scholarly journals Multiphasic Finite Element Framework for Modeling Hydrated Mixtures With Multiple Neutral and Charged Solutes

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Gerard A. Ateshian ◽  
Steve Maas ◽  
Jeffrey A. Weiss
Keyword(s):  
Finite Element ◽  
Electric Potential ◽  
Electrostatic Interactions ◽  
Biological Tissues ◽  
Solid Matrix ◽  
Natural Boundary Condition ◽  
Modeling Framework ◽  
Finite Element Software ◽  
Solute Fluxes ◽  
Electroneutrality Condition

Computational tools are often needed to model the complex behavior of biological tissues and cells when they are represented as mixtures of multiple neutral or charged constituents. This study presents the formulation of a finite element modeling framework for describing multiphasic materials in the open-source finite element software febio.1 Multiphasic materials may consist of a charged porous solid matrix, a solvent, and any number of neutral or charged solutes. This formulation proposes novel approaches for addressing several challenges posed by the finite element analysis of such complex materials: The exclusion of solutes from a fraction of the pore space due to steric volume and short-range electrostatic effects is modeled by a solubility factor, whose dependence on solid matrix deformation and solute concentrations may be described by user-defined constitutive relations. These solute exclusion mechanisms combine with long-range electrostatic interactions into a partition coefficient for each solute whose value is dependent upon the evaluation of the electric potential from the electroneutrality condition. It is shown that this electroneutrality condition reduces to a polynomial equation with only one valid root for the electric potential, regardless of the number and valence of charged solutes in the mixture. The equation of charge conservation is enforced as a constraint within the equation of mass balance for each solute, producing a natural boundary condition for solute fluxes that facilitates the prescription of electric current density on a boundary. It is also shown that electrical grounding is necessary to produce numerical stability in analyses where all the boundaries of a multiphasic material are impermeable to ions. Several verification problems are presented that demonstrate the ability of the code to reproduce known or newly derived solutions: (1) the Kedem–Katchalsky model for osmotic loading of a cell; (2) Donnan osmotic swelling of a charged hydrated tissue; and (3) current flow in an electrolyte. Furthermore, the code is used to generate novel theoretical predictions of known experimental findings in biological tissues: (1) current-generated stress in articular cartilage and (2) the influence of salt cation charge number on the cartilage creep response. This generalized finite element framework for multiphasic materials makes it possible to model the mechanoelectrochemical behavior of biological tissues and cells and sets the stage for the future analysis of reactive mixtures to account for growth and remodeling.

EFFECT OF BOUNDARY CONDITIONS ON PROCESS- INDUCED STRESSES IN A PLAIN WEAVE UNIT CELL

2021 ◽  
Author(s):  
K. BUKENYA ◽  
M. N. OLAYA ◽  
E. J. PINEDA ◽  
M. MAIARU
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Process Modeling ◽  
Complex Geometry ◽  
Polymer Matrix Composites ◽  
Unit Cell ◽  
Modeling Framework ◽  
Element Analysis ◽  
Finite Element Software ◽  
Aerospace Applications

Woven polymer matrix composites (PMCs) are leveraged in aerospace applications for their desirable specific properties, yet they are vulnerable to high residual stresses during manufacturing and their complex geometry makes experimental results difficult to observe. Process modeling is needed to characterize the effects of the curing and predict end stress states. Finite element software can be used to model woven architectures, however accurate representation of processing conditions remains a challenge when it comes to selecting boundary conditions. The effect of BCs on process-induced stress within woven PMCs is studied. The commercial Finite Element Analysis (FEA) software Abaqus is coupled with user-written subroutines in a process modeling framework. A two-dimensionally (2D) woven PMC repeating unit cell (RUC) is modeled with TexGen and Abaqus. Virtual curing is imposed on the bulk matrix. The BC study is conducted with Free, Periodic, Flat, and Flat-Free configurations. Results show that the end stress state is sensitive to the boundary condition assumptions. Flat BC results show great agreement with Periodic BCs. Residual stress results from process modeling are then compared with a linear-elastic thermal cooldown analysis in Abaqus. Cooldown results indicate an overestimation in matrix stresses compared with process modeling.

scholarly journals Finite Element Implementation of Mechanochemical Phenomena in Neutral Deformable Porous Media Under Finite Deformation

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Gerard A. Ateshian ◽  
Michael B. Albro ◽  
Steve Maas ◽  
Jeffrey A. Weiss
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Finite Deformation ◽  
Biological Tissues ◽  
Solid Matrix ◽  
Element Formulation ◽  
Momentum Exchange ◽  
Deformable Porous Media ◽  
Chemical Effects ◽  
Highly Nonlinear

