Experimental Planar Biaxial Testing

Porcine hind limbs were acquired from a local abattoir on the day of sacrifice for testing. Tissue was cooled and stored at 0°C prior to testing. No live animal handling was performed by any participants in this study. A total of four animals, seven muscles, and n = 16 total samples were used for testing. The biceps femoris muscle was harvested using standard dissection scalpels. Muscles were sliced along the orientation of fibers with a custom tool that provides 10 mm spacing between the dissection top and a high-profile histology blade (Labus and Puttlitz, 2016). Each ∼10 mm thick sample was then cut into a cruciform shape with a custom cruciform press, aligning the muscle fibers with one cruciform arm (Figure 1). Sample thickness was measured with a caliper mounted on a test stand that was zeroed to the stand platform. Thickness values were recorded in five locations on each sample – in the center of the sample and toward each cruciform arm – and averaged. Mean sample thickness was 8.90 mm with a standard error of 0.29 mm across the five measurements.

Planar biaxial materials testing overview, with (A) cruciform geometry, (B) representative planar biaxial sample, where the white arrow denotes the longitudinal direction and the white dashed square denotes approximate DIC region of interest (ROI), and (C) experimental stress-relaxation loading protocol schematic (note that axes are not to scale).

All materials testing was performed on a planar biaxial material testing system with 50 lb (∼220 N) load cells. Samples were gripped with 25 mm pyramid grips with an initial spacing of 30 mm between grips. Samples were subject to ten equibiaxial preconditioning cycles of 10% grip-to-grip strain (3 mm) and back to zero at 0.5 Hz prior to testing (Van Ee et al., 2000). A 0.02 N equibiaxial pre-load was then applied immediately prior to testing. The testing protocol included an equibiaxial ramp of 20% nominal (grip-to-grip) strain (6 mm) at 10%/s followed by a hold until 400 s to allow for tissue stress relaxation. Samples were then subject to equibiaxial constant rate stretch at 0.1%/s nominal (grip-to-grip) strain (0.03 mm/s) until failure. Failure was manually identified post hoc in stress-time curves where significant (>∼10%) decreases in stress were observed.

Digital image correlation software (Correlated Solutions, Inc.) was used to track strain during the constant rate ramp pull in a ∼10 × 10 mm region of interest (ROI) in the center of the sample. A solid in a reference configuration X that undergoes a deformation under an external load is placed into a deformed configuration x, which is described by the deformation gradient F (Eq. 1). For a 2D problem such as a single camera digital image correlation system, F is a 2 × 2 matrix of the deformations relative to orthogonal axes (Eq. 1). From F, 2D muscle ROI stretch λ (Eq. 2) can be calculated for the longitudinal and transverse orientations (Szczesny et al., 2012). Nominal (grip-to-grip) stretch was measured directly from grip displacement. Nominal stress S was determined by dividing load cell force by the product of sample arm length (30 mm) and mean sample thickness. A linearized modulus E=Δ⁢SΔ⁢λ was calculated from the initial and final points of the constant ramp pull data. For comparative purposes between orientations, we used nominal stress and implemented a finite element model to determine ROI Cauchy (true) stress and material properties. All stress-stretch data were averaged either over time (for stress-relaxation data) or over stretch (for constant ramp pull data) for model fitting.