Understanding FEBio Modules
Prepared for FEBio Studio 2
Overview
FEBio can solve many different types of physics problems, including structural mechanics, biphasic, fluid mechanics, etc. Features that belong to a particular type of physics are collected in what are called FEBio modules (also referred to as physics modules). Each module defines what type of analysis, materials, boundary conditions, etc., can be applied to a model. As described below, one of the first things the user has to do when starting a new model in FEBio Studio, is to select the FEBio module.
Creating a New Model
After launching FEBio Studio, the user is presented with a Welcome screen. From this welcome screen, a new model can be started by clicking the New Model link, or from the File\New Model menu. The user is then presented with the “New Model” dialog box, which provides a list of the physics modules that are available in FEBio (Figure 1). Selecting one of these modules for your new model focuses the menu options that are available in FEBio Studio to those that are pertinent to that particular analysis type. For instance, by selecting “Biphasic” as the analysis type, the Physics->Add Nodal BC… menu options will include “Prescribed fluid pressure”, but this option will not be available if the analysis type is set to Structural Mechanics.
The following sections help to explain the capabilities of each module and assists the user in choosing the correct one for their application. If the wrong one was chosen, or a user wants to change the module of an already created model, the module can be changed, as described towards the end of this document.
Overview of FEBio Modules
Structural Mechanics
The structural mechanics solver can be used to analyze deformable solid materials and rigid bodies, under quasi-static or dynamic conditions, and under finite deformations and finite rotations. Deformable solid materials are generically categorized as elastic or uncoupled elastic, to represent compressible and nearly-incompressible materials, respectively. Despite these generic names, some of the materials available in the structural mechanics solver exhibit inelastic behavior, such as viscoelastic materials, materials undergoing damage or plasticity, and materials undergoing fatigue failure. Rigid materials may be interfaced with deformable solids using rigid interfaces. Rigid bodies may also be connected to each other by kinematic pairs (such as revolute, prismatic, or spherical joints), or springs and dampers, generically called rigid connectors.
Contact interfaces of various types are available to examine sliding contact with or without friction, as well as tied contact between material domains with dissimilar finite element meshes.
Because of FEBio’s focus on biomechanics, a wide range of fibrous materials are available to model biological tissues, including discrete fiber bundles and continuous fiber distributions, where fibers may only sustain tension. FEBio provides users with the flexibility to combine any number of materials (such as discrete fiber bundles, ground matrix, swelling and growth materials) into solid mixtures.
The structural mechanics module solves for the nodal displacements in deformable elements, and for the position and rotation of rigid bodies. A finite element mesh is not necessarily required to model rigid bodies.
Limitations
The structural mechanics solver only analyzes problems under finite deformations and finite rotations. This means that the mesh is updated at every iteration and every time point to account for the current state of deformation. Even if the user adjusts the solver settings to converge in a single iteration at each time step, the mesh geometry gets updated. Therefore, the structural mechanics module cannot reproduce infinitesimal strain analyses exactly.
As of FEBio 4.7, the sliding contact interfaces do not enforce energy conservation under dynamic analyses. This may be a minor limitation if the contacting materials naturally dissipate a significant amount of energy (such as viscoelastic solids). However, dropping an elastic ball on a rigid ground may not produce a bouncing response with consistent height recovery over consecutive bounces.
Heat Transfer
The heat transfer solver may be used to examine transient or steady heat conduction in a non-deforming material. The heat transfer solver is available as a plugin.
Biphasic
The biphasic solver can analyze deformable porous-permeable (poroelastic) materials using the framework of mixture theory to model such materials as mixtures of a porous deformable solid and a fluid. This solver accommodates quasi-static as well as steady-state analyses. A biphasic material is constructed by combining any of the deformable solid materials available in the structural mechanics module with a hydraulic permeability material that describes the resistance to interstitial fluid flow within the porous solid matrix.
Each of the constituents of a biphasic material is modeled as an intrinsically incompressible material. Thus, a biphasic material is just like a sponge; when subjected to pure hydrostatic pressure, neither of the constituents can deform. However, just as squeezing a wet sponge exudes fluid, the volume of the biphasic mixture can change when interstitial fluid enters or leaves the pore space of the solid matrix. The pore structure is implicit in a biphasic model; the material’s porosity is specified as a user-defined parameter and its anisotropy can be modeled using a suitable hydraulic permeability constitutive relation. Various hydraulic permeability models exist, some of which allow the user to account for changes in permeability in response to the deformation of the solid matrix.
