In biomechanics, reliable modeling and quantification of material parameters and the study of constitutive models and computational tools concerning experimental observations of living tissue are a rapidly expanding field of research. The main reason for this interest is the ever-growing number of real-world clinical applications such as cardiovascular, osteoarticular, reproductive, osteoarticular, and regenerative biomechanics. The research objectives include understanding the cell biomechanics and mechanotransduction and novel methods for testing them, and studying a relationship between continuum mechanics and the structure and ultrastructure of tissue. These applications suggest developing efficient computational tools and exploring inverse problems formulations. We emphasize that an adequate treatment of inverse problems emerging in the fields as mentioned above requires optimization of nonsmooth, even nonconvex functions in general spaces. Such optimization problem, after discretization, leads to a massive number of unknown parameters. Furthermore, the constraint equations include elliptic, parabolic, and hyperbolic PDEs.

In summary, the capability of biomathematical models to realistically predict the various behavioral patterns observed in soft tissue is a long-standing challenging problem, from both the theoretical and the experimental standpoint. To advance towards this quest, we call for contributions to the proposed special issue.

Potential topics include but are not limited to the following:

• Soft tissue biomechanical models
• Applied, computational, or theoretical tissue mechanics continuum field theory
• Hyperelastic and viscoelastic quasi-incompressible transversely isotropic constitutive model formulation and identification
• Inverse problems or biomechanical parameter identification problems