Understanding Micropolar Theory in the Earth Sciences I: The Eigenfrequency $$\omega _r$$

Even though micropolar theories are widely applied for engineering applications such as the design of metamaterials, applications in the study of the Earth’s interior still remain limited and in particular in seismology. This is due to the lack of understanding of the required elastic material parameters present in the theory as well as the eigenfrequency $$\omega _r$$ ω r which is not observed in seismic data. By showing that the general dynamic equations of the Timoshenko’s beam is a particular case of the micropolar theory we are able to connect micropolar elastic parameters to physically measurable quantities. We then present an alternative micropolar model that, based on the same physical basis as the original model, circumvents the problem of the original eigenfrequency $$\omega _r$$ ω r laking in seismological data. We finally validate our model with a seismic experiment and show it is relevant to explain observed seismic dispersion curves.

Applications of micropolar SPH in geomechanics

A smoothed particle hydrodynamics code based on micropolar continua for geomaterials is developed for problems involving large deformation and shear strain localization. Two typical geotechnical problems, i.e., biaxial compression test and sand column collapse, are simulated using classical and micropolar model to demonstrate the performance of the newly proposed method. A parameter study is given on the scale effect in the micropolar continua.

Dynamic Characterization of Microstructured Materials Made of Hexagonal-Shape Particles with Elastic Interfaces

This work aims to present the dynamic character of microstructured materials made of hexagonal-shape particles interacting with elastic interfaces. Several hexagonal shapes are analyzed to underline the different constitutive behavior of each texture. The mechanical behavior at the macro scale is analyzed by considering a discrete model assumed as a benchmark of the problem and it is compared to a homogenized micropolar model as well as a classical one. The advantages of the micropolar description with respect to the classical one are highlighted when internal lengths and anisotropies of microstuctured materials are taken into consideration. Comparisons are presented in terms of natural frequencies and modes of vibrations.

Density–orientation coupling for a microcontinuum approach to nematic liquid crystals subject to electric field

A microcontinuum description of compressible liquid crystals is examined accounting for a constitutive model based on mass microdensity. As a first point, we discuss the effectiveness of the micropolar theory on compressible continua, which is limited to static problems. Then, by a micromorphic representation of mass density, we show the consistence of some classical constitutive models for compressible nematic liquid crystals and remark their connection with the microinertia tensor. After the analysis of a constitutive micropolar model, we discuss a static problem for a layer of compressible nematic liquid crystal in a planar configuration. The effects of an applied electric potential are considered remarking the coupling of density distribution with the molecular orientation.

Squeeze flow modeling with the use of micropolar fluid theory

The aim of this paper is to study the applicability of micropolar fluid theory to modeling and to calculating tribological squeeze flow characteristics depending on the geometrical dimension of the flow field. Based on analytical solutions in the lubrication regime of squeeze flow between parallel plates, calculations of the load capacity and time required to squeeze the film are performed and compared – as a function of the distance between the plates – for both fluid models: the micropolar model and the Newtonian model. In particular, maximum distance between the plates for which the micropolar effects of the fluid become significant will be established. Values of rheological constants of the fluids, both those experimentally determined and predicted by means of using equilibrium molecular dynamics, have been used in the calculations. The same analysis was performed as a function of dimensionless microstructural parameters.