Three-Dimensional Strain Fields in a Uniform Osteotomy Gap

Stable internal fixation usually results in a unique histological healing pattern which involves direct cortical reconstruction and an absence of periosteal bridging callus. While it has been suggested that longitudinal interfragmentary strain levels control this healing pattern, the complex, multiaxial strain fields in the interfragmentary region are not well understood. Based on an in-vivo study of gap healing in the sheep tibia by Mansmann et al. [13], we used several finite element models of simplified geometry to: 1) explore modeling assumptions on material linearity and deformation kinematics, and 2) examine the strain distribution in a healing fracture gap subjected to known levels of interfragmentary strain. We found that a general nonlinear material, nonlinear geometric analysis is necessary to model an osteotomy gap subjected to a maximum longitudinal strain of 100 percent. The large displacement, large strain conditions which were used in the in-vivo study result in complex, multiaxial strain fields in the gap. Restricting the maximum longitudinal strain to 10 percent allows use of a linear goemetric formulation without compromising the numerical results. At this reduced strain level a linear material model can be used to examine the extent of material yielding within a homogeneous osteotomy gap. Severe local strain variations occurred both through the thickness of the gap and radially from the endosteal to periosteal gap surfaces. The bone/gap interface represented a critical plane of high distortional and volumetric change and principal strain magnitudes exceeded the maximum longitudinal strains.

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Delamination in the scoring and folding of paperboard

TAPPI Journal ◽

10.32964/tj11.1.61 ◽

2012 ◽

Vol 11 (1) ◽

pp. 61-66 ◽

Cited By ~ 1

Author(s):

DOEUNG D. CHOI ◽

SERGIY A. LAVRYKOV ◽

BANDARU V. RAMARAO

Keyword(s):

Finite Element ◽

Plane Deformation ◽

Strain Analysis ◽

Local Strain ◽

Uniaxial Stress ◽

Material Model ◽

Element Model ◽

Plastic Behavior ◽

Stress Strain ◽

Strain Fields

Delamination between layers occurs during the creasing and subsequent folding of paperboard. Delamination is necessary to provide some stiffness properties, but excessive or uncontrolled delamination can weaken the fold, and therefore needs to be controlled. An understanding of the mechanics of delamination is predicated upon the availability of reliable and properly calibrated simulation tools to predict experimental observations. This paper describes a finite element simulation of paper mechanics applied to the scoring and folding of multi-ply carton board. Our goal was to provide an understanding of the mechanics of these operations and the proper models of elastic and plastic behavior of the material that enable us to simulate the deformation and delamination behavior. Our material model accounted for plasticity and sheet anisotropy in the in-plane and z-direction (ZD) dimensions. We used different ZD stress-strain curves during loading and unloading. Material parameters for in-plane deformation were obtained by fitting uniaxial stress-strain data to Ramberg-Osgood plasticity models and the ZD deformation was modeled using a modified power law. Two-dimensional strain fields resulting from loading board typical of a scoring operation were calculated. The strain field was symmetric in the initial stages, but increasing deformation led to asymmetry and heterogeneity. These regions were precursors to delamination and failure. Delamination of the layers occurred in regions of significant shear strain and resulted primarily from the development of large plastic strains. The model predictions were confirmed by experimental observation of the local strain fields using visual microscopy and linear image strain analysis. The finite element model predicted sheet delamination matching the patterns and effects that were observed in experiments.

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