Speaker
Description
Biological tissues are intrinsically viscoelastic and highly anisotropic, owing to the complex spatial distribution of embedded fibres, predominantly collagen. Accurately modeling these time-dependent, directionally biased mechanical responses under large deformations remains a cornerstone of theoretical biomechanics and holds significant diagnostic potential for biomedical applications.
To this end, we propose a theoretical and computational framework for anisotropic finite-strain viscoelasticity. The model relies on the multiplicative decomposition of the deformation gradient combined with an additive partitioning of the strain energy into distinct elastic and over-stress components, while constitutive anisotropy is introduced via a generalized structural tensor. Moreover, the evolution of the viscous strain is governed by a possibly anisotropic flow rule featuring five characteristic times. Remarkably, we show that this flow rule can be cast into a convenient variational form by taking either the contravariant or the covariant pull-back of the spatial evolution law. This structure facilitates computational implementation and avoids the issue of constraining the viscous spin.
Numerical simulations validate the model against benchmark behaviours, successfully reproducing stress relaxation, creep, and hysteresis. Additionally, non-homogeneous simple shear tests reveal a non-monotonic Poynting effect that is highly sensitive to fibre distribution and relative fibre-matrix stiffness. Finally, we discuss the framework's applicability to modeling the viscoelastic mechanics of reproductive tissues.