Regensburg 2022 – wissenschaftliches Programm
CPP 2.2: Vortrag
Montag, 5. September 2022, 09:45–10:00, H39
Nonlinear elasticity under constraints and predeformations: a group theoretical approach — •Segun Goh1,2, Hartmut Löwen2, and Andreas M. Menzel3 — 1Forschungszentrum Jülich, 52425 Jülich, Germany — 2Heinrich-Heine Universität Düsseldorf, 40225 Düsseldorf, Germany — 3Otto-von-Guericke-Universität Magdeburg, 39106 Magdeburg, Germany
The mechanical response of elastic materials frequently involves predeformations. Moreover, if an active or driven material is exposed to an external condition, a mismatch between the activity/driving and external condition may lead to a hidden predeformation in the system in its mechanical equilibrium state. Then the assumption of linear response breaks down, making descriptions of nonlinear elasticity compulsory even if the applied deformation is infinitesimally small. In this talk, we discuss how to develop a theoretical framework to meet this challenge and thereby, to address elasticity consistently for both small and large deformations. Specifically, employing concepts from group theory and Lie algebra, we suggest an idea to construct finite deformation gradients from infinitesimal group generators. Generalized nonlinear shear deformations and elastic moduli are defined subsequently. Possible applications will also be discussed.