Living biological tissues are complex structures that have the capacity of evolving
in response to external loads and environmental stimuli. The adequate modelling
of soft biological tissue behaviour is a key issue in successfully reproducing
biomechanical problems through computational analysis.
This study presents a general constitutive formulation capable of representing
the behaviour of these tissues through finite element simulation. It is based on
phenomenological models that, used in combination with the generalized mixing
theory, can numerically reproduce a wide range of material behaviours.
First, the passive behaviour of tissues is characterized by means of hyperelastic
and finite-strain damage models. A generalized damage model is proposed,
providing a flexible and versatile formulation that can reproduce a wide range of
tissue behaviour. It can be particularized to any hyperelastic model and requires
identifying only two material parameters. Then, the use of these constitutive
models with generalized mixing theory in a nite strain framework is described
and tools to account for the anisotropic behaviour of tissues are put forth.
The active behaviour of tissues is characterized through constitutive models
capable of reproducing the growth and remodelling phenomena. These are built
on the hyperelastic and damage formulations described above and, thus, represent
the active extension of the passive tissue behaviour. A growth model considering
biological availability is used and extended to include directional growth. In addition,
a novel constitutive model for homeostatic-driven turnover remodelling is
presented and discussed. This model captures the stiffness recovery that occurs
in healing tissues, understood as a recovery or reversal of damage in the tissue,
which is driven by both mechanical and biochemical stimuli.
Finally, the issue of correctly identifying the material parameters for computational
modelling is addressed. An inverse method using optimization techniques
is developed to facilitate the identification of these parameters.
Abstract
Living biological tissues are complex structures that have the capacity of evolving
in response to external loads and environmental stimuli. The adequate modelling
of soft biological tissue behaviour is a key issue in successfully reproducing
biomechanical problems [...]