A hybrid smoothed finite element method (H-SFEM) to solid mechanics problems

In this paper, a hybrid smoothed finite element method (H-SFEM) is developed for solid mechanics problems by combining techniques of finite element method (FEM) and Node-based smoothed finite element method (NS-FEM) using a triangular mesh. A parameter is equipped into H-SFEM, and the strain field is further assumed to be the weighted average between compatible stains from FEM and smoothed strains from NS-FEM. We prove theoretically that the strain energy obtained from the H-SFEM solution lies in between those from the compatible FEM solution and the NS-FEM solution, which guarantees the convergence of H-SFEM. Intensive numerical studies are conducted to verify these theoretical results and show that (1) the upper and lower bound solutions can always be obtained by adjusting ; (2) there exists a preferable at which the H-SFEM can produce the ultrasonic accurate solution.

Porohyperelastic analysis to explore mechanical properties of chondrocytes using numerical modeling and experiments : a finite element study

There are many continuum mechanical models have been developed such as liquid drop models, solid models, and so on for single living cell biomechanics studies. However, these models do not give a fully approach to exhibit a clear understanding of the behaviour of single living cells such as swelling behaviour, drag effect, etc. Hence, the porohyperelastic (PHE) model which can capture those aspects would be a good candidature to study cells behaviour (e.g. chondrocytes in this study). In this research, an FEM model of single chondrocyte cell will be developed by using this PHE model to simulate Atomic Force Microscopy (AFM) experimental results with the variation of strain rate. This material model will be compared with viscoelastic model to demonstrate the advantages of PHE model. The results have shown that the maximum value of force applied of PHE model is lower at lower strain rates. This is because the mobile fluid does not have enough time to exude in case of very high strain rate and also due to the lower permeability of the membrane than that of the protoplasm of chondrocyte. This behavior is barely observed in viscoelastic model. Thus, PHE model is the better model for cell biomechanics studies.

A finite element model of seat cushion indentation with a soft tissue human occupant model

Effective digital human model (DHM) simulation of automotive driver packaging ergonomics, safety and comfort depends on accurate modelling of occupant posture, which is strongly related to the mechanical interaction between human body soft tissue and flexible seat components. This paper presents a finite-element study simulating the deflection of seat cushion foam and supportive seat structures, as well as human buttock and thigh soft tissue when seated. The three-dimensional data used for modelling thigh and buttock geometry were taken on one 95th percentile male subject, representing the bivariate percentiles of the combined hip breadth (seated) and buttock-to-knee length distributions of a selected Australian and US population. A thigh-buttock surface shell based on this data was generated for the analytic model. A 6mm neoprene layer was offset from the shell to account for the compression of body tissue expected through sitting in a seat. The thigh-buttock model is therefore made of two layers, covering thin to moderate thigh and buttock proportions, but not more fleshy sizes. To replicate the effects of skin and fat, the neoprene rubber layer was modelled as a hyperelastic material with viscoelastic behaviour in a Neo-Hookean material model. Finite element (FE) analysis was performed in ANSYS V13 WB (Canonsburg, USA). It is hypothesized that the presented FE simulation delivers a valid result, compared to a standard SAE physical test and the real phenomenon of human-seat indentation. The analytical model is based on the CAD assembly of a Ford Territory seat. The optimized seat frame, suspension and foam pad CAD data were transformed and meshed into FE models and indented by the two layer, soft surface human FE model. Converging results with the least computational effort were achieved for a bonded connection between cushion and seat base as well as cushion and suspension, no separation between neoprene and indenter shell and a frictional connection between cushion pad and neoprene. The result is compared to a previous simulation of an indentation with a hard shell human finite-element model of equal geometry, and to the physical indentation result, which is approached with very high fidelity. We conclude that (a) SAE composite buttock form indentation of a suspended seat cushion can be validly simulated in a FE model of merely similar geometry, but using a two-layer hard/soft structure. (b) Human-seat indentation of a suspended seat cushion can be validly simulated with a simplified human buttock-thigh model for a selected anthropomorphism.

