Determination of passive viscoelastic response of the abdominal muscle and related constitutive modeling: Stress-relaxation behavior

Uniaxial relaxation tests were carried out for samples obtained from the abdominal wall. The experimental results clearly demonstrate the anisotropy and nonlinearity of the abdominal tissue. The stress relaxation was higher in the transverse direction (closer to muscle fibers) with an average value of the final stress ratio of 48%, than in the longitudinal direction with around 56% of this ratio for the oblique muscle. These tests, at several stretch levels, presented a different behavior depending on the region where the tissue sample was located. There was no dependence between the stress relaxation ratio and the stretch level for the oblique muscles in their longitudinal or transverse directions (p>0.01). In contrast, for rectus abdominis and linea alba a dependence between the stress relaxation ratio and stretch level was found. Our study revealed an increase in the stress relaxation ratio for the rectus abdominis (p<0.01) and a decrease for the linea alba with higher stretch levels (p<0.01). Overall good predictions ε<0.115 were obtained with the model proposed for the oblique muscle (no dependence on the stretch level) and to reproduce the non-linear viscoelastic response of rectus abdominis and linea alba.