# Mesoscopic theory of microcracks

@article{Papenfuss2002MesoscopicTO, title={Mesoscopic theory of microcracks}, author={Christina Papenfuss and P{\'e}ter V{\'a}n and Wolfgang Muschik}, journal={Archives of Mechanics}, year={2002}, volume={55}, pages={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…

## 28 Citations

### Griffith cracks in the mesoscopic microcrack theory

- Physics
- 2004

The mesoscopic concept is applied to the description of microcracked brittle materials. The mesoscopic equations are solved in a special case when the microcracks are developing according to the…

### A Mesoscopic Continuum Description of Dry Granular Materials

- Physics
- 2008

Abstract A study is made of the mesoscopic dynamics of granular materials by modeling a dry granular medium as a mixture with components, specified by a proposed continuous field variable. By…

### Macroscopic Internal Variables and Mesoscopic Theory: A Comparison Considering Liquid Crystals †

- PhysicsEntropy
- 2018

The alignment tensor of the liquid crystal theory can be introduced as an internal variable or as one generated by a mesoscopic background using the microscopic director as a mesoscope variable.

### Mesoscopic continuum mechanics applied to liquid crystals

- Physics
- 2010

Continuum mechanics is based on the balance equations of mass, momentum, angular momentum or spin, total or kinetic energy and internal energy. Additionally, one has to consider the balance of…

### Scalar, vectorial and tensorial damage parameters from the mesoscopic background

- Physics, Mathematics
- 2007

In the mesoscopic theory a distribution of different crack sizes and crack orientations is introduced. A scalar damage parameter, a second order damage tensor and a vectorial damage parameter are…

### Dynamics of the Size and Orientation Distribution of Microcracks and Evolution of Macroscopic Damage Parameters

- Physics
- 2007

Abstract We are dealing with damage of brittle materials caused by growth of microcracks. In our model the cracks are penny-shaped. They can only enlarge but not heal. For a single crack a…

### Continuum damage mechanics: combining thermodynamics with a thoughtful characterization of the microstructure

- Materials Science
- 2008

We formulate a macroscopic description of the mechanics of damaged materials. To represent the microstructure, the distribution of crack sizes is captured by way of the Minkowski functionals, or…

### Dynamics of Internal Variables from the Mesoscopic Background for the Example of Liquid Crystals and Ferrofluids

- PhysicsApplied Wave Mathematics
- 2009

The general concept of the mesoscopic theory is presented, and it is applied to the examples of liquid crystals and ferrofluids, and the well-known Landau-type equation for the alignment tensor in liquid crystals is recovered.

### Statistical Mesomechanics of Solid, Linking Coupled Multiple Space and Time Scales

- Physics
- 2005

This review begins with the description of a new challenge in solid mechanics: multiphysics and multiscale coupling, and its current situations. By taking spallation as an example, it is illustrated…

### On the macroscopic–mesoscopic mixture of a magnetorheological fluid

- PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2006

This paper is concerned with the modelling of a magnetorheological (MR) fluid in the presence of an applied magnetic field as a twofolded mixture—a macroscopic fluid continuum and mesoscopic…

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