Comparison between analytical and 3D finite element solutions for borehole stresses in anisotropic elastic rock

We present a rigorous validation of the analytical Amadei solution for the stress concentration around an arbitrarily orientated borehole in general anisotropic elastic media. First, we revisit the theoretical framework of the Amadei solution and present analytical insights that show that the solution does indeed contain all special cases of symmetry, contrary to previous understanding, provided that the reduced strain coefficients b11 and b55 are not equal. It is shown from theoretical considerations and published experimental data that the b11 and b55 are not equal for realistic rocks. Second, we develop a 3D finite element elastic model within a hybrid analytical–numerical workflow that circumvents the need to rebuild and remesh the model for every borehole and material orientation. Third, we show that the borehole stresses computed from the numerical model and the analytical solution match almost perfectly for different borehole orientations (vertical, deviated and horizontal) and for several cases involving isotropic, transverse isotropic and orthorhombic symmetries. It is concluded that the analytical Amadei solution is valid with no restriction on the borehole orientation or the symmetry of the elastic anisotropy.

Experimental impact and finite element analysis of a composite, portable road safety barrier

This thesis provides an experimental and computational platform for investigating the performance and behaviour of water filled, plastic portable road safety barriers in an isolated impact scenario. A schedule of experimental impact tests were conducted assessing the impact response of an existing design of road safety barrier utilising a novel horizontal impact testing system. A coupled finite element and smooth particle hydrodynamic model of the barrier system was developed and validated against the results of the experimental tests. The validated model was subsequently used to assess the effect of certain composite materials on the impact performance of the water filled, portable road safety barrier system.

Local stress-strain distribution and load transfer across cartilage matrix at micro-scale using combined microscopy-based finite element method

Articular cartilage is the load-bearing tissue that consists of proteoglycan macromolecules entrapped between collagen fibrils in a three-dimensional architecture. To date, the drudgery of searching for mathematical models to represent the biomechanics of such a system continues without providing a fitting description of its functional response to load at micro-scale level. We believe that the major complication arose when cartilage was first envisaged as a multiphasic model with distinguishable components and that quantifying those and searching for the laws that govern their interaction is inadequate. To the thesis of this paper, cartilage as a bulk is as much continuum as is the response of its components to the external stimuli. For this reason, we framed the fundamental question as to what would be the mechano-structural functionality of such a system in the total absence of one of its key constituents-proteoglycans. To answer this, hydrated normal and proteoglycan depleted samples were tested under confined compression while finite element models were reproduced, for the first time, based on the structural microarchitecture of the cross-sectional profile of the matrices. These micro-porous in silico models served as virtual transducers to produce an internal noninvasive probing mechanism beyond experimental capabilities to render the matrices micromechanics and several others properties like permeability, orientation etc. The results demonstrated that load transfer was closely related to the microarchitecture of the hyperelastic models that represent solid skeleton stress and fluid response based on the state of the collagen network with and without the swollen proteoglycans. In other words, the stress gradient during deformation was a function of the structural pattern of the network and acted in concert with the position-dependent compositional state of the matrix. This reveals that the interaction between indistinguishable components in real cartilage is superimposed by its microarchitectural state which directly influences macromechanical behavior.

Second-order elastic finite element analysis of steel structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included. The accuracy and efficiency of the technique is verified by comparisons with a number of plane and spatial structures, whose structural response has been reported in independent studies.

Geometric sensitivity of patient-specific finite element models of the spine to variability in user-selected anatomical landmarks

Software to create individualised finite element (FE) models of the osseoligamentous spine using pre-operative computed tomography (CT) data-sets for spinal surgery patients has recently been developed. This study presents a geometric sensitivity analysis of this software to assess the effect of intra-observer variability in user-selected anatomical landmarks. User-selected landmarks on the osseous anatomy were defined from CT data-sets for three scoliosis patients and these landmarks were used to reconstruct patient-specific anatomy of the spine and ribcage using parametric descriptions. The intra-observer errors in landmark co-ordinates for these anatomical landmarks were calculated. FE models of the spine and ribcage were created using the reconstructed anatomy for each patient and these models were analysed for a loadcase simulating clinical flexibility assessment. The intra-observer error in the anatomical measurements was low in comparison to the initial dimensions, with the exception of the angular measurements for disc wedge and zygapophyseal joint (z-joint) orientation and disc height. This variability suggested that CT resolution may influence such angular measurements, particularly for small anatomical features, such as the z-joints, and may also affect disc height. The results of the FE analysis showed low variation in the model predictions for spinal curvature with the mean intra-observer variability substantially less than the accepted error in clinical measurement. These findings demonstrate that intra-observer variability in landmark point selection has minimal effect on the subsequent FE predictions for a clinical loadcase.

