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Motion equations for continuous media and for rigid bodies

Jankowski J.

Vibrations in Physical Systems

2008

Vol. 23

177--182

Rigid condition plays an essential role in creating of motion equations for the body. The basic principles of balance, concerned with the global behavior of the body, translate in various forms when they are applied to the rigid body dynamics and to the continuum media theory. On the other hand, just for a rigid body the principles of balance of momentum and moment of momentum take some various forms when are applied to the chosen poles of reduction.

Analogie równań opisujących proces termodyfuzji w ośrodku ciągłym i mikropolarnym

Wieczorek B.

Roczniki Inżynierii Budowlanej

2008

z. 8

93--96

In the paper are presented the formulation thermodiffusion problems in viscoelastic solid with multicomponent body. There is analysed the model of the continuous medium and the micropolar medium. The balance of mass, momentum, angular momentum, energy and entropy in a solid are proposed for each of the ingredients. Next, the balance equations are obtained for the body. The physical equations of the process are obtained assuming the thermodynamic potentials. Next, the final systems of equations are obtained which describe a character of mutual reaction of heat, diffusion and stress fields.

A numerical framework for continuum damage - discontinuum transition

Borst R. de, Abellan M. A.

Archives of Mechanics

2002

Vol. 54, nr 5-6

377-387

A framework is derived for the proper and consistent description of a discontinuity (a crack) as the result of a damaging process in a continuous medium. The damaging process in the continuous medium is described using a gradient-enhanced damage theory, so that well-posedness of the boundary-value problem is maintained until the damage process is completed and a discontinuity arises. At that moment the partition-of-unity property of finite element shape functions is exploited to partition the displacement field into two continuous fields, separated via a Heaviside function. It is demonstrated that the additional boundary conditions that arise in a gradient-enhanced damage theory, can be accounted for in a natural and transparent manner.