Seminar on partial differential equations

Inertial evolution of non-linear viscoelastic solids in the face of (self-)collision

Antonín Češík

Charles University

Tuesday, 21. March 2023 - 9:00 to 10:00

in IM, rear building, ground floor and on Zoom

Link: https://cesnet.zoom.us/j/91015942151?pwd=dlF4ekVIUGFBRzdIVVUzbUp3MFNQdz09

Meeting ID: 910 1594 2151

Passcode: 051433

The recording of the lecture is available at: https://download.math.cas.cz/media/seminars/PDE/Necas_PDE_Seminar,_March_21,_2023.mp4

The talk discusses existence theory for collisions of (visco-)elastic bulk solids which are undergoing inertial evolution. In particular, our approach for contact is based only on the assumption of non-interpenetration of matter. Most other theories for contact of elastic solids include some phenomenological assumptions, which we do not need in our approach.

We are able to show existence of weak solutions including contact with an obstacle or with the solid itself, for arbitrarily large times and large deformations. Furthermore, our construction includes a characterization of the contact force which obeys conservation of momentum and an energy balance. This contact force is a vector-valued surface measure acting in the normal direction, and is constructed as a consequence of the non-interpenetration of matter.

This is a joint work with Giovanni Gravina and Malte Kampschulte.

We are able to show existence of weak solutions including contact with an obstacle or with the solid itself, for arbitrarily large times and large deformations. Furthermore, our construction includes a characterization of the contact force which obeys conservation of momentum and an energy balance. This contact force is a vector-valued surface measure acting in the normal direction, and is constructed as a consequence of the non-interpenetration of matter.

This is a joint work with Giovanni Gravina and Malte Kampschulte.