scholarly journals Equivalence Between Short-Time Biphasic and Incompressible Elastic Material Responses

2006 ◽  
Vol 129 (3) ◽  
pp. 405-412 ◽  
Author(s):  
Gerard A. Ateshian ◽  
Benjamin J. Ellis ◽  
Jeffrey A. Weiss
Keyword(s):  
Finite Element ◽  
Constitutive Relations ◽  
Strain Energy Function ◽  
Elasticity Tensor ◽  
Solid Matrix ◽  
Hydraulic Permeability ◽  
Elastic Responses ◽  
Incompressible Elasticity ◽  
Short Time ◽  
Term Response

Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under finite deformation, using two different constitutive relations for the solid matrix of cartilage, one of which accounts for the large disparity observed between the tensile and compressive moduli in this tissue. Demonstrating this equivalence under general conditions provides a rationale for using available finite element codes for incompressible elastic materials as a practical substitute for biphasic analyses, so long as only the short-time biphasic response is sought. In practice, an incompressible elastic analysis is representative of a biphasic analysis over the short-term response δt⪡Δ2∕∥C4∥∥K∥, where Δ is a characteristic dimension, C4 is the elasticity tensor, and K is the hydraulic permeability tensor of the solid matrix. Certain notes of caution are provided with regard to implementation issues, particularly when finite element formulations of incompressible elasticity employ an uncoupled strain energy function consisting of additive deviatoric and volumetric components.

Experimental and Biphasic FEM Determinations of the Material Properties and Hydraulic Permeability of the Meniscus in Tension1

2002 ◽  
Vol 124 (3) ◽  
pp. 315-321 ◽  
Author(s):  
Michelle A. LeRoux ◽  
Lori A. Setton
Keyword(s):  
Finite Element ◽  
Stress Relaxation ◽  
Transversely Isotropic ◽  
Element Model ◽  
Tensile Tests ◽  
Solid Matrix ◽  
Hydraulic Permeability ◽  
Permeability Coefficients ◽  
Matrix Properties ◽  
Biphasic Finite Element

Tensile tests and biphasic finite element modeling were used to determine a set of transversely isotropic properties for the meniscus, including the hydraulic permeability coefficients and solid matrix properties. Stress-relaxation tests were conducted on planar samples of canine meniscus samples of different orientations, and the solid matrix properties were determined from equilibrium data. A 3-D linear biphasic and tranversely isotropic finite element model was developed to model the stress-relaxation behavior of the samples in tension, and optimization was used to determine the permeability coefficients, k1 and k2, governing fluid flow parallel and perpendicular to the collagen fibers, respectively. The collagen fibrillar orientation was observed to have an effect on the Young’s moduli (E1=67.8MPa,E2=11.1MPa) and Poisson’s ratios (ν12=2.13,ν21=1.50,ν23=1.02). However, a significant effect of anisotropy on permeability was not detected (k1=0.09×10−16m4/Ns,k2=0.10×10−16m4/Ns). The low permeability values determined in this study provide insight into the extent of fluid pressurization in the meniscus and will impact modeling predictions of load support in the meniscus.

scholarly journals Assessment of the Viscoelastic Mechanical Properties of the Porcine Optic Nerve Head using Micromechanical Testing and Finite Element Modeling

2021 ◽  
Author(s):  
Babak N. Safa ◽  
A. Thomas Read ◽  
C. Ross Ethier
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Optic Nerve ◽  
Finite Element Modeling ◽  
Optic Nerve Head ◽  
Mechanical Response ◽  
Solid Matrix ◽  
Hydraulic Permeability ◽  
Element Modeling ◽  
Micromechanical Testing

AbstractOptic nerve head (ONH) biomechanics is centrally involved in the pathogenesis of glaucoma, a blinding ocular condition often characterized by elevation and fluctuation of the intraocular pressure and resulting loads on the ONH. Further, tissue viscoelasticity is expected to strongly influence the mechanical response of the ONH to mechanical loading, yet the viscoelastic mechanical properties of the ONH remain unknown. To determine these properties, we conducted micromechanical testing on porcine ONH tissue samples, coupled with finite element modeling based on a mixture model consisting of a biphasic material with a viscoelastic solid matrix. Our results provide a detailed description of the viscoelastic properties of the porcine ONH at each of its four anatomical quadrants (i.e., nasal, superior, temporal, and inferior). We showed that the ONH’s viscoelastic mechanical response can be explained by a dual mechanism of fluid flow and solid matrix viscoelasticity, as is common in other soft tissues. We obtained porcine ONH properties as follows: matrix Young’s modulus E=1.895 [1.056,2 .391] kPa (median [min., max.]), Poisson’s ratio ν=0.142 [0.060,0 .312], kinetic time-constant τ=214 [89,921] sec, and hydraulic permeability k=3.854 × 10−1 [3.457 × 10−2,9.994 × 10−1] mm4/(N sec). These values can be used to design and fabricate physiologically appropriate ex vivo test environments (e.g., 3D cell culture) to further understand glaucoma pathophysiology.

