Finite element crash simulations of the human body: Passive and active muscle modelling

Conventional dummy based testing procedures suffer from known limitations. This report addresses issues in finite element human body models in evaluating pedestrian and occupant crash safety measures. A review of material properties of soft tissues and characterization methods show a scarcity of material properties for characterizing soft tissues in dynamic loading. Experiments imparting impacts to tissues and subsequent inverse finite element mapping to extract material properties are described. The effect of muscle activation due to voluntary and non-voluntary reflexes on injuries has been investigated through finite element modelling.     

Mathematical modelling of the cardiovascular system

This paper is an introduction to the special issue of the Journal of Engineering Mathematic (Volume 47/3–4, 2003) on the mathematical modelling of the cardiovascular system. This issue includes the 2003 James Lighthill Memorial Paper written by Pedley [1] on the mathematical modelling of arterial fluid dynamics. This introduction is written to bring cardiovascular biomechanics to readers with a background in mathematical modelling and computational mechanics. The importance of mathematical modelling for physiological understanding, diagnostics, prosthesis development, patient selection and medical planning is indicated and discussed shortly. A subdivision into models for cardiac mechanics, pressure- and flow-wave propagation, mass transfer and fully three-dimensional fluid-structure interaction is made and references are given to the different contributions of the issue.     

Mathematical modelling of moisture-induced panel deformation

A new mathematical model is introduced to describe the moisture-induced deformation in an elastic panel. The problem for the stresses is found to be singularly perturbed in the aspect ratio squared, the domain being split into four asymptotic regions. Determination of the matching constants is made possible by the introduction of a stress function in the boundary layer. Explicit expressions are derived for the stress and deformation in the three-dimensional problem. The predictions for deformation are compared with experimental results; the agreement is reasonable. The moment of the moisture concentration is found to be the crucial factor in determining panel warp. A model, which consists of two coupled parabolic equations, is also proposed for moisture transport in exterior applications. The disparate time-scales allow the system to be reduced to a single partial differential equation. In one parameter régime, a multiple-scale analysis further reduces this partial differential equation to an averaged equation which only requires solution over the long moisture-diffusion time-scale.     

Mathematical modelling of toxicity-related trade-offs in metronomic chemotherapy

For better quality of life (QoL) for the cancer patients, metronomic chemotherapy (MCT) would be the rational option instead of conventional chemotherapy. However, in view of the recent arguments regarding the accumulation of toxicity in MCT, it is worthwhile to examine the role of pathophysiological constraints in retarding the curative potential of MCT. Drug application is stopped upon attaining a certain high level of toxicity and subsequent resumption is possible once the toxicity drops below a certain low level. Large delays in subsequent drug administration can thus effectively handle toxicity and it may retard the therapeutic potential due to excessive tumour growth in the absence of drug. Small delays, on the other hand, may result in inoperable pathophysiological states resulting in poor QoL. It is argued that only the intervention of domain knowledge of an expert oncologist with respect to drug administration decision can in fact clinch the trade-off issues arising out of the situation in favour of a sustainable QoL. A mathematical model that may act as a general guideline to tackle the trade-off issues in cancer treatment is provided. Rigorous simulation exercises are required to establish the concept of MCT in the backdrop of conventional cancer treatment practices.     

Mathematical modelling of creep/environment interactions

Physically-based creep Continuum Damage Mechanics (CDM) is briefly reviewed to introduce the formalism necessary for mathematical modelling of creep and fracture in the presence of a chemically-interacting fluid environment. A recently developed theory of creep in precipitation-hardened alloys is presented in the form of a constitutive equation and two important creep/environment interactions are discussed in detail. Spallation of oxide scales during creep of a low-alloy ferritic steel is one and is modelled using the new creep constitutive equation which incorporates particle-ageing as the principal intrinsic damage mechanism. Lack of experimental data has meant that only qualitative support for the model predictions could be given. Carbon dioxide gas bubble formation along grain boundaries in nickel alloys is the other form of environmental attack considered; a new kinetic model based upon oxyen diffusion-control is described and shown to be in quantitative agreement with a large experimental dataset.     

