Living soft tissues appear to promote the development and maintenance of a preferred mechanical state within a defined tolerance around a so-called set point. This phenomenon is often referred to as mechanical homeostasis. In contradiction to the prominent role of mechanical homeostasis in various (patho)physiological processes, its underlying micromechanical mechanisms acting on the level of individual cells and fibers remain poorly understood, especially how these mechanisms on the microscale lead to what we macroscopically call mechanical homeostasis. Here, we present a novel computational framework based on the finite element method that is constructed bottom up, that is, it models key mechanobiological mechanisms such as actin cytoskeleton contraction and molecular clutch behavior of individual cells interacting with a reconstructed three-dimensional extracellular fiber matrix. The framework reproduces many experimental observations regarding mechanical homeostasis on short time scales (hours), in which the deposition and degradation of extracellular matrix can largely be neglected. This model can serve as a systematic tool for future in silico studies of the origin of the numerous still unexplained experimental observations about mechanical homeostasis.

In this article, the nonlinear analysis of free vibrations, dynamic stability, and rotational dynamics of rotating annular circular thin plates, made of functionally graded material (FGM), is studied. Based on classical plate theory, von Karman's nonlinear plate theory, and assuming the FGM mechanical properties vary in the radial direction, the governing equations of motion are obtained by direct use of Newton's laws. A 1-D differential quadrature is used to solve the governing equations determining the natural frequencies, corresponding transverse mode shapes, and the critical speeds of rotation. The accuracy and convergence of the method are studied by comparing the results with the similar results whenever available in the literature. The influence of different parameters such as inner-to-outer radii ratio, thickness-to-outer radius ratio, graded index, angular velocity of the plate, and different boundary conditions on the natural frequencies of FG rotating plate are demonstrated by numerical examples. It is shown that fabricating a rotating disk with FGM can lead to an increase in its critical speed.

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