Static and free-vibration analyses of dental prosthesis and atherosclerotic human artery by refined finite element models

Static and modal responses of representative biomechanical structures are investigated in this paper by employing higher-order theories of structures and finite element approximations. Refined models are implemented in the domain of the Carrera unified formulation (CUF), according to which low- to high-order kinematics can be postulated as arbitrary and, eventually, hierarchical expansions of the generalized displacement unknowns. By using CUF along with the principle of virtual work, the governing equations are expressed in terms of fundamental nuclei of finite element arrays. The fundamental nuclei are invariant of the theory approximation order and can be opportunely employed to implement variable kinematics theories of bio-structures. In this work, static and free-vibration analyses of an atherosclerotic plaque of a human artery and a dental prosthesis are discussed. The results from the proposed methodologies highlight a number of advantages of CUF models with respect to already established theories and commercial software tools. Namely, (i) CUF models can represent correctly the higher-order phenomena related to complex stress/strain field distributions and coupled mode shapes; (ii) bio-structures can be modeled in a component-wise sense by only employing the physical boundaries of the problem domain and without making any geometrical simplification. This latter aspect, in particular, can be currently accomplished only by using three-dimensional analysis, which may be computationally unbearable as complex bio-systems are considered.