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Institute
A new formulation to calculate the shakedown limit load of Kirchhoff plates under stochastic conditions of strength is developed. Direct structural reliability design by chance con-strained programming is based on the prescribed failure probabilities, which is an effective approach of stochastic programming if it can be formulated as an equivalent deterministic optimization problem. We restrict uncertainty to strength, the loading is still deterministic. A new formulation is derived in case of random strength with lognormal distribution. Upper bound and lower bound shakedown load factors are calculated simultaneously by a dual algorithm.
Background:
Additional stabilization of the “comma sign” in anterosuperior rotator cuff repair has been proposed to provide biomechanical benefits regarding stability of the repair.
Purpose:
This in vitro investigation aimed to investigate the influence of a comma sign–directed reconstruction technique for anterosuperior rotator cuff tears on the primary stability of the subscapularis tendon repair.
Study Design:
Controlled laboratory study.
Methods:
A total of 18 fresh-frozen cadaveric shoulders were used in this study. Anterosuperior rotator cuff tears (complete full-thickness tear of the supraspinatus and subscapularis tendons) were created, and supraspinatus repair was performed with a standard suture bridge technique. The subscapularis was repaired with either a (1) single-row or (2) comma sign technique. A high-resolution 3D camera system was used to analyze 3-mm and 5-mm gap formation at the subscapularis tendon-bone interface upon incremental cyclic loading. Moreover, the ultimate failure load of the repair was recorded. A Mann-Whitney test was used to assess significant differences between the 2 groups.
Results:
The comma sign repair withstood significantly more loading cycles than the single-row repair until 3-mm and 5-mm gap formation occurred (P≤ .047). The ultimate failure load did not reveal any significant differences when the 2 techniques were compared (P = .596).
Conclusion:
The results of this study show that additional stabilization of the comma sign enhanced the primary stability of subscapularis tendon repair in anterosuperior rotator cuff tears. Although this stabilization did not seem to influence the ultimate failure load, it effectively decreased the micromotion at the tendon-bone interface during cyclic loading.
Clinical Relevance:
The proposed technique for stabilization of the comma sign has shown superior biomechanical properties in comparison with a single-row repair and might thus improve tendon healing. Further clinical research will be necessary to determine its influence on the functional outcome.
Extension fractures are typical for the deformation under low or no confining pressure. They can be explained by a phenomenological extension strain failure criterion. In the past, a simple empirical criterion for fracture initiation in brittle rock has been developed. In this article, it is shown that the simple extension strain criterion makes unrealistic strength predictions in biaxial compression and tension. To overcome this major limitation, a new extension strain criterion is proposed by adding a weighted principal shear component to the simple criterion. The shear weight is chosen, such that the enriched extension strain criterion represents the same failure surface as the Mohr–Coulomb (MC) criterion. Thus, the MC criterion has been derived as an extension strain criterion predicting extension failure modes, which are unexpected in the classical understanding of the failure of cohesive-frictional materials. In progressive damage of rock, the most likely fracture direction is orthogonal to the maximum extension strain leading to dilatancy. The enriched extension strain criterion is proposed as a threshold surface for crack initiation CI and crack damage CD and as a failure surface at peak stress CP. Different from compressive loading, tensile loading requires only a limited number of critical cracks to cause failure. Therefore, for tensile stresses, the failure criteria must be modified somehow, possibly by a cut-off corresponding to the CI stress. Examples show that the enriched extension strain criterion predicts much lower volumes of damaged rock mass compared to the simple extension strain criterion.
A generalized shear-lag theory for fibres with variable radius is developed to analyse elastic fibre/matrix stress transfer. The theory accounts for the reinforcement of biological composites, such as soft tissue and bone tissue, as well as for the reinforcement of technical composite materials, such as fibre-reinforced polymers (FRP). The original shear-lag theory proposed by Cox in 1952 is generalized for fibres with variable radius and with symmetric and asymmetric ends. Analytical solutions are derived for the distribution of axial and interfacial shear stress in cylindrical and elliptical fibres, as well as conical and paraboloidal fibres with asymmetric ends. Additionally, the distribution of axial and interfacial shear stress for conical and paraboloidal fibres with symmetric ends are numerically predicted. The results are compared with solutions from axisymmetric finite element models. A parameter study is performed, to investigate the suitability of alternative fibre geometries for use in FRP.
