Shape change and deformation
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The shape of a system of solids can change: the solids of the system can deform and their relative positions can change. The description of the changes is not fixed once for all. There are many ways to quantify the shape changes, i.e., to define the velocities of deformation. These velocities of deformation are important because they introduce the internal forces with their power, the power of the internal forces. We give two example: in the first one we consider the system made of two rigid solids, in the second one we consider a solid with large deformation. Observation leads us to define new velocities of deformation useful to predict the smooth and the the non-smooth motion of solids and systems of solids.
KeywordsContinuum mechanics Shape change Deformation Internal forces Large deformations Collisions Flattening Principle of virtual power Equations of motion Constitutive laws
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Conflict of interest
The author declares that he has no conflict of interest.
- 2.Antman SS (2005) Nonlinear Problems of Elasticity, 2nd edn. Appl Math Sci, vol 107. Springer, New YorkGoogle Scholar
- 3.Argoul P (2013) The non-smooth view for contact dynamics by Michel Frémond extended to the modeling of crowd movements. Discret Cont Dyn Syst Ser S 2(2). doi: 10.3934/dcdss.2013.6.547
- 4.Argoul P, Pécol P, Cumunel G, Erlicher S (2013) A discrete crowd movement model for holding hands pedestrians. In: EUROMECH - Colloquium 548, Direct and variational methods for non smooth problems in mechanics, June 24–26Google Scholar
- 9.Frémond M (2007) Collisions. Edizioni del Dipartimento di Ingegneria Civile, Università di Roma “Tor Vergata”, ISBN: 978-88-6296-000-7Google Scholar
- 12.Salençon J (2005) Mécanique des milieux continus. I., Éditions de l’École Polytechnique, PalaiseauGoogle Scholar
- 13.Kabalan B (2016) Crowd dynamics: modeling pedestrian movement and associated generated forces. Ph.D. thesis, Université Paris-Est, Champs-sur-Marne, FranceGoogle Scholar
- 15.Lions JL, Magenes E (1972) Non-Homogeneous Boundary Value Problems and Applications, Vol 1, ISBN: 978-3-642-65163-2 (Print) 978-3-642-65161-8 (Online), SpringerGoogle Scholar
- 16.Pécol P (2011) Modélisation 2D discréte du mouvement des piétons. Application à l’évacuation des structures du génie civil et à l’interaction foule-passerelle. Ph.D. thesis, Université Paris-Est, Champs-sur-Marne, FranceGoogle Scholar