Uniaxial, biaxial, and planar tension properties of deep fascia and a constitutive model to simultaneously reproduce these strain states

This study aims to provide an in-depth analysis of the mechanical behavior of deep fascia through a comprehensive multidimensional characterization, including uniaxial, biaxial, and planar tension tests. To determine material parameters via test fitting, both a newly developed coupled exponential energy function and a previously proposed uncoupled exponential model-both considering two perpendicular fiber directions-are evaluated. For the uniaxial response, the mean stress measured was 3.96 MPa in the longitudinal direction and 0.6 MPa in the transverse direction at a stretch <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo> <mml:mrow><mml:mi>λ</mml:mi></mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:math> of 1.055. In planar tension tests, stress values of 0.43 MPa and 0.11 MPa were recorded for the longitudinal and transverse directions, respectively, at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>λ</mml:mi></mml:mrow> </mml:math> = 1.72. Under equibiaxial loading conditions, the mean stresses were 3.16 MPa and 1.2 MPa for the longitudinal and transverse directions when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>λ</mml:mi></mml:mrow> </mml:math> reached 1.037, respectively. The fitting results indicate that while the uncoupled exponential model effectively captures the uniaxial and equibiaxial experimental data, it fails to predict other mechanical responses accurately. In contrast, the coupled exponential strain energy function (SEF) demonstrates robust performance in both fitting and prediction. Additionally, an analysis was conducted to assess how the number and combination of tests influence the determination of material parameters. Findings suggest that a single biaxial test incorporating three loading ratios is sufficient to accurately capture and predict uniaxial, planar tension, and other biaxial strain states.