Room 515, Cosmology Building, National Taiwan University + Cisco WebEx, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館515研討室+ Cisco WebEx)
Modeling Poroelasticity and Other Multiphysics and Multicomponent Phenomena in Biomechanics
Alexander Cheng (University of Mississippi)
Abstract
Biological materials, such as human flesh, bones, cartilages, brain tissue, and blood vessels, are porous solid impregnated with a fluid, such as blood or interstitial fluid; hence should be modeled as poroelastic materials.There are generally three ways to introduce mathematical modeling to physical phenomena. One is the phenomenological approach, favored by engineers. If one observes a physical quantity that is closely related to another, linear or nonlinear relationship can be written between them, or their spatial and temporal gradients. These are called laws or constitutive laws, such as Fourier law, Darcy’s law, and generalized Hooke’s law in elasticity. The constants relating them are constitutive constants, which are empirical and require laboratory measurements.Another approach is based on thermodynamics laws of work, energy, and entropy. Force multiplies displacement is work, which can be stored as potential (strain) energy or heat energy. These laws obey the minimum energy principle; hence variational calculus is used to derive the needed equations. Similar principle exists for the energy dissipation.
We may consider the above two approaches as the physics-based approaches. In these approaches, different masses occupy different space. Continuum properties are defined as averaged quantities over a representative volume element (RVE). To build a model, it typically starts from a well-known simpler model, and then add new effects to it, often in an ad hoc fashion.There also exists a third and more mathematical approach, known as the mixture theory. The theory assumes that masses can coexist at a single point, each with a volume fraction. Their displacement, velocity, and acceleration can be defined. The most general relations can be constructed with coefficients. There is generally no direct physical meaning of these coefficients. For application purposes, they need to be reduced to match with the known engineering models. In that process, it is possible to retain certain additional effects that were not previously known or observed. This may inspire that one day such observation and measurement can be made. However, the reduction of such a complex system can sometimes lead to unphysical results, such as in the poroelasticity case, in which an erroneous effective stress coefficient was derived using the mixture theory.
This talk explores the mathematical modeling of porous medium in the presence of solid, fluid, heat, and chemical potential, and their reciprocal coupling under the Onsager theorem, using the physics-based approaches.
Meeting number (access code): 2517 691 9150
Meeting password: XtWiJxWb625
Organizer: Tai-Chia Lin (NTU)
