Simulation of cancer prognosis

Most mechanobiology phenomena commonly involve biological growth and deformation. In this work, we propose an innovative model of cancerous growth which posits that an expandable tumor can be described as a poroelastic medium consisting of solid and fluid components. In our biologically informed mechanical description of tumor growth dynamics, we derive the governing equations of the tumor’s growth and incorporate them with large deformation and materially nonlinear constitutive equations to improve the accuracy and efficiency of our simulation. Meanwhile, the dynamic finite element equations (DFE) for coupled displacement field and pressure field are formulated and solved. The 3-dimensional porous model is introduced. Numerical results are presented and discussed.

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The Numerical Simulation for Vibroacoustic Phenomena of a Slender Elastic Shell

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.479-481.1365 ◽

2012 ◽

Vol 479-481 ◽

pp. 1365-1370

Author(s):

Zhi Xi Yang ◽

Sheng Hua Qiu

Keyword(s):

Numerical Simulation ◽

Finite Element ◽

Thin Shell ◽

Acoustic Pressure ◽

Pressure Field ◽

Elastic Shell ◽

Numerical Examples ◽

Longitudinal Acoustic ◽

3 Dimensional ◽

Variational Formulas

The vibroacoustic phenomena for the slender elastic thin shell filled with water by finite element method is introduced in this paper. The unsymmetric (u, p) variational formulas and finite element procedures are implemented for 3 dimensional structures of vibroacoustic environment based on the displacement field u and the fluid acoustic pressure field p. As illustrated by numerical examples, the longitudinal acoustic pressure eigenmodes will be occurred besides the transverse bendable eigenmodes of the slender shell, nonetheless the eigenvalues and the order of eigenmodes for the fluid acoustic pressure field can only be determined by the flexibility and geometry stiffness of the slender shell.

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A Study on Thermoelastic Interaction in a Poroelastic Medium with and without Energy Dissipation

Mathematics ◽

10.3390/math8081286 ◽

2020 ◽

Vol 8 (8) ◽

pp. 1286

Author(s):

Tareq Saeed

Keyword(s):

Finite Element Method ◽

Finite Element ◽

The Finite Element Method ◽

Governing Equations ◽

Poroelastic Medium ◽

Thermoelastic Medium ◽

Finite Element Scheme ◽

Element Scheme ◽

Thermoelastic Interaction ◽

Without Energy Dissipation

In the current work, a new generalized model of heat conduction has been constructed taking into account the influence of porosity on a poro-thermoelastic medium using the finite element method (FEM). The governing equations are presented in the context of the Green and Naghdi (G-N) type III theory with and without energy dissipations. The finite element scheme has been adopted to present the solutions due to the complex formulations of this problem. The effects of porosity on poro-thermoelastic material are investigated. The numerical results for stresses, temperatures, and displacements for the solid and the fluid are graphically presented. This work provides future investigators with insight regarding details of non-simple poro-thermoelasticity with different phases.

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