Simulation of Soft Tissue Failure Using the Material Point Method

[+] Author and Article Information
Irina Ionescu

Department of Bioengineering, and Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112

James E. Guilkey

Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112

Martin Berzins, Robert M. Kirby

Scientific Computing and Imaging Institute, School of Computing, University of Utah, Salt Lake City, UT 84112

Jeffrey A. Weiss1

Department of Bioengineering, and Scientific Computing and Imaging Institute, University of Utah, 50 South Central Campus Drive, Room 2480, Salt Lake City, Utah 84112-9202jeff.weiss@utah.edu


Corresponding author.

J Biomech Eng 128(6), 917-924 (Jun 19, 2006) (8 pages) doi:10.1115/1.2372490 History: Received December 21, 2005; Revised June 19, 2006

Understanding the factors that control the extent of tissue damage as a result of material failure in soft tissues may provide means to improve diagnosis and treatment of soft tissue injuries. The objective of this research was to develop and test a computational framework for the study of the failure of anisotropic soft tissues subjected to finite deformation. An anisotropic constitutive model incorporating strain-based failure criteria was implemented in an existing computational solid mechanics software based on the material point method (MPM), a quasi-meshless particle method for simulations in computational mechanics. The constitutive model and the strain-based failure formulations were tested using simulations of simple shear and tensile mechanical tests. The model was then applied to investigate a scenario of a penetrating injury: a low-speed projectile was released through a myocardial material slab. Sensitivity studies were performed to establish the necessary grid resolution and time-step size. Results of the simple shear and tensile test simulations demonstrated the correct implementation of the constitutive model and the influence of both fiber family and matrix failure on predictions of overall tissue failure. The slab penetration simulations produced physically realistic wound tracts, exhibiting diameter increase from entrance to exit. Simulations examining the effect of bullet initial velocity showed that the anisotropy influenced the shape and size of the exit wound more at lower velocities. Furthermore, the size and taper of the wound cavity was smaller for the higher bullet velocity. It was concluded that these effects were due to the amount of momentum transfer. The results demonstrate the feasibility of using MPM and the associated failure model for large-scale numerical simulations of soft tissue failure.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Schematic indicating the two types of material failure represented in the failure model. (a) Matrix failure via shear strain. As the material strains under shear the fibers remain undeformed whereas the matrix is driven to failure, cleaving between fibers. (b) Fiber failure via elongation along the fiber direction. Under tensile strain, the “stiffer” fibers reach their stretch limit before the “softer” matrix.

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Figure 2

Illustration of the steps in the MPM algorithm for particles occupying a single cell of the background grid. (a) A representation of four material points (filled circles), overlaid with the computational grid (solid lines). Arrows represent displacement vectors. (b) The material point state vector (mass, volume, velocity, etc.) is projected to the nodes of the computational grid. (c) The discrete form of the equations of motion is solved on the computational grid, resulting in updated nodal velocities and positions. (d) The updated nodal kinematics are interpolated back to the material points, and their state is updated. (e) In the standard MPM algorithm, the computational grid is reset to its original configuration, and the process is repeated. (f) In the modification algorithm, the grid is not reset, but is allowed to move with the particles, thereby retaining the optimal distribution of particles with respect to the grid.

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Figure 3

Geometries used for simulating mechanical tests. (a) Along-fiber shear, a thin square specimen was deformed to failure with the help of two rigid drivers moving in opposite directions. The collagen fibers were oriented along the shearing direction, resulting in large in-plane shear strain and minimal fiber strain. (b) Tensile test, a tapered tensile test specimen was stretched to failure along the direction of the fiber family. Symmetry boundary conditions were enforced on the half model.

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Figure 4

Schematic of the material symmetry that was used for the projectile penetration simulations of a myocardial slab. The local fiber direction rotated 180 deg through the thickness of the slab.

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Figure 5

Theoretical and MPM predictions for fiber stress versus strain during uniaxial extension. Separate simulations were carried out with the fiber orientation aligned with the direction of the extension and transverse to the direction of extension. Excellent agreement was obtained between the theoretical and MPM predictions using both explicit and implicit time integration.

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Figure 6

Shear strain and failure patterns for simulations of a thin sheet under along-fiber shear, using both explicit and implicit time integration. (a) Maximum shear strain for the model just before initiation of failure. (b) Failure distribution for the model with failure, with explicit time integration. (c) Failure distribution for the model with failure, with implicit time integration. The location of the maximum shear strains in the model without failure features coincides with the location of failure initiation. At the particle level, subsequent deformation after matrix failure is reached results in total failure.

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Figure 7

Fiber strain and failure patterns for simulations of a tensile test using explicit time integration. (a) and (b) Fiber strain for grid reset and no grid reset cases, respectively, immediately before failure. (c) and (d) Failure distributions for the grid reset and no grid reset cases, respectively. Failure initiated at the location of the maximum fiber strain. As the material was fiber-reinforced, once the fibers failed, total material failure followed.

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Figure 8

Time sequence of images for the projectile penetration of a myocardial slab. Bullet velocity was 50m∕s. Colors indicate failure status of material points: blue = no failure, green = matrix failure, yellow = fiber failure, red = total failure.

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Figure 9

Wound profile for the projectile penetration of a myocardial slab. The wound profile shows a central area of complete tissue disruption surrounded by layers of failed particles. The wound tract presents a diameter increase from entrance to exit. Initial bullet velocity was 50m∕s.

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Figure 10

Influence of projectile speed on the exit wound. Figure 4 shows the local fiber direction for the simulation. The appearance of the exit wound shows that the material symmetry had a greater influence at lower projectile speeds than at higher speeds. The failed particles were distributed randomly in the case of the injury at a higher speed (a), whereas in the lower-speed case (b) the failure pattern reflected the underlying fiber orientation.



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