Extended “LMPHETS” Finite Element Models for Coupled Mechano-Electro-Chemical Transport in Soft Tissues

2002 ◽  
Author(s):  
B. R. Simon ◽  
G. A. Radtke ◽  
P. H. Rigby ◽  
S. K. Williams ◽  
Z. P. Liu
Keyword(s):  
Finite Element ◽  
Soft Tissues ◽  
Electrical Potential ◽  
Fluid Pressure ◽  
Nonlinear Material ◽  
Solid Matrix ◽  
Test Problems ◽  
Finite Element Models ◽  
Material Interfaces ◽  
Mobile Species

Soft tissues are hydrated fibrous materials that exhibit nonlinear material response and undergo finite straining during in vivo loading. A continuum model of these structures (“LMPHETS” [1,2]) is a porous solid matrix (with charges fixed to the solid fibers) saturated by a mobile fluid (water) and multiple species (e.g., three mobile species designated by α, β = p, m, b where p = +, m = −, and b = ± charge) dissolved in the mobile fluid. A “mixed” LMPHETS theory and finite element models (FEMs) were presented [1] in which the “primary fields” are the displacements, ui = xi − Xi and the mechano-electro-chemical potentials, ν˜ξ* (ξ, η = f, e, m, b) that are continuous across material interfaces. “Secondary fields” (discontinuous at material boundaries) are mechanical fluid pressure, pf; electrical potential, μ˜e; and concentration or “molarity”, cα = dnα / dVf. Here an extended version of these models is described and numerical results are presented for representative test problems associated with transport in soft tissues.

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.

Porohyperelastic-Transport Finite Element Models of the Eye Using ABAQUS

2004 ◽  
Author(s):  
P. H. Rigby ◽  
R. I. Park ◽  
B. R. Simon
Keyword(s):  
Finite Element ◽  
Anterior Chamber ◽  
Soft Tissues ◽  
Ganglion Cells ◽  
Vitreous Body ◽  
Flow Fields ◽  
Finite Element Models ◽  
Tissue Fluid ◽  
Fluid Flux ◽  
Mobile Species

Glaucoma is related to damage to nerve ganglion cells in the optic nerve head (ONH) including the lamina cribrosa, (LC). This disease is associated with elevated intraocular pressure (IOP) and possibly reduced trabecular meshwork (TM) outflow. The ABAQUS program was used to develop axisymmetric porohyperelastic (PHE) pore fluid finite element models (FEMs) to determine deformations, stresses, tissue fluid pressures (pf), and mobile fluid flux in the eye. These FEMs simulated aqueous pressure-fluid flow fields in the anterior chamber via the TM and posterior pressure-flow fields in the vitreous body (VIT) and ONH. Constant inlet flow at the ciliary processes (CP) was applied. The anterior chamber was modeled as a highly porous material containing large amounts of fluid whereas the VIT was modeled as a gel with mobile fluid. All ocular soft tissues were considered to be linear, isotropic PHE materials. Posterior transport was regulated by varying the permeability of the LC, retina, choroid, and sclera material layers. Two FEMs, i.e. IOP=15 mm Hg (normal) and IOP=44 mm Hg (glaucoma) were developed by varying the permeability of the TM. Deformations and tissue fluid pressures, fluid flux (relative fluid velocities), and stresses were determined and agree well with experimental data and other numerical model results. The displacement of the LC was 21–62 μm; the LC pressure gradient was 25–73 mm Hg/mm; and the posterior outflow ranged from 5%–15% of the inflow at the CP. The PHE material law can be extended to include nonlinear permeability effects and mobile species transport using a porohyperelastic-transport-swelling (PHETS) theory in future FEMs.

One-Dimensional Mixed Poroelastic-Transport-Swelling (MPHETS) Finite Element Models for Soft Tissues

2000 ◽  
Author(s):  
Jason W. Nichol ◽  
Bruce R. Simon ◽  
Stuart K. Williams
Keyword(s):  
Finite Element ◽  
Soft Tissues ◽  
Transport Model ◽  
Element Model ◽  
Solid Matrix ◽  
Finite Element Models ◽  
Flow Conditions ◽  
One Dimensional ◽  
Dimensional Finite Element ◽  
Water Species

Abstract A hydrated soft tissue structure can be viewed as a poroelastic transport model, or specifically a porous, incompressible, fibrous solid matrix, which is saturated by an incompressible fluid (water) containing both positively and negatively charged species. We present a one-dimensional finite element model (FEM), derived from a Mixed-Poro-HyperElastic-Transport-Swelling (MPHETS)model. This FEM can be used to model various soft tissues, such as arteries, and provides a powerful tool to study coupled ion transport under various mechanical loading and water/ species flow conditions.

