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Technical Briefs

Automatic Generation of User Material Subroutines for Biomechanical Growth Analysis

[+] Author and Article Information
Jonathan M. Young

Department of Mechanical Engineering, 409 Hopeman Engineering Building, University of Rochester, Rochester, NY 14627jyoung@me.rochester.edu

Jiang Yao

Department of Mechanical Engineering, 407 Hopeman Engineering Building, University of Rochester, Rochester, NY 14627jiyao@me.rochester.edu

Ashok Ramasubramanian

Department of Mechanical Engineering, Steinmetz Hall 207, Union College, Schenectady, NY 12308ramasuba@union.edu

Larry A. Taber

Department of Biomedical Engineering, Washington University, Campus Box 1097, One Brookings Drive, St. Louis, MO 63130-4899lat@wustl.edu

Renato Perucchio

Department of Mechanical Engineering, 415 Hopeman Engineering Building, University of Rochester, Rochester, NY 14627rlp@me.rochester.edu

J Biomech Eng 132(10), 104505 (Sep 28, 2010) (5 pages) doi:10.1115/1.4002375 History: Received April 16, 2010; Revised June 25, 2010; Posted August 16, 2010; Published September 28, 2010; Online September 28, 2010

The analysis of the biomechanics of growth and remodeling in soft tissues requires the formulation of specialized pseudoelastic constitutive relations. The nonlinear finite element analysis package ABAQUS allows the user to implement such specialized material responses through the coding of a user material subroutine called UMAT . However, hand coding UMAT subroutines is a challenge even for simple pseudoelastic materials and requires substantial time to debug and test the code. To resolve this issue, we develop an automatic UMAT code generation procedure for pseudoelastic materials using the symbolic mathematics package MATHEMATICA and extend the UMAT generator to include continuum growth. The performance of the automatically coded UMAT is tested by simulating the stress-stretch response of a material defined by a Fung-orthotropic strain energy function, subject to uniaxial stretching, equibiaxial stretching, and simple shear in ABAQUS . The MATHEMATICA UMAT generator is then extended to include continuum growth by adding a growth subroutine to the automatically generated UMAT . The MATHEMATICA UMAT generator correctly derives the variables required in the UMAT code, quickly providing a ready-to-use UMAT . In turn, the UMAT accurately simulates the pseudoelastic response. In order to test the growth UMAT , we simulate the growth-based bending of a bilayered bar with differing fiber directions in a nongrowing passive layer. The anisotropic passive layer, being topologically tied to the growing isotropic layer, causes the bending bar to twist laterally. The results of simulations demonstrate the validity of the automatically coded UMAT , used in both standardized tests of hyperelastic materials and for a biomechanical growth analysis.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Analytical and numerical results of the hyperelasticity tests, where both the reference (dashed) and deformed (solid) configurations are presented. The stress results are reported at the centroid of the element.

Grahic Jump Location
Figure 2

Model predicted deformed configurations of axial growth in the bilayered bar with anisotropic fibers in the passive domain. The growing layer (dark) extends along its axis, but by being topologically tied to the passive layer (light) the bar curls into a circle. The anisotropic fiber directions are indicated in each test in the reference state. The amount of twist is related to the cosine of the angle between the fiber directions and the axis of the bar. Note that contact was not included in the model. Therefore, in the π/4 and π/2 cases ((c) and (d)), the curling bar mesh is allowed to self-penetrate.

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