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The deformation and damage laws of non-homogeneous irregular structural planes in rocks are the basis for studying the stability of rock engineering. To investigate the damage characteristics of rock containing non-parallel fissures, uniaxial compression tests and numerical simulations were conducted on sandstone specimens containing three non-parallel fissures inclined at 0°, 45° and 90° in this study. The characteristics of crack initiation and crack evolution of fissures with different inclinations were analyzed. A constitutive model for the discontinuous fractures of fissured sandstone was proposed. The results show that the fracture behaviors of fissured sandstone specimens are discontinuous. The stress–strain curves are non-smooth and can be divided into nonlinear crack closure stage, linear elastic stage, plastic stage and brittle failure stage, of which the plastic stage contains discontinuous stress drops. During the uniaxial compression test, the middle or ends of 0° fissures were the first to crack compared to 45° and 90° fissures. The end with small distance between 0° and 45° fissures cracked first, and the end with large distance cracked later. After the final failure, 0° fissures in all specimens were fractured, while 45° and 90° fissures were not necessarily fractured. Numerical simulation results show that the concentration of compressive stress at the tips of 0°, 45° and 90° fissures, as well as the concentration of tensile stress on both sides, decreased with the increase of the inclination angle. A constitutive model for the discontinuous fractures of fissured sandstone specimens was derived by combining the logistic model and damage mechanic theory. This model can well describe the discontinuous drops of stress and agrees well with the whole processes of the stress–strain curves of the fissured sandstone specimens.
Direct methods comprising limit and shakedown analysis is a branch of computational mechanics. It plays a significant role in mechanical and civil engineering design. The concept of direct method aims to determinate the ultimate load bearing capacity of structures beyond the elastic range. For practical problems, the direct methods lead to nonlinear convex optimization problems with a large number of variables and onstraints. If strength and loading are random quantities, the problem of shakedown analysis is considered as stochastic programming. This paper presents a method so called chance constrained programming, an effective method of stochastic programming, to solve shakedown analysis problem under random condition of strength. In this our investigation, the loading is deterministic, the strength is distributed as normal or lognormal variables.
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.
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.
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.
We propose the so-called chance constrained programming model of stochastic programming theory to analyze limit and shakedown loads of structures under random strength with a lognormal distribution. A dual chance constrained programming algorithm is developed to calculate simultaneously both the upper and lower bounds of the plastic collapse limit and the shakedown limit. The edge-based smoothed finite element method (ES-FEM) is used with three-node linear triangular elements.
Background
Osteoporosis is associated with the risk of fractures near the hip. Age and comorbidities increase the perioperative risk. Due to the ageing population, fracture of the proximal femur also proves to be a socio-economic problem. Preventive surgical measures have hardly been used so far.
Methods
10 pairs of human femora from fresh cadavers were divided into control and low-volume femoroplasty groups and subjected to a Hayes fall-loading fracture test. The results of the respective localization and classification of the fracture site, the Singh index determined by computed tomography (CT) examination and the parameters in terms of fracture force, work to fracture and stiffness were evaluated statistically and with the finite element method. In addition, a finite element parametric study with different position angles and variants of the tubular geometry of the femoroplasty was performed.
Findings
Compared to the control group, the work to fracture could be increased by 33.2%. The fracture force increased by 19.9%. The used technique and instrumentation proved to be standardized and reproducible with an average poly(methyl methacrylate) volume of 10.5 ml. The parametric study showed the best results for the selected angle and geometry.
Interpretation
The cadaver studies demonstrated the biomechanical efficacy of the low-volume tubular femoroplasty. The numerical calculations confirmed the optimal choice of positioning as well as the inner and outer diameter of the tube in this setting. The standardized minimally invasive technique with the instruments developed for it could be used in further comparative studies to confirm the measured biomechanical results.
Purpose
The aim of this study was to compare several osteosynthesis techniques (intramedullary headless compression screws, T-plates, and Kirschner wires) for distal epiphyseal fractures of proximal phalanges in a human cadaveric model.
Methods
A total of 90 proximal phalanges from 30 specimens (index, ring, and middle fingers) were used for this study. After stripping off all soft tissue, a transverse distal epiphyseal fracture was simulated at the proximal phalanx. The 30 specimens were randomly assigned to 1 fixation technique (30 per technique), either a 3.0-mm intramedullary headless compression screw, locking plate fixation with a 2.0-mm T-plate, or 2 oblique 1.0-mm Kirschner wires. Displacement analysis (bending, distraction, and torsion) was performed using optical tracking of an applied random speckle pattern after osteosynthesis. Biomechanical testing was performed with increasing cyclic loading and with cyclic load to failure using a biaxial torsion-tension testing machine.
Results
Cannulated intramedullary compression screws showed significantly less displacement at the fracture site in torsional testing. Furthermore, screws were significantly more stable in bending testing. Kirschner wires were significantly less stable than plating or screw fixation in any cyclic load to failure test setup.
Conclusions
Intramedullary compression screws are a highly stable alternative in the treatment of transverse distal epiphyseal phalangeal fractures. Kirschner wires seem to be inferior regarding displacement properties and primary stability.
Clinical relevance
Fracture fixation of phalangeal fractures using plate osteosynthesis may have the advantage of a very rigid reduction, but disadvantages such as stiffness owing to the more invasive surgical approach and soft tissue irritation should be taken into account. Headless compression screws represent a minimally invasive choice for fixation with good biomechanical properties.