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Mesoscopic theory of microcracks

Papenfuss C., Van P., Muschik W.

Archives of Mechanics

2003

Vol. 55, nr 5-6

481-499

The mesoscopic concept is a way to deal with complex materials with an internal structure within continuum mechanics. It consists of extending the domain of the balance equations by mesoscopic variables and of introducing a local distribution function of these variables as a statistical element. In our case microcracks are modelled as penny-shaped and are completely characterized by their diameter and the unit normal to the crack surface. Two examples of crack dynamics are given as well as a possible definition of a damage parameter. Orientational order parameters (fabric-alignment tensors) are defined and balance-like dynamic equations for them are derived.

Nonlinear dynamics of the alignment tensor in the presence of electric fields

Papenfuss C.

Archives of Mechanics

1998

Vol. 50, nr 3

559--566

In the mesoscopic theory field quantities are introduced, which depend not only on position and time, but also on an additional orientational variable, the microscopic director. The orientation distribution function (ODF) gives the fraction of particles of a particular orientation. An equation of motion for the second order alignment tensor, including the influence of electromagnetic fields and of spatial inhomogeneities, is derived. The starting point are the mesoscopic balance equations of mass and of angular momentum. A constitutive equation on the mesoscopic level is discussed. The two balance equations together with the constitutive equation yield an equation of motoin for the ODF. This finally leads to a nonlinear partial differential equation for the alignment tensor, which involves also the alignment tensor, which involves also the fourth and the sixth moment of the ODF.