# zbMATH — the first resource for mathematics

An introduction to unilateral dynamics. (English) Zbl 1123.70014
Frémond, Michel (ed.) et al., Novel approaches in civil engineering. Berlin: Springer (ISBN 3-540-41836-9/hbk). Lect. Notes Appl. Comput. Mech. 14, 1-46 (2004).
The paper deals with finite-dimensional multibody multicontact systems. The description of each unilateral interaction (contact) is formalized with the help of contact dynamics technique, introduced earlier by the author [Nonsmooth mechanics and applications, CISM Courses Lect. 302, 1–82 (1988; Zbl 0703.73070)]. This technique operates with the unilateral contact, possibly frictional and/or collisional, between rigid bodies in terms of elementary convex analysis. Mathematically, the resulting evolution problems in the smooth case are governed by differential inclusions. Such an approach allows to construct efficient numerical procedures which are demonstrated by two examples.
Contents: 1. Purpose; 2. The differential handling of inequality conditions; 3. Frictionless confinement of a particle; 4. Multicontact systems; 5. Contact laws; 6. Time-stepping; 7. Nonsmooth dynamics and collisions; 8. Energy balance and calculus for differential measures (examples); 9. Behaviour of a masonry structure; 10. Stress distribution in a conical grain pile.
For the entire collection see [Zbl 1026.00016].

##### MSC:
 70E55 Dynamics of multibody systems 70F10 $$n$$-body problems 74M15 Contact in solid mechanics