The most common choice for the solid constituent of a biphasic material is an elastic solid, whose compressibility represents that of the pore space. Using an uncoupled elastic solid in a biphasic mixture implies that the user does not wish to allow significant changes to the pore volume under various loading conditions. In either case, the biphasic material remains permeable to the interstitial fluid, as interstitial fluid flow may be driven by an externally applied pressure gradient. But ‘squeezing’ a biphasic material with an uncoupled elastic solid would produce negligible fluid exudation.
Sliding and tied contact interfaces are also available for biphasic materials. These contact interfaces automatically satisfy continuity of the contact traction, normal fluid flux, and interstitial fluid pressure within the contact region. The sliding biphasic interface accommodates frictionless or frictional contact.
In addition to biphasic materials, the biphasic solver can accommodate the full range of deformable solid materials and rigid bodies available in the structural mechanics module.
The biphasic module solves for nodal displacements and fluid pressure in deformable elements, and for the position and rotation of rigid bodies.
Limitations
The limitations listed for the structural mechanics module also apply to the biphasic module. In addition, the biphasic solver does not accommodate dynamic analyses. A rigid material may not be selected as the porous solid constituent of a biphasic material.
Biphasic-Solute
The biphasic-solute solver was introduced as a precursor to, and testbed for the multiphasic solver. It introduces a single neutral solute into a biphasic mixture to model solute transport in porous media. See the next section for a more detailed description of this type of solver.
Multiphasic
The multiphasic solver analyzes materials consisting of mixtures of a solid constituent, a solvent, and any number of neutral or electrically charged solutes, under quasi-static or steady-state conditions. It represents a generalization of the biphasic and biphasic-solute solvers. It subsumes all the materials available in the structural mechanics, biphasic, and biphasic-solute modules.
All constituents of a multiphasic mixture are assumed to be intrinsically incompressible. The solvent and solutes form a solution (a fluid mixture). The solid matrix may itself consist of a mixture of solid constituents (with associated stiffness) and solid-bound molecules (with associated electrical charge and molar volume, but no stiffness). The multiphasic solver accommodates reactions among the solutes and solid-bound molecules, including chemical reactions and growth and remodeling reactions.
In multiphasic materials it is assumed that solutes occupy negligible volume and molar fractions. Solutes encounter resistance as they flow within the solvent, due to frictional momentum exchanges with solvent molecules; they may similarly encounter resistance as they flow within the porous solid matrix, due to frictional interactions with that matrix. However, due to their low volume and molar fractions, it is assumed that solutes don’t interact with each other.
A multiphasic material requires the specification of a solid material representing the porous-permeable deformable matrix; a hydraulic permeability material representing the frictional drag between the solvent and the porous solid matrix; a solute material that specifies the frictional interactions of each solute with the solvent and solid matrix, as well as the fraction of pore volume accessible to that solute (called the solubility); and an osmotic coefficient to account for the contribution of solutes to the osmotic pressure of the fluid solution.
A diffusivity material requires the specification of a scalar free diffusivity, to model the frictional interactions of the solute with the solvent, and a diffusivity tensor to represent the combined frictional interactions of the solute with the solvent and porous solid matrix. Anisotropic and deformation-dependent constitutive relations are available for the diffusivity tensor.
Osmotic effects may be neglected by setting the value of the osmotic coefficient to zero. Frictional interactions between the solute and solid matrix may be neglected by setting the diffusivity tensor to the value of the free diffusivity. Steric volume exclusion of the solute from a fraction of the pore space may be neglected by setting the solubility to unity.
The multiphasic solver assumes that electroneutrality of the mixture is enforced at all times, implying that the net electric charge of the mixture is always zero. This electroneutrality constraint is associated with an electric potential, in the same manner that the intrinsic incompressibility constraint of all the mixture constituents is associated with a fluid pressure. A mechano-chemical potential is associated with the solvent, which accounts for the contributions of its hydraulic and osmotic pressures. This mechano-chemical potential is converted into an effective fluid pressure for the purpose of the finite element analysis. An electro-chemical potential is associated with each solute, to account for its physico-chemical activity in the fluid solution (related to its concentration) and the electrical part of the Lorentz force acting on its charge. This electro-chemical potential is converted into an effective concentration for the purpose of the finite element analysis.
Sliding and tied contact interfaces are also available for multiphasic materials. These contact interfaces automatically satisfy continuity of the contact traction, normal fluid flux, normal solute flux, effective fluid pressure and effective solute concentrations within the contact region. The sliding multiphasic interface currently accommodates frictionless contact, although a frictional multiphasic contact algorithm will be released soon.
The multiphasic module solves for nodal displacements, effective fluid pressure and effective solute concentrations in deformable elements, and for the position and rotation of rigid bodies.
