Cosserat Elasticity of Lattice Solids

We discuss a model of fibrous solids composed of three families of continuously distributed Kirchhoff rods embedded in a matrix material. This is a special case of Cosserat elasticity in which the basic kinematic descriptors are a single deformation field and three rotation fields, one for each fiber family. The fibers are assumed to convect with the underlying continuum deformation as material curves. Various kinds of internal connectivity, imposing restrictions of the fiber rotations fields, are considered.

A Continuum Deformation Approach for Growth Analysis of COVID-19 in the United States

The COVID-19 global pandemic has significantly impacted every aspect of life all over the world. The United States is reported to have suffered more than 20% of the global casualties from this pandemic. It is imperative to investigate the growth dynamics of the disease in the US based on varying geographical and governmental factors that best manifest itself in each State of the Country. This paper utilizes a hybrid machine learning and continuum deformation-based approach for analyzing the stability and growth rate of the pandemic. To this end, principal stress values of the pandemic continuum body are obtained using Mohr’s Circle method and overlapping, moving windows of data are analysed successively. This helps in finding the correlations between the growth rate and Governments’ action/Public’s reaction. Government actions include “state of emergency”, “shelter at place”, and “phase declarations”. We also consider the vaccination rate milestones, which shows us the coordinated Governments’ action/Public’s reaction. Finally, a number of recommendations are made to the Governments and people for better management of future pandemics.

A Continuum Deformation Approach for Growth Analysis of COVID-19 in the United States

The COVID-19 global pandemic has significantly impacted every aspect of life all over the world. The United States is reported to have suffered more than 20% of the global casualties from this pandemic. It is imperative to investigate the growth dynamics of the disease in the US based on varying geographical and governmental factors that best manifest itself in each state of the country. This paper utilizes a hybrid machine learning and continuum deformation-based approach for analyzing the stability of the rapid COVID-19 growth. The proposed continuum deformation model is used to learn the parameters of pandemic growth based on the training data of total cases, deaths, and recoveries in each state of the United States from March 12, 2020 to January 28, 2021. Using this approach, multiple periods of the nationwide and State-level pandemic growth patterns are discovered and analyzed.

Linear theory for the mechanics of third-gradient continua reinforced with fibers resistance to flexure

A linear model, framed in the setting of the second strain gradient theory, is presented for the mechanics of an elastic solid reinforced with fibers resistant to flexure. The kinematics and bending resistance of the fibers are formulated via the second and third gradient of the continuum deformation. The corresponding Euler equations and admissible boundary conditions are then obtained by means of iterated integration by parts and variational principles arising in the third gradient of virtual displacement. In particular, within the prescription of superposed incremental deformations, we derive a compatible linear model from which a complete analytical solution describing the deformations of fiber composites is obtained. The proposed linear model predicts smooth and dilatational shear angle distributions over the domain of interest, which are also aligned with the results obtained from the corresponding nonlinear theory.