Computational aspects of the numerical modelling of softening, damage and permanent set in soft biological tissues

•A formulation to model the softening on soft biological tissues has been proposed.•Formulation and computational aspects are presented and discussed.•Experimental data of soft tissues has been fitted.•Numerical samples that proof the feasibility of the numerical model are presented.

A constitutive model is proposed for the description of the inelastic effects of biological tissues. The model can reproduce the Mullins effect, preconditioning, rupture and residual strains by the introduction of three weight factors characterizing the structural state of the material. The collagen fibers are crimped in the slack configuration and are unable to sustain load. As a result, a general theoretical and numerical framework for the constitutive modelling of biological soft tissue including inelastic effects is obtained. Finally, a comparison of numerical and experimental data is provided in order to show the reliability and effectiveness of the assumed formulation.