Biological soft tissues and cells may be subjected to mechanical as well as chemical (osmotic) loading under their natural physiological environment or various experimental conditions. The interaction of mechanical and chemical effects may be very significant under some of these conditions, yet the highly nonlinear nature of the set of governing equations describing these mechanisms poses a challenge for the modeling of such phenomena. This study formulated and implemented a finite element algorithm for analyzing mechanochemical events in neutral deformable porous media under finite deformation. The algorithm employed the framework of mixture theory to model the porous permeable solid matrix and interstitial fluid, where the fluid consists of a mixture of solvent and solute. A special emphasis was placed on solute-solid matrix interactions, such as solute exclusion from a fraction of the matrix pore space (solubility) and frictional momentum exchange that produces solute hindrance and pumping under certain dynamic loading conditions. The finite element formulation implemented full coupling of mechanical and chemical effects, providing a framework where material properties and response functions may depend on solid matrix strain as well as solute concentration. The implementation was validated using selected canonical problems for which analytical or alternative numerical solutions exist. This finite element code includes a number of unique features that enhance the modeling of mechanochemical phenomena in biological tissues. The code is available in the public domain, open source finite element program FEBio (http://mrl.sci.utah.edu/software).

Multiscale Constitutive Model Development and Finite Element Implementation for Magnetostrictive Materials

2007 ◽  
Author(s):  
William S. Oates
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Axial Magnetic Field ◽  
Mean Field Approximation ◽  
Ferromagnetic Behavior ◽  
Length Scale ◽  
Modeling Framework ◽  
Finite Element Software ◽  
Finite Element Implementation ◽  
Magnetostrictive Materials

A multiscale constitutive model is developed and applied to magnetostrictive materials to predict multi-axial ferromagnetic switching. The modeling framework is an extension of a one-dimensional homogenized energy model that employs a stochastic distribution of localized magnetic moments. Here, the model is extended to multi-axial ferromagnetic switching in a polycrystalline ferromagnetic material. A mean-field approximation is adopted to quantify ferromagnetic switching from multi-axial magnetic field loading at the single crystal length scale. Polycrystalline ferromagnetic behavior is modeled by homogenizing stochastic distributions of underlying microscopic fields associated with material inhomogeneities at the grain length scale. Approximations of the stochastic distributions are made to improve computational efficiency for finite element implementation. The constitutive model is numerically validated and implemented in the commercial finite element software, COMSOL.

A Finite Element Algorithm for Large Deformation Biphasic Frictional Contact Between Porous-Permeable Hydrated Soft Tissues

2021 ◽  
Author(s):  
Brandon Zimmerman ◽  
Steve A. Maas ◽  
Jeffrey A. Weiss ◽  
Gerard A. Ateshian
Keyword(s):  
Finite Element ◽  
Open Source ◽  
Large Deformation ◽  
Interstitial Fluid ◽  
Frictional Contact ◽  
Biological Tissues ◽  
Contact Algorithm ◽  
Finite Element Software ◽  
Developed Surface ◽  
Element Algorithm

Abstract The frictional response of porous and permeable hydrated biological tissues such as articular cartilage is significantly dependent on interstitial fluid pressurization. To model this response, it is common to represent such tissues as biphasic materials, consisting of a binary mixture of a porous solid matrix and an interstitial fluid. However, no computational algorithms currently exist in either commercial or open-source software that can model frictional contact between such materials. Therefore, this study formulates and implements a finite element algorithm for large deformation biphasic frictional contact in the open-source finite element software FEBio. This algorithm relies on a local form of a biphasic friction model that has been previously validated against experiments, and implements the model into our recently-developed surface-to-surface contact algorithm. Contact constraints, including those specific to pressurized porous media, are enforced with the penalty method regularized with an active-passive augmented Lagrangian scheme. Numerical difficulties specific to challenging finite deformation biphasic contact problems are overcome with novel smoothing schemes for fluid pressures and Lagrange multipliers. Implementation accuracy is verified against semi-analytical solutions for biphasic frictional contact, with extensive validation performed using canonical cartilage friction experiments from prior literature. Essential details of the formulation are provided in this paper, and the source code of this biphasic frictional contact algorithm is made available to the general public.

Finite Element Implementation of Neutral Solute Transport in Porous Biological Soft Tissues Under Finite Deformation

2011 ◽  
Author(s):  
Gerard A. Ateshian ◽  
Michael B. Albro ◽  
Steve Maas ◽  
Jeffrey A. Weiss
Keyword(s):  
Finite Element ◽  
Transport Properties ◽  
Finite Deformation ◽  
Pore Volume ◽  
Soft Tissues ◽  
Biological Tissues ◽  
Solute Concentration ◽  
Porous Solid ◽  
Solid Matrix ◽  
Waste Products

The physiological function of biological tissues and cells is critically dependent on the transport of various solutes, such as nutrients, cytokines, hormones, and waste products. Transport in such media may be significantly hindered by the porous solid matrix, which may impart anisotropic transport properties to the solutes. Furthermore, large deformations of soft tissues and cells may significantly alter these transport properties due to concomitant alterations in pore volume and structure. Another potential influence of the porous solid matrix is steric volume exclusion resulting from the ratio of solute size and pore size distribution. This steric effect implies that solute concentration inside a tissue or cell may be less than the concentration in a surrounding bath, and this limit on solubility may be exacerbated under finite deformation due to changes in pore volume. Finally, the osmotic pressurization of the interstitial fluid may deviate from ideal physico-chemical behavior and this deviation may be dependent on the state of strain in the solid matrix. Therefore, a finite element framework that can accommodate solid-solute momentum exchanges, strain-induced anisotropy in transport properties and solubility, and strain-dependent non-ideal osmotic response, can provide an important modeling tool in the biomechanics of soft tissues and cells.

