Development of a Nonlinear Finite Element Code for Computational Biomechanics and Biophysics

Despite the progress that hase tools that were not specifically designed to target this particular area of application. Software designed specific been made since the inception of the finite element method, the field of biomechanics has generally relied on softwarally for the field of computational biomechanics does not appear to exist. To overcome this limitation, FEBio was developed, an acronym for “Finite Elements for Biomechanics”, which provided an open-source framework for developing finite element software that is tailored to the specific needs of the biomechanics and biophysics communities. The proposed work added an extendible framework to FEBio that greatly facilitates the implementation of novel features and provides an ideal platform for exploring novel computational approaches. This framework supports plugins, which simplify the process of adding new features even more since plugins can be developed independently from the main source code. Using this new framework, this work extended FEBio in two important areas of interest in biomechanics. First, as tetrahedral elements continue to be the preferred modeling primitive for representing complex geometries, several tetrahedral formulations were investigated in terms of their robustness and accuracy for solving problems in computational biomechanics. The focus was on the performance of quadratic tetrahedral formulations in large deformation contact analyses, as this is an important area of application in biomechanics. Second, the application of prestrain to computational models has been recognized as an important component in simulations of biological tissues in order to accurately predict the mechanical response. As this remains challenging to do in existing software packages, a general computational framework for applying prestrain was incorporated in the FEBio software. The work demonstrated via several examples how plugins greatly simplify the development of novel features. In addition, it showed that the quadratic tetrahedral formulations studied in this work are viable alternatives for contact analyses. Finally, it demonstrated the newly developed prestrain plugin and showed how it can be used in various applications of prestrain.