Limitations
The limitations listed for the biphasic module also apply to the multiphasic module module. In addition, the multiphasic solver does not accommodate body forces. The referential mass density of solid-bound molecules is not included in the list of degrees of freedom in a multiphasic analysis. Their solution is obtained once the iterative solution for solid displacement, fluid pressure and solute concentrations have converged at a given time point: The referential mass density of SBMs is updated at integration point at the end of each time step. This approach is computationally more efficient, as it reduces the number of equations to solve in an analysis. However, in some cases the resulting solution for the SBM mass densities may oscillate numerically or fail to reach a constant steady-state value when such a behavior might be expected. In such cases, users may model SBMs as solutes with zero diffusivity, in which case they are treated as nodal degrees of freedom.
Fluid Mechanics
The fluid mechanics (a.k.a. computational fluid dynamics or CFD) solver can be used to analyze fluid flow in non-deformable fluid domains, under dynamic and steady-state conditions. It accommodates Newtonian and non-Newtonian viscous fluids. It models fluids as compressible materials undergoing an isothermal process. The compressibility of the fluid is determined by the specification of its bulk modulus, which represents a physical property of the fluid. A realistic value of the bulk modulus of liquids can produce a nearly-incompressible response.
The fluid solver includes a number of specialized boundary conditions that help stabilize the fluid analysis over truncated fluid domains, such as back flow and tangential stabilization at outflow boundaries. It also includes lumped-parameter outflow conditions, such as fluid flow resistance (R) or RCR circuits (C=capacitance) to simulate Windkessel-type outflow conditions.
The fluid solver primarily accommodates laminar flow conditions, including vortex shedding. Turbulent flow may be modeled using direct numerical simulation (DNS), which becomes computationally expensive.
The fluid module solves for nodal fluid velocities and fluid dilatation.
Fluid-FSI Mechanics
The fluid-FSI solver combines the CFD and structural mechanics solvers. The fluid domain may deform as fluid flows within it. The fluid domain may also interact with solid structures that surround it or are immersed in it. FEBio’s fluid-FSI solver uses an arbitrary Lagrangian-Eulerian (ALE) formulation to accommodate the deformation of the fluid mesh.
The solid domains of an FSI analysis may be modeled using any elastic or uncoupled elastic solid material, as well as rigid bodies. All the contact interfaces of the structural mechanics solver remain available in the fluid-FSI solver, though they only work at the interfaces between solid materials. All of the specialized boundary conditions of the fluid solver remain available in the fluid-FSI solver.
The fluid-FSI module solves for nodal fluid velocities, fluid dilatation, and solid displacements in deformable domains, as well as rigid body positions and rotations.
Additionally, the fluid-FSI module incorporates biphasic-FSI materials, which consist of a deformable porous solid matrix infused with a viscous fluid. As for all fluid analysis modules, users may specify the type of viscous fluid (e.g., Newtonian, Carreau, etc.). In addition, they may specify the hydraulic permeability of the porous solid. Setting the hydraulic permeability exactly to zero is equivalent to turning off the flow resistance due to frictional interactions between the fluid and porous solid matrix (i.e., infinitely high permeability is simulated in FEBio by setting the permeability to zero exactly). The hydraulic permeability of a biphasic-FSI material may be titrated (e.g., via a load curve) to turn the flow on and off in a particular domain.
Fluid-Solutes
The fluid-solutes module makes it possible to model solute transport in a viscous fluid. For example, it may be used to examine the transport of solutes in blood flow. The solutes behave in the same manner as in multiphasic analyses (they may be electrically charged or neutral, they may undergo reactive processes, and they are assumed to occupy a negligible volume fraction). The fluid-solutes solver accommodates diffusion, convection, chemical reactions, electrical charge effects, and external body forces. It can accommodate high-Peclet flow conditions.
Reaction-Diffusion and Reaction-Diffusion-Convection
The reaction-diffusion and reaction-diffusion-convection solvers are plugins that implements non-linear reaction-diffusion-convection equations. They allow users to model chemical reactions in a non-deformable mixture framework. The chemical species are considered solutes that diffuse in a solvent but can also be bound to the solid phase of the mixture. This plugin replicates some functionality of the multiphasic module, but since it assumes the matrix does not deform, many calculations can be optimized for improved performance. The plugin can also be used to solve traditional chemical reactions without the mixture framework.
Changing the Physics Module
If the user started the model with an incorrect module selected, or if the user wants to change the module (e.g. modifying a structural mechanics model by adding biphasic components), this can be done from the menu Physics\Edit Physics Modules. This will open the Physics Modules dialog box, where users can select the correct module (Figure 2).
The dependencies, displayed near the bottom of the dialog box, lists the additional modules that will be loaded for a particular FEBio module. For instance, for a biphasic analysis, the solid (i.e. structural mechanics) module will be loaded alongside with the biphasic module.