Analysis of strain-rate dependent mechanical behavior of single chondrocyte : a finite element study

Various studies have been conducted to investigate the effects of impact loading on cartilage damage and chondrocyte death. These have shown that the rate and magnitude of the applied strain significantly influence chondrocyte death, and that cell death occurred mostly in the superficial zone of cartilage suggesting the need to further understand the fundamental mechanisms underlying the chondrocytes death induced at certain levels of strain-rate. To date there is no comprehensive study providing insight on this phenomenon. The aim of this study is to examine the strain-rate dependent behavior of a single chondrocyte using a computational approach based on Finite Element Method (FEM). An FEM model was developed using various mechanical models, which were Standard Neo-Hookean Solid (SnHS), porohyperelastic (PHE) and poroviscohyperelastic (PVHE) to simulate Atomic Force Microscopy (AFM) experiments of chondrocyte. The PVHE showed, it can capture both relaxation and loading rate dependent behaviors of chondrocytes, accurately compared to other models.

Second-order elastic finite element analysis of structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included.

Experimental and finite element analysis to identify the source of vibration of a coach

This paper presents an investigation on the cause of severe vibration problem of a coach with four-cylinder engine running at an idle state using vibration and impact hammer modal experiments to obtain the main vibration frequency components and the natural characteristics of the coach. The vibration results indicate that the main vibration component comes from the vibration transmitted from the engine to the chassis frame, which is closely related with the engine idle speed. Based on structural simulation analysis of the coach’s chassis frame and comparison with modal testing, the coach severe vibration problem was due to coupling resonance between the engine idle frequency and the fourth natural frequency of the chassis frame. The solution to eliminate the vibration problem is provided by changing the local structure stiffness of the chassis frame. The contribution of this paper lies in providing a solution to solve similar problems.

Finite element analysis of the in-plane shear behaviour of masonry panels confined with reinforced grouted cores

A combined experimental and numerical program was conducted to study the in-plane shear behaviour of hollow concrete masonry panels containing reinforced grout cores. This paper is focused on the numerical program. A two dimensional macromodelling strategy was used to simulate the behaviour of the confined masonry (CM) shear panels. Both the unreinforced masonry and the confining element were modelled using macromasonry properties and the steel reinforcement was modelled as an embedded truss element located within the grout using perfectly bonded constraint. The FE model reproduced key behaviours observed in the experiments, including the shear strength, the deformation and the crack patterns of the unconfined and confined masonry panels. The predictions of the validated model were used to evaluate the existing in-plane shear expressions available in the national masonry standards and research publications.

Using patient specific finite element models to understand the biomechanics of paediatric spinal deformity surgery

Adolescent idiopathic scoliosis (AIS) is a spinal deformity, which may require surgical correction by attaching rods to the patient’s spine using screws inserted into the vertebrae. Complication rates for deformity correction surgery are unacceptably high. Determining an achievable correction without overloading the adjacent spinal tissues or implants requires an understanding of the mechanical interaction between these components. We have developed novel patient specific modelling software to create individualized finite element models (FEM) representing the thoracolumbar spine and ribcage of scoliosis patients. We are using these models to better understand the biomechanics of spinal deformity correction.

Determination of strain-rate-dependent mechanical behavior of living and fixed osteocytes and chondrocytes using atomic force microscopy and inverse finite element analysis

The aim of this paper is to determine the strain-rate-dependent mechanical behavior of living and fixed osteocytes and chondrocytes, in vitro. Firstly, Atomic Force Microscopy (AFM) was used to obtain the force-indentation curves of these single cells at four different strain-rates. These results were then employed in inverse finite element analysis (FEA) using Modified Standard neo-Hookean Solid (MSnHS) idealization of these cells to determine their mechanical properties. In addition, a FEA model with a newly developed spring element was employed to accurately simulate AFM evaluation in this study. We report that both cytoskeleton (CSK) and intracellular fluid govern the strain-rate-dependent mechanical property of living cells whereas intracellular fluid plays a predominant role on fixed cells’ behavior. In addition, through the comparisons, it can be concluded that osteocytes are stiffer than chondrocytes at all strain-rates tested indicating that the cells could be the biomarker of their tissue origin. Finally, we report that MSnHS is able to capture the strain-rate-dependent mechanical behavior of osteocyte and chondrocyte for both living and fixed cells. Therefore, we concluded that the MSnHS is a good model for exploration of mechanical deformation responses of single osteocytes and chondrocytes. This study could open a new avenue for analysis of mechanical behavior of osteocytes and chondrocytes as well as other similar types of cells.