Flexural bearing capacity of RC hollow slab beam strengthened by steel plates of different thicknesses

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Long Liu ◽  
Lifeng Wang ◽  
Ziwang Xiao
Keyword(s):  
Finite Element ◽  
Bearing Capacity ◽  
Steel Plate ◽  
Plate Thickness ◽  
Research Field ◽  
Steel Plates ◽  
Nonlinear Material ◽  
Finite Element Models ◽  
Content Type ◽  
Flexural Bearing Capacity

PurposeThe flexural reinforcement of bridges in-service has been an important research field for a long time. Anchoring steel plate at the bottom of beam is a simple and effective method to improve its bearing capacity. The purpose of this paper is to explore the influence of anchoring steel plates of different thicknesses on the bearing capacity of hollow slab beam and to judge its working status.Design/methodology/approachFirst, static load experiments are carried out on two in-service RC hollow slab beams; meanwhile, nonlinear finite element models are built to study the bearing capacity of them. The nonlinear material and shear slip effect of studs are considered in the models. Second, the finite element models are verified, and the numerical simulation results are in good agreement with the experimental results. Finally, the finite element models are adopted to carry out the research on the influence of different steel plate thicknesses on the flexural bearing capacity and ductility.FindingsWhen steel plates of different thicknesses are adopted to reinforce RC hollow slab beams, the bearing capacity increases with the increase of the steel plate thickness in a certain range. But when the steel plate thickness reaches a certain level, bearing capacity is no longer influenced. The displacement ductility coefficient decreases with the increase of steel plate thickness.Originality/valueBased on experimental study, this paper makes an extrapolation analysis of the bearing capacity of hollow slab beams reinforced with steel plates of different thicknesses through finite element simulation and discusses the influence on ductility. This method not only ensures the accuracy of bearing capacity evaluation but also does not need many samples, which is economical to a certain extent. The research results provide a basis for the reinforcement design of similar bridges.

Comparison of flexural capacity of different hollow slab beams with/without pavement layer reinforced by steel plates

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Long Liu ◽  
Lifeng Wang ◽  
Ziwang Xiao
Keyword(s):  
Finite Element ◽  
Bearing Capacity ◽  
Steel Plate ◽  
Plate Thickness ◽  
Experimental Results ◽  
Nonlinear Material ◽  
Finite Element Models ◽  
Rc Beams ◽  
Flexural Capacity ◽  
Content Type

PurposeReinforcement of reinforced concrete (RC) beams in-service have always been an important research field, anchoring steel plate in the bottom of the beams is a kind of common reinforcement methods. In actual engineering, the contribution of pavement layer to the bearing capacity of RC beams is often ignored, which underestimates the bearing capacity and stiffness of RC beams to a certain extent. The purpose of this paper is to study the effect of pavement layer on the RC beams before and after reinforcement.Design/methodology/approachFirst, static load experiments are carried out on three in-service RC hollow slab beams, meanwhile, nonlinear finite element models are built to study the bearing capacity of them. The nonlinear material and shear slip effect of studs are considered in the models. Second, the finite element models are verified, and the numerical simulation results are in good agreement with the experimental results. Last, the finite element models are adopted to carry out the research on the influence of different steel plate thicknesses on the flexural bearing capacity and ductility.FindingsThe experimental results showed that pavement layers increase the flexural capacity of hollow slab beams by 16.7%, and contribute to increasing stiffness. Ductility ratio of SPRCB3 and PRCB2 was 30% and 24% lower than that of RCB1, respectively. The results showed that when the steel plate thickness was 1 mm–6 mm, the bearing capacity of the hollow slab beam increased gradually from 2158.0 kN.m to 2656.6 kN.m. As the steel plate thickness continuously increased to 8 mm, the ultimate bearing capacity increased to 2681.0 kN.m. The increased thickness did not cause difference to the bearing capacity, because of concrete crushing at the upper edge.Originality/valueIn this paper, based on the experimental study, the bearing capacity of hollow beam strengthened by steel plate with different thickness is extrapolated by finite element simulation, and its influence on ductility is discussed. This method not only guarantees the accuracy of the bearing capacity evaluation, but also does not require a large number of samples, and has certain economy. The research results provide a basis for the reinforcement design of similar bridges.

scholarly journals The method of direct finite perturbation of numerical models for studying of the dynamic, stiffness and strength properties for thin-walled elements of engineering constructions.

2014 ◽  
Vol 2014 (4) ◽  
pp. 114-124
Author(s):  
Юрий Костенко ◽  
Yuriy Kostenko ◽  
Анатолий Чепурной ◽  
Anatoliy Chepurnoy ◽  
Александр Литвиненко ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Numerical Models ◽  
Dynamic Stiffness ◽  
Strength Properties ◽  
Test Problems ◽  
Finite Element Models ◽  
Direct Perturbation ◽  
Thin Walled

The methods of direct perturbation for finite element models of thin-walled engineering constructions for sensitivity analysis of their strength, stiffness and dynamic characteristics to the change in their thickness are proposed. The approach for prediction of distribution for natural frequencies migration as result of change in their thickness are presented. The applicability of the linearized models to determine displacements, stresses and natural frequencies slightly thinned design compared to the nominal (original) are shown. The examples of test problems are given.