The mechanical behavior of the large intestine beyond the ultimate stress has never been investigated. Stretching beyond the ultimate stress may drastically impair the tissue microstructure, which consequently weakens its healthy state functions of absorption, temporary storage, and transportation for defecation. Due to closely similar microstructure and function with humans, biaxial tensile experiments on the porcine large intestine have been performed in this study. In this paper, we report hyperelastic characterization of the large intestine based on experiments in 102 specimens. We also report the theoretical analysis of the experimental results, including an exponential damage evolution function. The fracture energies and the threshold stresses are set as damage material parameters for the longitudinal muscular, the circumferential muscular and the submucosal collagenous layers. A biaxial tensile simulation of a linear brick element has been performed to validate the applicability of the estimated material parameters. The model successfully simulates the biomechanical response of the large intestine under physiological and non-physiological loads.
Edge-based and face-based smoothed finite element methods (ES-FEM and FS-FEM, respectively) are modified versions of the finite element method allowing to achieve more accurate results and to reduce sensitivity to mesh distortion, at least for linear elements. These properties make the two methods very attractive. However, their implementation in a standard finite element code is nontrivial because it requires heavy and extensive modifications to the code architecture. In this article, we present an element-based formulation of ES-FEM and FS-FEM methods allowing to implement the two methods in a standard finite element code with no modifications to its architecture. Moreover, the element-based formulation permits to easily manage any type of element, especially in 3D models where, to the best of the authors' knowledge, only tetrahedral elements are used in FS-FEM applications found in the literature. Shape functions for non-simplex 3D elements are proposed in order to apply FS-FEM to any standard finite element.
Combining physiological relevance and throughput for in vitro cardiac contractility measurement
(2020)
Despite increasing acceptance of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) in safety pharmacology, controversy remains about the physiological relevance of existing in vitro models for their mechanical testing. We hypothesize that existing signs of immaturity of the cell models result from an improper mechanical environment. We cultured hiPSC-CMs in a 96-well format on hyperelastic silicone membranes imitating their native mechanical environment, resulting in physiological responses to compound stimuli.We validated cell responses on the FLEXcyte 96, with a set of reference compounds covering a broad range of cellular targets, including ion channel modulators, adrenergic receptor modulators and kinase inhibitors. Acute (10 - 30 min) and chronic (up to 7 days) effects were investigated. Furthermore, the measurements were complemented with electromechanical models based on electrophysiological recordings of the used cell types.hiPSC-CMs were cultured on freely-swinging, ultra-thin and hyperelastic silicone membranes. The weight of the cell culture medium deflects the membranes downwards. Rhythmic contraction of the hiPSC-CMs resulted in dynamic deflection changes which were quantified by capacitive distance sensing. The cells were cultured for 7 days prior to compound addition. Acute measurements were conducted 10-30 minutes after compound addition in standard culture medium. For chronic treatment, compound-containing medium was replaced daily for up to 7 days. Electrophysiological properties of the employed cell types were recorded by automated patch-clamp (Patchliner) and the results were integrated into the electromechanical model of the system.Calcium channel agonist S Bay K8644 and beta-adrenergic stimulator isoproterenol induced significant positive inotropic responses without additional external stimulation. Kinase inhibitors displayed cardiotoxic effects on a functional level at low concentrations. The system-integrated analysis detected alterations in beating shape as well as frequency and arrhythmic events and we provide a quantitative measure of these.
Pressure distribution to the distal biceps tendon at the radial tuberosity: a biomechanical study
(2020)
Purpose
Mechanical impingement at the narrow radioulnar space of the tuberosity is believed to be an etiological factor in the injury of the distal biceps tendon. The aim of the study was to compare the pressure distribution at the proximal radioulnar space between 2 fixation techniques and the intact state.
Methods
Six right arms and 6 left arms from 5 female and 6 male frozen specimens were used for this study. A pressure transducer was introduced at the height of the radial tuberosity with the intact distal biceps tendon and after 2 fixation methods: the suture-anchor and the cortical button technique. The force (N), maximum pressure (kPa) applied to the radial tuberosity, and the contact area (mm²) of the radial tuberosity with the ulna were measured and differences from the intact tendon were detected from 60° supination to 60° pronation in 15° increments with the elbow in full extension and in 45° and 90° flexion of the elbow.
Results
With the distal biceps tendon intact, the pressures during pronation were similar regardless of extension and flexion and were the highest at 60° pronation with 90° elbow flexion (23.3 ± 53.5 kPa). After repair of the tendon, the mean peak pressure, contact area, and total force showed an increase regardless of the fixation technique. Highest peak pressures were found using the cortical button technique at 45° flexion of the elbow and 60° pronation. These differences were significantly different from the intact tendon. The contact area was significantly larger in full extension and 15°, 30°, and 60° pronation using the cortical button technique.
Conclusions
Pressures on the distal biceps tendon at the radial tuberosity increase during pronation, especially after repair of the tendon.
