Finite Element Formulation of Multiphasic Shell Elements for Cell Mechanics Analyses in FEBio

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Jay C. Hou ◽  
Steve A. Maas ◽  
Jeffrey A. Weiss ◽  
Gerard A. Ateshian
Keyword(s):  
Finite Element ◽  
Cell Membrane ◽  
Degrees Of Freedom ◽  
Fluid Pressure ◽  
3D Models ◽  
Solid Matrix ◽  
Cell Physiology ◽  
Element Formulation ◽  
Isolated Cells ◽  
Shell Elements

With the recent implementation of multiphasic materials in the open-source finite element (FE) software FEBio, three-dimensional (3D) models of cells embedded within the tissue may now be analyzed, accounting for porous solid matrix deformation, transport of interstitial fluid and solutes, membrane potential, and reactions. The cell membrane is a critical component in cell models, which selectively regulates the transport of fluid and solutes in the presence of large concentration and electric potential gradients, while also facilitating the transport of various proteins. The cell membrane is much thinner than the cell; therefore, in an FE environment, shell elements formulated as two-dimensional (2D) surfaces in 3D space would be preferred for modeling the cell membrane, for the convenience of mesh generation from image-based data, especially for convoluted membranes. However, multiphasic shell elements are yet to be developed in the FE literature and commercial FE software. This study presents a novel formulation of multiphasic shell elements and its implementation in FEBio. The shell model includes front- and back-face nodal degrees-of-freedom for the solid displacement, effective fluid pressure and effective solute concentrations, and a linear interpolation of these variables across the shell thickness. This formulation was verified against classical models of cell physiology and validated against reported experimental measurements in chondrocytes. This implementation of passive transport of fluid and solutes across multiphasic membranes makes it possible to model the biomechanics of isolated cells or cells embedded in their extracellular matrix (ECM), accounting for solvent and solute transport.

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).

On the Reliable Modeling of the Collapse and Post-Collapse Behavior of Pipelines

2009 ◽  
Author(s):  
Rita G. Toscano ◽  
Eduardo N. Dvorkin
Keyword(s):  
Finite Element ◽  
3D Models ◽  
Material Modeling ◽  
Computational Techniques ◽  
Code Verification ◽  
Shell Elements ◽  
Steel Pipes ◽  
Pressure Tests ◽  
Manufacturing Tolerances ◽  
Collapse Behavior

Finite element simulations are nowadays a standard industrial tool for exploring the effect of manufacturing tolerances on the collapse and collapse propagation pressure of tubular goods. Hence, it is of the highest importance that sound computational techniques are used and that the model results are validated using experimental results. Regarding the modeling of steel pipes collapse and post-collapse behavior, in this paper we discuss: applicability of 2D models; shell elements for the 3D models; nonlinearities to include in the models; material modeling; modeling of residual stresses; boundary conditions for simulating different pressure tests; code verification and results validation. Regarding the link between production process and manufacturing tolerances we briefly review some results that we obtained for the case of the UOE process.

scholarly journals Generalized finite element formulation for efficient first-order plastic hinge analysis

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983636
Author(s):  
Dae-Jin Kim ◽  
Hong-Jun Son ◽  
Yousun Yi ◽  
Sung-Gul Hong
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Plastic Hinge ◽  
Computational Cost ◽  
Finite Element Formulation ◽  
Solution Technique ◽  
Element Formulation ◽  
Plastic Hinges ◽  
First Order ◽  
Generalized Finite Element

This article presents generalized finite element formulation for plastic hinge modeling based on lumped plasticity in the classical Euler–Bernoulli beam. In this approach, the plastic hinges are modeled using a special enrichment function, which can describe the weak discontinuity of the solution at the location of the plastic hinge. Furthermore, it is also possible to insert a plastic hinge at an arbitrary location of the element without modifying its connectivity or adding more elements. Instead, the formations of the plastic hinges are achieved by hierarchically adding more degrees of freedom to existing elements. Due to these features, the proposed methodology can efficiently perform the first-order plastic hinge analysis of large-frame structures. A generalized finite element solution technique based on the static condensation scheme is also proposed in order to reduce the computational cost of a series of linear elastic problems, which is in general the most time-consuming portion of the first-order plastic hinge analysis. The effectiveness and accuracy of the proposed method are verified by analyzing several representative numerical examples.