scholarly journals A Practical Finite Element Modeling Strategy to Capture Cracking and Crushing Behavior of Reinforced Concrete Structures

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 506 ◽  
Author(s):  
Alexandre Mathern ◽  
Jincheng Yang
Keyword(s):  
Finite Element ◽  
Reinforced Concrete ◽  
Constitutive Relations ◽  
Fe Analysis ◽  
Rc Beams ◽  
Cracking Behavior ◽  
Concrete Cracking ◽  
Rc Structures ◽  
Nonlinear Fe Analysis ◽  
Modeling Strategy

Nonlinear finite element (FE) analysis of reinforced concrete (RC) structures is characterized by numerous modeling options and input parameters. To accurately model the nonlinear RC behavior involving concrete cracking in tension and crushing in compression, practitioners make different choices regarding the critical modeling issues, e.g., defining the concrete constitutive relations, assigning the bond between the concrete and the steel reinforcement, and solving problems related to convergence difficulties and mesh sensitivities. Thus, it is imperative to review the common modeling choices critically and develop a robust modeling strategy with consistency, reliability, and comparability. This paper proposes a modeling strategy and practical recommendations for the nonlinear FE analysis of RC structures based on parametric studies of critical modeling choices. The proposed modeling strategy aims at providing reliable predictions of flexural responses of RC members with a focus on concrete cracking behavior and crushing failure, which serve as the foundation for more complex modeling cases, e.g., RC beams bonded with fiber reinforced polymer (FRP) laminates. Additionally, herein, the implementation procedure for the proposed modeling strategy is comprehensively described with a focus on the critical modeling issues for RC structures. The proposed strategy is demonstrated through FE analyses of RC beams tested in four-point bending—one RC beam as reference and one beam externally bonded with a carbon-FRP (CFRP) laminate in its soffit. The simulated results agree well with experimental measurements regarding load-deformation relationship, cracking, flexural failure due to concrete crushing, and CFRP debonding initiated by intermediate cracks. The modeling strategy and recommendations presented herein are applicable to the nonlinear FE analysis of RC structures in general.

scholarly journals Impact of tumor-parenchyma biomechanics on liver metastatic progression: a multi-model approach

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yafei Wang ◽  
Erik Brodin ◽  
Kenichiro Nishii ◽  
Hermann B. Frieboes ◽  
Shannon M. Mumenthaler ◽  
...  
Keyword(s):  
Time Scales ◽  
Constitutive Relations ◽  
Elastic Tissue ◽  
Metastatic Progression ◽  
Patient Death ◽  
Metastatic Growth ◽  
Tumor Parenchyma ◽  
Short Time ◽  
Model Approach

AbstractColorectal cancer and other cancers often metastasize to the liver in later stages of the disease, contributing significantly to patient death. While the biomechanical properties of the liver parenchyma (normal liver tissue) are known to affect tumor cell behavior in primary and metastatic tumors, the role of these properties in driving or inhibiting metastatic inception remains poorly understood, as are the longer-term multicellular dynamics. This study adopts a multi-model approach to study the dynamics of tumor-parenchyma biomechanical interactions during metastatic seeding and growth. We employ a detailed poroviscoelastic model of a liver lobule to study how micrometastases disrupt flow and pressure on short time scales. Results from short-time simulations in detailed single hepatic lobules motivate constitutive relations and biological hypotheses for a minimal agent-based model of metastatic growth in centimeter-scale tissue over months-long time scales. After a parameter space investigation, we find that the balance of basic tumor-parenchyma biomechanical interactions on shorter time scales (adhesion, repulsion, and elastic tissue deformation over minutes) and longer time scales (plastic tissue relaxation over hours) can explain a broad range of behaviors of micrometastases, without the need for complex molecular-scale signaling. These interactions may arrest the growth of micrometastases in a dormant state and prevent newly arriving cancer cells from establishing successful metastatic foci. Moreover, the simulations indicate ways in which dormant tumors could “reawaken” after changes in parenchymal tissue mechanical properties, as may arise during aging or following acute liver illness or injury. We conclude that the proposed modeling approach yields insight into the role of tumor-parenchyma biomechanics in promoting liver metastatic growth, and advances the longer term goal of identifying conditions to clinically arrest and reverse the course of late-stage cancer.