Year	Entry
2007	Ateshian GA, Ellis BJ, Weiss JA. Equivalence between short-time biphasic and incompressible elastic material responses. J Biomech Eng. June 2007;129(3):405-412.
2007	Anderson AE, Ellis BJ, Weiss JA. Verification, validation and sensitivity studies in computational biomechanics. Comput Methods Biomech Biomed Eng. June 2007;10(3):171-184.
2006	Erdemir A, Viveiros ML, Ulbrecht JS, Cavanagh PR. An inverse finite-element model of heel-pad indentation. J Biomech. 2006;39(7):1279-1286.
2009	Ateshian GA, Rajan V, Chahine NO, Canal CE, Hung CT. Modeling the matrix of articular cartilage using a continuous fiber angular distribution predicts many observed phenomena. J Biomech Eng. June 2009;131(6):061003.
2001	Bergmann G, Deuretzbacher G, Heller M, Graichen F, Rohlmann A, Strauss J, Duda GN. Hip contact forces and gait patterns from routine activities. J Biomech. July 2001;34(7):859-871.
2005	Anderson AE, Peters CL, Tuttle BD, Weiss JA. Subject-specific finite element model of the pelvis: development, validation and sensitivity studies. J Biomech Eng. June 2005;127(3):365-373.
2005	Blemker SS, Delp SL. Three-dimensional representation of complex muscle architectures and geometries. Ann Biomed Eng. May 2005;33(5):661-673.
1991	Wayne JS, Woo SL-Y, Kwan MK. Application of the u-p finite element method to the study of articular cartilage. J Biomech Eng. November 1991;113(4):397-403.
1992	Spilker RL, Donzelli PS, Mow VC. A transversely isotropic biphasic finite element model of the meniscus. J Biomech. September 1992;25(9):1027-1045.
2003	Crawford RP, Rosenberg WS, Keaveny TM. Quantitative computed tomography-based finite element models of the human lumbar vertebral body: effect of element size on stiffness, damage, and fracture strength predictions. J Biomech Eng. August 2003;125(4):434-438.
1997	Ateshian GA, Warden W, Kim JJ, Grelsamer RP, Mow VC. Finite deformation biphasic material properties of bovine articular cartilage from confined compression experiments. J Biomech. November–December 1997;30:1157.
1986	Holmes MH. Finite deformation of soft tissue: analysis of a mixture model in uni-axial compression. J Biomech Eng. November 1986;108(4):372-381.
2008	Anderson AE, Ellis BJ, Maas SA, Peters CL, Weiss JA. Validation of finite element predictions of cartilage contact pressure in the human hip joint. J Biomech Eng. October 2008;130(5):051008.
1974	Belytschko T, Kulak RF, Schultz AB, Galante JO. Finite element stress analysis of an intervertebral disc. J Biomech. May 1974;7(3):277-285.
1984	Armstrong CG, Lai WM, Mow VC. An analysis of the unconfined compression of articular cartilage. J Biomech Eng. May 1984;106(2):165-173.
1993	Laible JP, Pflaster DS, Krag MH, Simon BR, Haugh LD. A poroelastic-swelling finite element model with application to the intervertebral disc. Spine. April 1993;18(5):659-670.
2012	Maas SA, Ellis BJ, Ateshian GA, Weiss JA. FEBio: finite elements for biomechanics. J Biomech Eng. January 2012;134(1):011005.
1998	Puso MA, Weiss JA. Finite element implementation of anisotropic quasi-linear viscoelasticity using a discrete spectrum approximation. J Biomech Eng. February 1998;120(1):62-70.
1980	Mow VC, Kuei SC, Lai WM, Armstrong CG. Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiments. J Biomech Eng. February 1980;102(1):73-84.
1992	Cifuentes AO, Kalbag A. A performance study of tetrahedral and hexahedral elements in 3-D finite element structural analysis. Finite Elem Anal Des. 1992;12(3-4):313-318.
1991	Suh J-K, Spilker RL, Holmes MH. A penalty finite element analysis for nonlinear mechanics of biphasic hydrated soft tissue under large deformation. Int J Num Meth Eng. November 1991;32(7):1411-1439.
2005	Weiss JA, Gardiner JC, Ellis BJ, Lujan TJ, Phatak NS. Three-dimensional finite element modeling of ligaments: technical aspects. Med Eng Phys. December 2005;27(10):845-861.
2003	Park S, Krishnan R, Nicoll SB, Ateshian GA. Cartilage interstitial fluid load support in unconfined compression. J Biomech. December 2003;36(12):1785-1796.
2001	Gardiner JC, Weiss JA, Rosenberg TD. Strain in the human medial collateral ligament during valgus loading of the knee. Clin Orthop Relat Res. October 2001;391:266-274.
2003	Gardiner JC, Weiss JA. Subject-specific finite element analysis of the human medial collateral ligament during valgus knee loading. J Orthop Res. 2003;21(6):1098-1106.
2005	Lujan TJ, Lake SP, Plaizier TA, Ellis BJ, Weiss JA. Simultaneous measurement of three-dimensional joint kinematics and ligament strains with optical methods. J Biomech Eng. February 2005;127(1):193-197.
2011	Tadepalli SC, Erdemir A, Cavanagh PR. Comparison of hexahedral and tetrahedral elements in finite element analysis of the foot and footwear. J Biomech. August 11, 2011;44(12):2337-2343.
1996	Weiss JA, Maker BN, Govindjee S. Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput Meth Appl Mech Eng. August 15, 1996;135(1-2):107-128.
1987	Oomens CWJ, van Campen DH, Grootenboer HJ. A mixture approach to the mechanics of skin. J Biomech. 1987;20(9):877-885.

Year

Entry

2007

Ateshian GA, Ellis BJ, Weiss JA. Equivalence between short-time biphasic and incompressible elastic material responses. J Biomech Eng. June 2007;129(3):405-412.

2007

Anderson AE, Ellis BJ, Weiss JA. Verification, validation and sensitivity studies in computational biomechanics. Comput Methods Biomech Biomed Eng. June 2007;10(3):171-184.

2006

Erdemir A, Viveiros ML, Ulbrecht JS, Cavanagh PR. An inverse finite-element model of heel-pad indentation. J Biomech. 2006;39(7):1279-1286.

2009

Ateshian GA, Rajan V, Chahine NO, Canal CE, Hung CT. Modeling the matrix of articular cartilage using a continuous fiber angular distribution predicts many observed phenomena. J Biomech Eng. June 2009;131(6):061003.

2001

Bergmann G, Deuretzbacher G, Heller M, Graichen F, Rohlmann A, Strauss J, Duda GN. Hip contact forces and gait patterns from routine activities. J Biomech. July 2001;34(7):859-871.