growing soft tissues, such as developing mammalian brains and plant leaves, are now widely understood to be leading drivers of morphogenesis. Hence, turning common perception on its head, instability and bifurcation can now be considered desirable for modelling the engineering and natural designs of soft solids—thereby introducing the concept of “buckliphilia”—as opposed to being solely associated with structural failure in the past.
Recent advances in theoretical, experimental, and computational mechanics, now including data-driven and machine-learning methodologies, are propelling exciting new developments in this field. This colloquium will bring together world-leading experts in the field to consolidate the state of the art; and explore future directions of research in stability and bifurcation problems in nonlinear solid mechanics.
- Theoretical, computational, and experimental aspects of bifurcation problems.
- Instability-driven morphogenesis and pattern formation.
- Instabilities associated with multi-physics coupling in soft solids: coupling with electromagnetism, thermal energy, (bio) chemistry, and (cell) biology.