Numerical investigation of the effective mechanical properties and local stress distributions of TPMS-based and strut-based lattices for biomedical applications.

Porous structures, including those with lattice geometries, have been shown to mimic the mechanical properties of the human bone. Apart from the widely known strut-based lattices, the Triply Periodic Minimal Surfaces (TPMS) concept has been introduced recently to create surface-based lattices and to tailor their mechanical behaviors. In this study, the numerical investigation of the effective elastic properties, the anisotropic behavior, and the local stress distributions of a broad range of topologies provide us with a complete numerical tool to assist bone implant design. The comparison database of the lattices includes TPMS-based lattices, both sheet, and skeletal, as well as strut-based lattices. The lattices are subjected to periodic boundary conditions and also, a homogenization method is deployed to simulate the response of the lattice unit cells determining their apparent equivalent stiffness. A correlation among the lattice topologies, their effective mechanical properties, and the local Von Mises stress concentrations in them is observed. The stress distribution of various topologies with the same elastic modulus is examined to combine all the investigations. Finally, a large variety of numerical results are presented to allow the comparison of the lattice structures and the selection of the optimal configuration that mimics the elastic properties of the bone.

Verification of Selected Failure Criteria for Adhesive Bonded Elements with Different Stiffness through the Use of Methacrylic Adhesive.

This study presents the testing results of methacrylic adhesive single-lap joints made from elements with different stiffness and of the adhesive itself, using cast specimens. Methods for the preparation and testing of material specimens of the adhesive joints have been presented. Moreover, an attempt was undertaken to determine the strength criterion and find out which of the presented calculation methods enables the most precise assessment of strength in the tested group of single-lap joints, that differ in terms of the adhered stiffness and thickness. For this purpose, C45 steel and 5754 aluminium flat bars were bonded. Stress distributions were determined for failure forces obtained in the experiment by means of three basic analytic and numerical methods. Stress and strain states were compared, indicating the highest consistency for the value of normal peel stresses acting in the direction perpendicular to the direction of the joint tension. Reduced stresses provided by the analyses reached values higher than those which were achieved during the specimen tension testing.

Weight Function Method for Stress Intensity Factors of Semi-Elliptical Surface Cracks on Functionally Graded Plates Subjected to Non-Uniform Stresses.

In this paper, a weight function method based on the first four terms of a Taylor's series expansion is proposed to determine the stress intensity factors of functionally graded plates with semi-elliptical surface cracks. Cracked surfaces that are subjected to constant, linear, parabolic and cubic stress fields are considered. The weight functions for the surface, deepest and general points on the crack faces of long and deep cracked functionally graded plates are derived, which has never been done before in the literature. The accuracy of the method in this study is then validated by comparing the results with those of finite element modeling. The numerical results indicate that the derived weight functions are highly accurate and robust enough to predict the stress intensity factors for cracked functionally graded plates subjected to non-uniform stress distributions. The weight function method is therefore a time-saving technique and suitable for handling non-uniform stress fields.

Effects of Material Nonlinearities on Design of Composite Constructions-Elasto-Plastic Behaviour.

Usually, the design of composite structures is limited to the linear elastic analysis only. The experimental results discussed in the paper demonstrate the physical non-linear behaviour both for unidirectional and woven roving composites. It is mainly connected with the micromechanical damages in composite structures, particularly with the effects of matrix cracking modeled in the form of elastic-plastic physical relations. In the present paper, the effects of both physical and geometrical non-linearities are taken into account. Their influence on the limit states (understood in the sense of buckling or failure/damage) of composite structures is discussed. The numerical examples deal with the behaviour of composite pressure vessels components, such as a cylindrical shell and the reinforcement of the junction of shells. The optimisation method of the reinforcement thickness is also formulated and solved herein.

The Influence of Facial Asymmetry on Stress Distributions in Temporomandibular Joints for Patients with Mandibular Prognathism / 医用生物力学

Objective To explore the effects of facial asymmetry on stress distributions in temporomandibular joints (TMJs) for patients with mandibular prognathism. Methods Eight 3D maxillofacial models were established in MIMICS based on cone-beam CT of 4 mandibular prognathism patients with asymmetry and 4 mandibular prognathism patients without asymmetry. Muscle forces and boundary conditions corresponding to the unilateral occlusion (unilateral molar chewing) were applied on the models in ABAQUS. The maximum and the minimum principal stresses of TMJ were chosen for analysis. Results There were significant differences in the maximum and minimum principal stresses at the condyles between the mandibular prognathism patients with and without facial asymmetry under unilateral occlusions (P<0-05). Compared with patients without facial asymmetry, the stresses on the condyle in patients with asymmetry increased by 2-3 times, and the stresses on articular fossa increased by 5-7 times. Among the mandibular prognathism patients with asymmetry, the stresses of the ipsilateral TMJ in patients with temporomandibular disorder (TMD) were significantly higher than those in patients without TMD. Conclusions Facial asymmetry increased the stresses of the articular fossa and condyle in patients with mandibular prognathism. TMD would cause greater stresses in ipsilateral TMJ of the mandibular prognathism patient with asymmetry. Therefore, different treatment strategies should be considered for mandibular prognathism with facial asymmetry.

Three-Dimensional Contractile Mechanics of Artery Accounting for Curl of Axial Strip Sectioned from Vessel Wall.

PURPOSE: It is well known that a sliced ring of arterial wall opens by a radial cut. An axial strip sectioned from arterial wall also curls into an arc. These phenomena imply that there exist residual strains in the circumferential and axial directions. How much do the axial residual strains affect the stress distributions of arterial wall? The aim of the present study is to know stress distributions of arterial wall with the residual strains under the passive and constricted conditions. METHODS: We analyzed the stress distributions under passive and constricted conditions with considering a Riemannian stress-free configuration. In the analysis, we used strain energy functions to describe the passive and active mechanical properties of artery. RESULTS: The present study provided distributions of stretch ratio with reference to the stress-free state (Riemannian stress-free configuration) and stress with and without the curl of axial strip of a homogenous cylindrical arterial model under the passive and constricted smooth muscle conditions. The circumferential and axial stresses with activated smooth muscle (noradrenaline 10-5 M) at the intraluminal pressure 16 kPa and the axial stretch ratio 1.5 with reference to the unloaded vessel decreased by 3.5 and 13.8% at the inner surface with considering the axial residual strain, respectively. CONCLUSIONS: We have shown that the Riemannian stress-free configuration is appropriate tool to analyze stress distributions of arterial wall under passive and activated conditions with the residual stresses.

Stress distributions and cell flows in a growing cell aggregate.

We discuss the short-time response of a multicellular spheroid to an external pressure jump. Our experiments show that 5 min after the pressure jump, the cell density increases in the centre of the spheroid but does not change appreciably close to the surface of the spheroid. This result can be explained if the cells are polarized which we show to be the case. Motivated by the experimental results, we develop a theory for polarized spheroids where the cell polarity is radial (except in a thin shell close to the spheroid surface). The theory takes into account the dependence of cell division and apoptosis rates on the local stress, the cell polarity and active stress generated by the cells and the dependence of active stress on the local pressure. We find a short-time increase of the cell density after a pressure jump that decays as a power law from the spheroid centre, which is in reasonable agreement with the experimental results. By comparing our theory to experiments, we can estimate the isotropic compression modulus of the tissue.