Approximate Macroscale Constitutive Relations Using a Finite Element Based Constitutive Equations for Microscale Contact

2008 ◽  
Author(s):  
Ali Sepehri ◽  
Kambiz Farhang
Keyword(s):  
Finite Element ◽  
Contact Force ◽  
Rough Surfaces ◽  
Constitutive Relations ◽  
Cumulative Effect ◽  
Element Model ◽  
Tangential Component ◽  
Total Force ◽  
Asperity Contact ◽  
Elastic Plastic

Three dimensional elastic-plastic contact of two nominally flat rough surfaces is considered. Equations governing the shoulder-shoulder contact of asperities are derived based on the asperity-asperity constitutive relations from a finite element model of their elastic-plastic interaction. Shoulder-shoulder asperity contact yields a slanted contact force consisting of both tangential (parallel to mean plane) and normal components. Multiscale modeling of the elastic-plastic rough surface contact is presented in which asperity-level FE-based constitutive relations are statistically summed to obtain total force in the normal and tangential direction. The equations derived are in the form of integral functions and provide expectation of contact force components between two rough surfaces. An analytical fusion technique is developed to combine the piecewise asperity level constitutive relations. This is shown to yield upon statistical summation the cumulative effect resulting in the contact force between two rough surfaces with two components, one in the normal direction and a half-plane tangential component.

scholarly journals COMPUTATION FOR THE DELAMINATION IN THE LAMINATE COMPOSITE MATERIAL USING A COHESIVE ZONE MODEL BY ABAQUS

2020 ◽  
Vol 57 (6A) ◽  
pp. 61
Author(s):  
Hoa Cong Vu
Keyword(s):  
Finite Element ◽  
Cohesive Zone Model ◽  
Constitutive Relations ◽  
Damage Zone ◽  
Damage Model ◽  
Zone Model ◽  
Element Formulation ◽  
Cohesive Elements ◽  
Element Mesh ◽  
Variable Mode

In this paper, a damage model using cohesive damage zone for the simulation of progressive delamination under variable mode is presented. The constitutive relations, based on liner softening law, are using for formulation of the delamination onset and propagation. The implementation of the cohesive elements is described, along with instructions on how to incorporate the elements into a finite element mesh. The model is implemented in a finite element formulation in ABAQUS. The numerical results given by the model are compare with experimental data

Experimental Validation of Non-Fourier Thermal Response in Porous Media

2001 ◽  
Author(s):  
A. G. Agwu Nnanna ◽  
K. T. Harris ◽  
A. Haji-Sheikh
Keyword(s):  
Heat Flux ◽  
Porous Media ◽  
Experimental Validation ◽  
Thermal Response ◽  
Lag Time ◽  
Equation Model ◽  
Thermal Parameters ◽  
Solid Matrix ◽  
Microscale Model ◽  
Short Time

Abstract An experimental validation of non-Fourier behavior in porous media due to short time thermal perturbation is presented. The governing energy equation is formulated based on the two-equation model and the non-Fourier model. This formulation leads to the emergence of four thermal parameters: lag-time in heat flux τq, lag-time τt in temperature due to interstitial heat transfer coefficient h, and lag-time in the transient response of the temperature gradient τx in the heat flux equation. These parameters account for the microstructural thermal interaction between the fluid and neighboring solid matrix as well as the delay time needed for both phases to approach thermal equilibrium. An experimental verification of the microscale model was performed under standard laboratory conditions. The values of the aforementioned thermal parameters were determined to compute the fluid and solid temperatures. Results predicted from three models (classical Fourier, non-Fourier, and experimental) were compared. It indicates an excellent agreement between the non-Fourier and the experimental model, and a significant deviation of Fourier prediction from the experimental results.

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