scholarly journals Low-Cycle Fatigue Crack Initiation Simulation and Life Prediction of Powder Superalloy Considering Inclusion-Matrix Interface Debonding

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4018
Author(s):  
Shuming Zhang ◽  
Yuanming Xu ◽  
Hao Fu ◽  
Yaowei Wen ◽  
Yibing Wang ◽  
...  
Keyword(s):  
Finite Element ◽  
Crack Initiation ◽  
Life Prediction ◽  
Damage Mechanics ◽  
Low Cycle Fatigue ◽  
Fatigue Crack Initiation ◽  
Fatigue Loading ◽  
Interface Debonding ◽  
Damage Evolution Equation ◽  
Finite Element Software

From the perspective of damage mechanics, the damage parameters were introduced as the characterizing quantity of the decrease in the mechanical properties of powder superalloy material FGH96 under fatigue loading. By deriving a damage evolution equation, a fatigue life prediction model of powder superalloy containing inclusions was constructed based on damage mechanics. The specimens containing elliptical subsurface inclusions and semielliptical surface inclusions were considered. The CONTA172 and TARGE169 elements of finite element software (ANSYS) were used to simulate the interfacial debonding between the inclusions and matrix, and the interface crack initiation life was calculated. Through finite element modeling, the stress field evolution during the interface debonding was traced by simulation. Finally, the effect of the position and shape size of inclusions on interface debonding was explored.

Effect of crack on free vibration of a pre-stressed curved plate

2021 ◽  
pp. 095440622199486
Author(s):  
Can Gonenli ◽  
Hasan Ozturk ◽  
Oguzhan Das
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequency ◽  
Present Model ◽  
Mode Shapes ◽  
Load Parameter ◽  
Flexible Plate ◽  
Cantilever Plate ◽  
Finite Element Software ◽  
Aspect Ratios

In this study, the effect of crack on free vibration of a large deflected cantilever plate, which forms the case of a pre-stressed curved plate, is investigated. A distributed load is applied at the free edge of a thin cantilever plate. Then, the loading edge of the deflected plate is fixed to obtain a pre-stressed curved plate. The large deflection equation provides the non - linear deflection curve of the large deflected flexible plate. The thin curved plate is modeled by using the finite element method with a four-node quadrilateral element. Three different aspect ratios are used to examine the effect of crack. The effect of crack and its location on the natural frequency parameter is given in tables and graphs. Also, the natural frequency parameters of the present model are compared with the finite element software results to verify the reliability and validity of the present model. This study shows that the different mode shapes are occurred due to the change of load parameter, and these different mode shapes cause a change in the effect of crack.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

Research on Mesh Optimization of the Finite Element Calculation about Three-Dimensional Foundation Pit

2012 ◽  
Vol 487 ◽  
pp. 855-859
Author(s):  
Shi Lun Feng ◽  
Yu Ming Zhou ◽  
Pu Lin Li ◽  
Jun Li ◽  
Zhi Yong Li ◽  
...  
Keyword(s):  
Finite Element ◽  
Complex Geometry ◽  
Three Dimensional ◽  
Mesh Optimization ◽  
Design Calculation ◽  
Foundation Pit ◽  
3D Design ◽  
Finite Element Software ◽  
Core Language ◽  
Grid Division

Abaqus finite element software can implement three-dimensional excavation design calculation, so authors used Python of Abaqus core language made the 3D design of foundation pit supporting program come ture and also did intensive study of mesh optimization during the process. Authors also did intensive comparison and analysis about grid division of the complex geometry foundation pit, through a regularization partion about a variety of special-shaped pit, we made the automatic division about the structural grid of all kinds of shapes foundation pit successful. On this basis, we achieved better calculation effects of the model. The article will introduce problems about optimization of grid in procedure.

scholarly journals Characterization of Mechanical Heterogeneity in Dissimilar Metal Welded Joints

Materials ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4145
Author(s):  
He Xue ◽  
Zheng Wang ◽  
Shuai Wang ◽  
Jinxuan He ◽  
Hongliang Yang
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Welded Joints ◽  
Structural Integrity ◽  
Material Interfaces ◽  
Mechanical Heterogeneity ◽  
Finite Element Software ◽  
Dissimilar Metal ◽  
Stress Changes

Dissimilar metal welded joints (DMWJs) possess significant localized mechanical heterogeneity. Using finite element software ABAQUS with the User-defined Material (UMAT) subroutine, this study proposed a constitutive equation that may be used to express the heterogeneous mechanical properties of the heat-affected and fusion zones at the interfaces in DMWJs. By eliminating sudden stress changes at the material interfaces, the proposed approach provides a more realistic and accurate characterization of the mechanical heterogeneity in the local regions of DMWJs than existing methods. As such, the proposed approach enables the structural integrity of DMWJs to be analyzed in greater detail.

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