Mathematical modelling and computer simulation of nitriding

Abstract

Mathematical modelling of matter transmission during gas nitriding has been deduced by a numerical calculation in the present study. The diffusion coefficient of nitrogen in 38CrMoAl steel and the matter transmission coefficent in the interfacial reaction have been measured. Owing to the large difference between the nitrogen activity at the surface of the workpiece and that of the gas phase during the nitriding process, it is very difficult to control the nitrogen potential and balance the nitrogen activity. In order to solve this problem, is it proposed that the nitrogen potential is dynamically controlled by computer. Under conditions of high nitriding speed, the computer controlled technique used in practical manufacture shows good reproducibility and can control the nitrogen potential accurately, thereby reducing the brittleness of the nitrided layer.     

模拟听觉的机器故障诊断设备的框架

文章先分析谱相关和人耳听觉的某些相似特性,如两者都不管信号的初相位,即使相位相差90°的正弦和余弦信号,只要频率相同人耳听到的是同样的声音,而谱相关系数也接近于1。然后,利用谱相关系数模拟人耳听觉的某些特性,提出一个机器故障诊断设备的框架。     

Mathematical modelling of dimensional accuracy in vacuum assisted casting

Vacuum assisted casting (VAC) is one of the prototype making processes used to generate replicas of plastic components (PC) for batch production activities (like: investment casting applications). In the present study, the outcome of the Taguchi model has been used for developing a mathematical model for dimensional accuracy (DA) using Buckingham's π-theorem for VAC of PC. Four input parameters, namely material type, mixing ratio (hardener: softener), de-mould time and de-mould temperature, were selected to give output in the form of DA. This study will provide the main effects of these variables on DA and will shed light on the mechanism of DA in VAC for replicas of PC. The comparison with experimental results will also serve as further validation of the model.     

Mathematical modelling of microsegregation in eutectic and peritectic binary alloys

Abstract

A mathematical model of microsegregation for eutectic and peritectic binary alloys was implemented using a finite volume method to solve the differential equations for mass transport. In this model simple ideas are used to handle phase boundaries and coarsening without the need to employ node jumping schemes or any transformation of variables to fix the domain size. Some model results were compared with available analytical solutions, revealing excellent agreement, which proved the approach useful to solve dissolution and diffusion coupled problems as well as microsegregation ones. Furthermore, good agreement was observed between the model results and measurements of eutectic volume fractions published previously for an Al–Cu alloy. The model was also capable of showing some important features of a typical peritectic transformation. Some instability was observed during model calculations, but it was easily handled by a time step refining technique.     

Potential and limits of functional modelling in the CAD process

This paper gives a survey of the beginning and newest computer-aided functional modelling by German researchers. The basic principles of functional modelling are established and a representative function model is illustrated by the example of an emergency power unit. Some important methods for computer-aided modelling according to the function model are explained in detail. Following this the limits of functional modelling are outlined by describing the working arrangements of working principles using a flowchart representation of the function structure.     

Quantitative analysis of harmonic convergence in mosquito auditory interactions

This article analyses the hearing and behaviour of mosquitoes in the context of inter-individual acoustic interactions. The acoustic interactions of tethered live pairs of Aedes aegypti mosquitoes, from same and opposite sex mosquitoes of the species, are recorded on independent and unique audio channels, together with the response of tethered individual mosquitoes to playbacks of pre-recorded flight tones of lone or paired individuals. A time-dependent representation of each mosquito''s non-stationary wing beat frequency signature is constructed, based on Hilbert spectral analysis. A range of algorithmic tools is developed to automatically analyse these data, and used to perform a robust quantitative identification of the ‘harmonic convergence’ phenomenon. The results suggest that harmonic convergence is an active phenomenon, which does not occur by chance. It occurs for live pairs, as well as for lone individuals responding to playback recordings, whether from the same or opposite sex. Male–female behaviour is dominated by frequency convergence at a wider range of harmonic combinations than previously reported, and requires participation from both partners in the duet. New evidence is found to show that male–male interactions are more varied than strict frequency avoidance. Rather, they can be divided into two groups: convergent pairs, typified by tightly bound wing beat frequencies, and divergent pairs, that remain widely spaced in the frequency domain. Overall, the results reveal that mosquito acoustic interaction is a delicate and intricate time-dependent active process that involves both individuals, takes place at many different frequencies, and which merits further enquiry.     

Mathematical modeling of the process of sublimation drying

A complex physicomathematical analysis of vacuum sublimation drying has been given. Approaches to calculation and designing of sublimation dryers have been proposed. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 1, pp. 48–55, January–February, 2006.     

