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he adult spinal column is made up of 26 bones, called vertebrae: 7 cervical in the neck, 12 thoracic in the rib area, 5 lumbar in the lower back, a sacrum and a coccyx. Located between adjacent vertebrae are intervertebral discs. The human intervertebral disc acts as the body’s shock absorber to properly diffuse the stresses that the spine encounters. It is made up of the inner, gel-like nucleus pulposus and the outer annulus fibrosus. Fluid flows through the disc in a diurnal cycle At the beginning of each day, the disc is fully hydrated, but as the day progresses, fluid is forced to flow out of the disc; this flow helps to carry nutrients into and waste out of the disc .
The exploration of biomechanical properties of living tissues is fundamental to the analysis of structural behaviour of the musculoskeletal system. It is known that mechanical properties of living tissues are time dependent. Creep, relaxation, constant strain rate loading, and cyclic loading represent the various physiological loading conditions that the human body confronts. For example, higher strain rates of loading can be used for simulating vehicular accidents or trauma, medium strain rates of loading for daily activity, creep for the prolonged static posture, and cyclic loading for work in vibrating environments, i.
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Fluid-saturated porous solids, e.g., polymer foams, metal foams, sponges or biological tissues, consist of a porous solid skeleton matrix ﬁlled with a pore-ﬂuid. Based on the Theory of Porous Media (TPM), these types of materials could be described by biphasic models. The Theory of Porous Media is a macroscopic theory of immiscible and superimposed continua with internal interactions deﬁned by the classical theory of mixtures combined with the concept of volume fractions. Thus, the properties of the constituents are averaged over a representative volume element occupied by the whole mixture. Therefore, in the resulting homogenized or smeared model, material points of each constituent exist at each geometric point. The volume fractions are introduced as scalar structural variables that describe the local composition of the mixture . The reader who was interested in a broad review of the fundamentals of this theory was referred to the work of Bowen [4, 5], de Boer and Ehlers , or Ehlers [7–9]. In the framework of the TPM approach, the material behaviour of the porous solid skeleton ranges from elastic [10, 11], viscoelastic , Elasto-plastic [13,14] to Elasto-viscoplastic .
The present article proceeds from two basic assumptions, namely material incompressibility of both constituents (skeleton material and pore-ﬂuid) and geometrically linear solid deformations, where the effective skeleton stress is determined by a linear viscoelasticity law based on a generalized rheological spring-dashpot model. Fluid viscosity is taken into account by the drag force, where the permeability is deformation dependent, governed by the actual porosity of the solid skeleton. Moreover, thermal effects as well as mass exchanges between the two constituents are excluded. The arising pure mechanical, linear viscoelastic two-phase model was capable of describing the material response of hydrated soft tissues under mechanical loading, where the biphasic formulation promotes the understanding of the material behaviour within.
To give an example, the behaviour of intervertebraldisc and articular cartilage as a biphasic material consisting of an organic solid matrix (collagen and proteoglycans) and an interstitial ﬂuid (water and electrolytes) is described. In this context, the assumption of material incompressibility is valid under physiological levels of pressure .Like many other biological tissues, intervertebraldisc exhibits a signiﬁcant viscoelastic behavior because of the ﬂow-dependent ﬂuid–solid interaction and the ﬂow-independent viscoelastic skeleton properties .Therefore the objective of this thesis research is to develop poroviscoelastic, finite deformation, dynamic finite element model.