A New Hierarchical Technique for the Multiscale Modeling of Carbon Nanostructures

2005 ◽  
Author(s):  
Arash Mahdavi ◽  
Eric Mockensturm
Keyword(s):  
Finite Element ◽  
Atomic Structure ◽  
Carbon Nanostructures ◽  
Degrees Of Freedom ◽  
Finite Size ◽  
Multiscale Methods ◽  
Atomic Scale ◽  
Modeling Technique ◽  
Element Formulation ◽  
Kinematic Constraints

We present a new hierarchical modeling technique called the Consistent Atomic-scale Finite Element (CAFE´) method [1]. Unlike traditional approaches for linking the atomic structure to its equivalent continuum [2-7], this method directly connects the atomic degrees of freedom to a reduced set of finite element degrees of freedom without passing through an intermediate homogenized continuum. As a result, there is no need to introduce stress and strain measures at the atomic level. This technique partitions atoms to masters and salves and reduces the total number of degrees of freedom by establishing kinematic constraints between them [5-6]. The Tersoff-Brenner interatomic potential [8] is used to calculate the consistent tangent stiffness matrix of the structure. In this finite element formulation, all local and non-local interactions between carbon atoms are taken into account using overlapping finite elements (Figure 1b). In addition, a consistent hierarchical finite element modeling technique is developed for adaptively coarsening and refining the mesh over different parts of the model (Figure 2a, 2b). The stiffness of higher-rank elements is approximated using the stiffness of lower-rank elements and kinematic constraints. This process is consistent with the underlying atomic structure and, by refining the mesh, molecular dynamic results will be recovered. This method is valid across the scales and can be used to concurrently model atomistic and continuum phenomena so, in contrast with most other multiscale methods [4-7], there is no need to introduce artificial boundaries for coupling atomistic and continuum regions. Effect of the length scale of the nanostructure is also included in the model by building the hierarchy of elements from bottom up using a finite size atom cluster as the building block (Figures 2a, 2b). In this method by introducing two independent field variables, the so-called inner displacement is taken into account (Fig. 3b). Applicability of the method is shown with several examples of deformation of carbon nanostructures such as graphene sheet, nanotube, and nanocone, subjected to different loads and boundary conditions.

Shell Element Formulation Based Finite Element Modeling, Analysis and Experimental Validation of Incremental Sheet Forming Process

2015 ◽  
Author(s):  
Govind N. Sahu ◽  
Sumit Saxena ◽  
Prashant K. Jain ◽  
J. J. Roy ◽  
M. K. Samal ◽  
...  
Keyword(s):  
Finite Element ◽  
Thickness Distribution ◽  
Shell Element ◽  
Time Profile ◽  
Experimental Results ◽  
Computational Time ◽  
Element Formulation ◽  
Forming Process ◽  
Element Analysis ◽  
Shell Elements

This paper presents the effect of shell element formulations on the response parameters of incremental sheet metal forming process. In this work, computational time, profile prediction and thickness distribution are investigated by both finite element analysis and experimentally. The experimental results show that the thickness distribution is in good agreement with the results obtained with Belytschko-Tsay (BT) and Improved Flanagan-Belytschko (IFB) shell element formulations. These two shell element formulations do trade-off between computational time and accuracy. For more accurate results, the BT shell element formulation is better and for less computational time with good results, the IFB shell element is preferable. Finally, BT shell element formulation has been chosen for FE Analysis of ISF process in HyperWorks, since the results of thickness distribution and profile prediction is in better agreement with the experimental results as well as the computational time is less among the shell elements.

scholarly journals Dynamics of on-board rotors on finite-length journal bearings subject to multi-axial and multi-frequency excitations: numerical and experimental investigations

