Formulation and application of certain primal and mixed finite element models of finite deformations of elastic bodies

2005 ◽  
pp. 334-365 ◽  
Author(s):  
J. T. Oden
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Finite Deformations ◽  
Finite Element Models ◽  
Elastic Bodies

Coupled Porohyperelastic Mass Transport (PHEXPT) Finite Element Models for Soft Tissues Using ABAQUS

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Jonathan P. Vande Geest ◽  
B. R. Simon ◽  
Paul H. Rigby ◽  
Tyler P. Newberg
Keyword(s):  
Finite Element ◽  
Mass Transport ◽  
Soft Tissues ◽  
Convective Transport ◽  
Finite Deformations ◽  
Nonlinear Material ◽  
Finite Element Models ◽  
Finite Element Software ◽  
Mobile Species ◽  
Highly Nonlinear

Finite element models (FEMs) including characteristic large deformations in highly nonlinear materials (hyperelasticity and coupled diffusive/convective transport of neutral mobile species) will allow quantitative study of in vivo tissues. Such FEMs will provide basic understanding of normal and pathological tissue responses and lead to optimization of local drug delivery strategies. We present a coupled porohyperelastic mass transport (PHEXPT) finite element approach developed using a commercially available ABAQUS finite element software. The PHEXPT transient simulations are based on sequential solution of the porohyperelastic (PHE) and mass transport (XPT) problems where an Eulerian PHE FEM is coupled to a Lagrangian XPT FEM using a custom-written FORTRAN program. The PHEXPT theoretical background is derived in the context of porous media transport theory and extended to ABAQUS finite element formulations. The essential assumptions needed in order to use ABAQUS are clearly identified in the derivation. Representative benchmark finite element simulations are provided along with analytical solutions (when appropriate). These simulations demonstrate the differences in transient and steady state responses including finite deformations, total stress, fluid pressure, relative fluid, and mobile species flux. A detailed description of important model considerations (e.g., material property functions and jump discontinuities at material interfaces) is also presented in the context of finite deformations. The ABAQUS-based PHEXPT approach enables the use of the available ABAQUS capabilities (interactive FEM mesh generation, finite element libraries, nonlinear material laws, pre- and postprocessing, etc.). PHEXPT FEMs can be used to simulate the transport of a relatively large neutral species (negligible osmotic fluid flux) in highly deformable hydrated soft tissues and tissue-engineered materials.

A simple node-to-segment contact technique of finite element models of elastic bodies to attain the node-to-node contact accuracy

2013 ◽  
Vol 228 (7) ◽  
pp. 1089-1093 ◽  
Author(s):  
Kisu Lee
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Contact Point ◽  
Finite Element Models ◽  
Elastic Bodies ◽  
Contact Constraint

By modifying the contact point displacement with a simple and systematic way, it has been explained that the node-to-segment contact solution can become as accurate as that of the node-to-node contact constraint. The accuracy of the solution is demonstrated by the numerical simulation using a punch sliding on the slab.

scholarly journals Enriched two dimensional mixed finite element models for linear elasticity with weak stress symmetry

2020 ◽  
Vol 79 (9) ◽  
pp. 2678-2700
Author(s):  
Philippe R.B. Devloo ◽  
Sônia M. Gomes ◽  
Thiago O. Quinelato ◽  
Shudan Tian
Keyword(s):  
Finite Element ◽  
Linear Elasticity ◽  
Mixed Finite Element ◽  
Finite Element Models ◽  
Two Dimensional
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