Clinical relevance
Mechanical impingement could play a role in both the etiology of primary distal biceps tendon ruptures and the complications occurring after fixation of the tendon using certain techniques.
Three-dimensional (3D) full-field measurements provide a comprehensive and accurate validation of finite element (FE) models. For the validation, the result of the model and measurements are compared based on two respective point-sets and this requires the point-sets to be registered in one coordinate system. Point-set registration is a non-convex optimization problem that has widely been solved by the ordinary iterative closest point algorithm. However, this approach necessitates a good initialization without which it easily returns a local optimum, i.e. an erroneous registration. The globally optimal iterative closest point (Go-ICP) algorithm has overcome this drawback and forms the basis for the presented open-source tool that can be used for the validation of FE models using 3D full-field measurements. The capability of the tool is demonstrated using an application example from the field of biomechanics. Methodological problems that arise in real-world data and the respective implemented solution approaches are discussed.
Virgin passive colon biomechanics and a literature review of active contraction constitutive models
(2022)
The objective of this paper is to present our findings on the biomechanical aspects of the virgin passive anisotropic hyperelasticity of the porcine colon based on equibiaxial tensile experiments. Firstly, the characterization of the intestine tissues is discussed for a nearly incompressible hyperelastic fiber-reinforced Holzapfel–Gasser–Ogden constitutive model in virgin passive loading conditions. The stability of the evaluated material parameters is checked for the polyconvexity of the adopted strain energy function using positive eigenvalue constraints of the Hessian matrix with MATLAB. The constitutive material description of the intestine with two collagen fibers in the submucosal and muscular layer each has been implemented in the FORTRAN platform of the commercial finite element software LS-DYNA, and two equibiaxial tensile simulations are presented to validate the results with the optical strain images obtained from the experiments. Furthermore, this paper also reviews the existing models of the active smooth muscle cells, but these models have not been computationally studied here. The review part shows that the constitutive models originally developed for the active contraction of skeletal muscle based on Hill’s three-element model, Murphy’s four-state cross-bridge chemical kinetic model and Huxley’s sliding-filament hypothesis, which are mainly used for arteries, are appropriate for numerical contraction numerical analysis of the large intestine.
When confining pressure is low or absent, extensional fractures are typical, with fractures occurring on unloaded planes in rock. These “paradox” fractures can be explained by a phenomenological extension strain failure criterion. In the past, a simple empirical criterion for fracture initiation in brittle rock has been developed. But this criterion makes unrealistic strength predictions in biaxial compression and tension. A new extension strain criterion overcomes this limitation by adding a weighted principal shear component. The weight is chosen, such that the enriched extension strain criterion represents the same failure surface as the Mohr–Coulomb (MC) criterion. Thus, the MC criterion has been derived as an extension strain criterion predicting failure modes, which are unexpected in the understanding of the failure of cohesive-frictional materials. In progressive damage of rock, the most likely fracture direction is orthogonal to the maximum extension strain. The enriched extension strain criterion is proposed as a threshold surface for crack initiation CI and crack damage CD and as a failure surface at peak P. Examples show that the enriched extension strain criterion predicts much lower volumes of damaged rock mass compared to the simple extension strain criterion.
FEM shakedown analysis of structures under random strength with chance constrained programming
(2022)
Direct methods, comprising limit and shakedown analysis, are a branch of computational mechanics. They play a significant role in mechanical and civil engineering design. The concept of direct methods aims to determine the ultimate load carrying capacity of structures beyond the elastic range. In practical problems, the direct methods lead to nonlinear convex optimization problems with a large number of variables and constraints. If strength and loading are random quantities, the shakedown analysis can be formulated as stochastic programming problem. In this paper, a method called chance constrained programming is presented, which is an effective method of stochastic programming to solve shakedown analysis problems under random conditions of strength. In this study, the loading is deterministic, and the strength is a normally or lognormally distributed variable.
The connective tissues such as tendons contain an extracellular matrix (ECM) comprising collagen fibrils scattered within the ground substance. These fibrils are instrumental in lending mechanical stability to tissues. Unfortunately, our understanding of how collagen fibrils reinforce the ECM remains limited, with no direct experimental evidence substantiating current theories. Earlier theoretical studies on collagen fibril reinforcement in the ECM have relied predominantly on the assumption of uniform cylindrical fibers, which is inadequate for modelling collagen fibrils, which possessed tapered ends. Recently, Topçu and colleagues published a paper in the International Journal of Solids and Structures, presenting a generalized shear-lag theory for the transfer of elastic stress between the matrix and fibers with tapered ends. This paper is a positive step towards comprehending the mechanics of the ECM and makes a valuable contribution to formulating a complete theory of collagen fibril reinforcement in the ECM.