A transversely isotropic hyperelastic constitutive model of the PDL. Analytical and computational aspects.

This study describes the development of a constitutive law for the modelling of the periodontal ligament (PDL) and its practical implementation into a commercial finite element code. The constitutive equations encompass the essential mechanical features of this biological soft tissue: non-linear behaviour, large deformations, anisotropy, distinct behaviour in tension and compression and the fibrous characteristics. The approach is based on the theory of continuum fibre-reinforced composites at finite strain where a compressible transversely isotropic hyperelastic strain energy function is defined. This strain energy density function is further split into volumetric and deviatoric contributions separating the bulk and shear responses of the material. Explicit expressions of the stress tensors in the material and spatial configurations are first established followed by original expressions of the elasticity tensors in the material and spatial configurations. As a simple application of the constitutive model, two finite element analyses simulating the mechanical behaviour of the PDL are performed. The results highlight the significance of integrating the fibrous architecture of the PDL as this feature is shown to be responsible for the complex strain distribution observed.

Biomechanical properties of oesophagus wall under loading.

In this investigation, firstly, the biomechanical properties of different parts of oesophagus were determined. Oesophagus stress and strain are the greatest in the cervical part for all age groups. The human oesophagus deforms unevenly, depending on the direction of load in relation to the organ's axis, it exhibits anisotropical behaviour. With the age the values of mechanical parameters of the oesophagus wall reduce, in particular beginning from 45 years of age, but the modulus of elasticity increases. Biomechanical properties of the oesophagus depend on the architecture of its structure. By loading the organ in the circumferential direction, microfibrilae rupture and deformation of the muscular fibres occurs. With increase of load, collagenous fibres straighten and microruptures in collagenous fibrilae occur. With stretching of oesophagus longitudinally, collagenous fibres partially preserve their wavy and helical configuration. Therefore, higher resistance of the oesophageal wall occurs in the longitudinal direction.