2021 ◽  
Vol 22 ◽  
pp. 35
Author(s):  
Yvon Briend ◽  
Eric Chatelet ◽  
Régis Dufour ◽  
Marie-Ange Andrianoely ◽  
Franck Legrand ◽  
...  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Experimental Validation ◽  
Parametric Instability ◽  
Experimental Investigations ◽  
Element Formulation ◽  
Hydrodynamic Bearing ◽  
Mass Unbalance ◽  
Moving Base ◽  
Technology Applications

On-board rotating machinery subject to multi-axial excitations is encountered in a wide variety of high-technology applications. Such excitations combined with mass unbalance forces play a considerable role in their integrity because they can cause parametric instability and rotor–stator interactions. Consequently, predicting the rotordynamics of such machines is crucial to avoid triggering undesirable phenomena or at least limiting their impacts. In this context, the present paper proposes an experimental validation of a numerical model of a rotor-shaft-hydrodynamic bearings system mounted on a moving base. The model is based on a finite element approach with Timoshenko beam elements having six degrees of freedom (DOF) per node to account for the bending, torsion and axial motions. Classical 2D rectangular finite elements are also employed to obtain the pressure field acting inside the hydrodynamic bearing. The finite element formulation is based on a variational inequality approach leading to the Reynolds boundary conditions. The experimental validation of the model is carried out with a rotor test rig, designed, built, instrumented and mounted on a 6-DOF hydraulic shaker. The rotor’s dynamic behavior in bending, torsion and axial motions is assessed with base motions consisting of mono- and multi-axial translations and rotations with harmonic, random and chirp sine profiles. The comparison of the predicted and measured results achieved in terms of shaft orbits, full spectrums, transient history responses and power spectral densities is very satisfactory, permitting the experimental validation of the model proposed.

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.

An Efficient Finite Element Modeling of Composite Stiffened Shells

2014 ◽  
Vol 553 ◽  
pp. 673-678
Author(s):  
Hamid Sheikh ◽  
Liang Huang
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Degrees Of Freedom ◽  
Torsional Rigidity ◽  
Shell Element ◽  
Beam Element ◽  
Shell Elements ◽  
Element Modeling ◽  
Stiffened Shells ◽  
Element Technique

This paper presents an efficient finite element modeling technique for stiffened composite shells having different stiffening arrangements. The laminated shell skin is modeled with a triangular degenerated curved shell element having 3 corner nodes and 3 mid-side nodes. An efficient curved beam element compatible with the shell element is developed for the modeling of stiffeners which may have different lamination schemes. The formulation of the 3 nod degenerated beam element may be considered as one of the major contributions. The deformation of the beam element is completely defined in terms of the degrees of freedom of shell elements and it does not require any additional degrees of freedom. As the usual formulation of degenerated beam elements overestimates their torsional rigidity, a torsion correction factor is introduced for different lamination schemes. Numerical examples are solved by the proposed finite element technique to assess its performance.

Quench Process Modeling and Optimization

2000 ◽  
Author(s):  
Ravi S. Bellur-Ramaswamy ◽  
Nahil A. Sobh ◽  
Robert B. Haber ◽  
Daniel A. Tortorelli
Keyword(s):  
Particle Size ◽  
Finite Element ◽  
Process Parameters ◽  
Degrees Of Freedom ◽  
Programming Algorithm ◽  
Precipitate Size ◽  
Rate Theory ◽  
Element Formulation ◽  
Balancing Energy ◽  
Finite Element Node

Abstract We optimize continuous quench process parameters to produce a desired precipitate distribution in aluminum alloy extrudates. To perform this task, an optimization problem is defined and solved using a standard nonlinear programming algorithm. Ingredients of this algorithm include a cost function, constraint functions and their sensitivities with respect to the process parameters. These functions are dependent on the temperature and precipitate size which are obtained by balancing energy to determine the temperature distribution and by using a reaction-rate theory to determine a discrete precipitate particle size distribution. Both the temperature and the precipitate models are solved via the finite element method. Since we use a discrete particle size model, there are as many as 105 degrees-of-freedom per finite element node. After we compute the temperature and precipitate size distributions, we must also compute their sensitivities. This seemingly intractable computational task is resolved by using an element-by-element discontinuous Galerkin finite element formulation and a direct differentiation sensitivity analysis which allows us to perform all of the computations on a PC.

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