Equivalent Mixed “PHETS” and “MPHETS” Poroelasttc-Transport-Swelling Finite Element Models for Soft Biological Tissues

1999 ◽  
Author(s):  
B. R. Simon ◽  
S. K. Williams ◽  
J. Liu ◽  
J. W. Nichol ◽  
P. H. Rigby ◽  
...  
Keyword(s):  
Finite Element ◽  
Chemical Potential ◽  
Biological Tissues ◽  
Finite Element Models ◽  
Material Interfaces ◽  
Soft Biological Tissues ◽  
Fibrous Matrix ◽  
Charged Species ◽  
Pressure Fields ◽  
Swelling Model

Abstract A soft hydrated tissue structure can be viewed as a “PETS” (poroelastic-transport-swelling) model, i.e., as a continuum composed of an incompressible porous solid (fibrous matrix with fixed charge density, FCD) that is saturated by a mobile incompressible fluid (water) containing mobile positively (p) and negatively (m) charged species. Previously, we described two PETS models — a “semi-mixed” porohyperelastic PHETS model (Simon et al. 1998) and a “fully mixed” MPHETS model (Simon et al. 1999) using FEMs (finite element models) that included geometric and material nonlinearity and coupled electrical/chemical/mechanical transport of the fluid and charged species. Here, we demonstrate the equivalence of the PHETS and MPHETS formulations that are useful when the solid and fluid materials are incompressible and the electrical-chemical potential and mechanical-osmotic pressure fields are discontinuous at material interfaces.

Fracture Prediction for the Proximal Femur Using Finite Element Models: Part I—Linear Analysis

1991 ◽  
Vol 113 (4) ◽  
pp. 353-360 ◽  
Author(s):  
J. C. Lotz ◽  
E. J. Cheal ◽  
W. C. Hayes
Keyword(s):  
Finite Element ◽  
Fracture Risk ◽  
Strain Gage ◽  
Proximal Femur ◽  
Material Properties ◽  
The United States ◽  
Nonlinear Material ◽  
Finite Element Models ◽  
Model Predictions

Over 90 percent of the more than 250,000 hip fractures that occur annually in the United States are the result of falls from standing height. Despite this, the stresses associated with femoral fracture from a fall have not been investigated previously. Our objectives were to use three-dimensional finite element models of the proximal femur (with geometries and material properties based directly on quantitative computed tomography) to compare predicted stress distributions for one-legged stance and for a fall to the lateral greater trochanter. We also wished to test the correspondence between model predictions and in vitro strain gage data and failure loads for cadaveric femora subjected to these loading conditions. An additional goal was to use the model predictions to compare the sensitivity of several imaging sites in the proximal femur which are used for the in vivo prediction of hip fracture risk. In this first of two parts, linear finite element models of two unpaired human cadaveric femora were generated. In Part II, the models were extended to include nonlinear material properties for the cortical and trabecular bone. While there was poor correspondence between strain gage data and model predictions, there was excellent agreement between the in vitro failure data and the linear model, especially using a von Mises effective strain failure criterion. Both the onset of structural yielding (within 22 and 4 percent) and the load at fracture (within 8 and 5 percent) were predicted accurately for the two femora tested. For the simulation of one-legged stance, the peak stresses occurred in the primary compressive trabeculae of the subcapital region. However, for a simulated fall, the peak stresses were in the intertrochanteric region. The Ward’s triangle (basicervical) site commonly used for the clinical assessment of osteoporosis was not heavily loaded in either situation. These findings suggest that the intertrochanteric region may be the most sensitive site for the assessment of fracture risk due to a fall and the subcapital region for fracture risk due to repetitive activities such as walking.

Analytical Solutions to Axisymmetric Plane Strain Porous Media-Transport Models in Large Arteries

2008 ◽  
Author(s):  
Jonathan P. Vande Geest ◽  
Bruce R. Simon
Keyword(s):  
Plane Strain ◽  
Analytical Solutions ◽  
Soft Tissues ◽  
Fluid Pressure ◽  
Convective Transport ◽  
Species Transport ◽  
Mobile Species ◽  
Starting Point ◽  
Strain Stress ◽  
Numerical Finite Element

Theoretical and numerical finite element models (FEMs) have been developed for analysis of coupled structural-fluid-species transport in soft tissues [1–3]. Here analytical solutions for coupled diffusive-convective transport of a single, neutral species in soft tissues are presented. Based on experimental observations [4], osmotic pressure and partial Onsager coupling of species transport can be neglected for large mobile species in rabbit carotid arteries. These analytical solutions provide a starting point for development of solutions to more complex problems and allow verification of the associated FEMs under development in our laboratory. The analytical solutions will allow comparison of elastic and poroelastic-species transport for axisymmetric, plane strain in thick-walled arteries including expressions for displacement, strain, stress, pore fluid pressure, and concentration fields. The initial models considered here will be steady state (SS) solutions for compressible, linear, isotropic materials undergoing small strains.

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