Mathematical simulation of the process of peat ignition

Within the framework of a mathematical model of a porous reacting medium, the statement and numerical solution of the problem of occurrence of combustion (smouldering) of peat as a result of the action of a low fire seat are given. It is found that at moderate temperatures, T ≤ 700 K, the smouldering of the initial reagent is limited by the processes of drying, pyrolysis, and by the reaction of oxidation of the carbon residue. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 1, pp. 191–199, January–February, 2008.     

Mathematical modeling of the process compaction of wood

Within the framework of the mechanics of heterophase systems a mathematical model for the process of pressing wood has been offered; this model takes account of the influence of its complex rheological properties and surface phenomena in thin interlayers of water on the change in a porous structure. With numerical methods, a study has been made of the influence of the sample’s humidity and temperature fields on the strength and quality of the material obtained. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 78, No. 5, pp. 62–69, September–October, 2005.     

Gaussian process modelling of austenite formation in steel

Abstract

The present paper introduces the Gaussian process model for the empirical modelling of the formation of austenite during the continuous heating of steels. A previous paper has examined the application of neural networks to this problem, but the Gaussian process model is a more general probabilistic model which avoids some of the arbitrariness of neural networks, and is somewhat more amenable to interpretation. It is demonstrated that the model leads to an improvement in the significance of the trends of the Ac₁ and Ac₃ temperatures as a function of the chemical composition and heating rate. In some cases, these predicted trends are more plausible than those obtained with the neural network analysis. Additionally, it is shown that many of the trace alloying elements present in steels are irrelevant in determining the austenite formation temperatures.     

Mathematical modelling of transient processes in convective heated surfaces of boilers

The paper presents a one-dimensional mathematical model for simulating the transient processes which occur in convective heated surfaces of boilers, namely superheaters and economizers. The proposed model is based on solving equation describing the energy conservation and is simplified because the mass and momentum balance equations are omitted. The suggested method considers the superheater or economizer model as one with distributed parameters. The temperature of the separating wall is determined from the equation of transient heat conduction. In order to obtain a grater accuracy of the results, the wall was divided into two control volumes making it possible to compute the temperatures on its both surfaces. All thermo-physical properties of the operating media and the material of the separating walls are computed in real time. The space-time heat transfer coefficients are also computed on-line considering the actual tube pitches and assuming cross-flow of the combustion gases. In the proposed model the boundary conditions can be time-dependent. In order to experimentally verify the proposed method for modelling the processes occurring in convective surfaces of power boilers, a series of measurements of the platen superheater and economizer in an OP-210 boiler (with steam capacity of 210×10³?kg/h) were carried out. Comparing the results of measurements of the steam and feed water temperature with computation results, satisfactory convergence is found.     

Oscillator analogy for modelling the manufacturing systems dynamics

The purpose of this paper is to present an approach of modelling and analysis of the dynamic behaviour of manufacturing systems. The manufacturing system is considered to be responding to an excitation, namely a demand that varies over time, by producing a number of parts over time. This resembles a mechanical system that displaces its mass responding to a varying input force. Based on this analogy, this paper establishes a manufacturing system's modelling method. A system identification technique is used for deriving inertia, damping and stiffness from the manufacturing system's response to different excitations. Based on these attributes, the response of a manufacturing system to any given input can be estimated. Furthermore, a definition for assessing manufacturing flexibility, based on this approach, is being discussed.     

Mathematical modelling of atheroma plaque formation and development in coronary arteries

Atherosclerosis is a vascular disease caused by inflammation of the arterial wall, which results in the accumulation of low-density lipoprotein (LDL) cholesterol, monocytes, macrophages and fat-laden foam cells at the place of the inflammation. This process is commonly referred to as plaque formation. The evolution of the atherosclerosis disease, and in particular the influence of wall shear stress on the growth of atherosclerotic plaques, is still a poorly understood phenomenon. This work presents a mathematical model to reproduce atheroma plaque growth in coronary arteries. This model uses the Navier–Stokes equations and Darcy''s law for fluid dynamics, convection–diffusion–reaction equations for modelling the mass balance in the lumen and intima, and the Kedem–Katchalsky equations for the interfacial coupling at membranes, i.e. endothelium. The volume flux and the solute flux across the interface between the fluid and the porous domains are governed by a three-pore model. The main species and substances which play a role in early atherosclerosis development have been considered in the model, i.e. LDL, oxidized LDL, monocytes, macrophages, foam cells, smooth muscle cells, cytokines and collagen. Furthermore, experimental data taken from the literature have been used in order to physiologically determine model parameters. The mathematical model has been implemented in a representative axisymmetric geometrical coronary artery model. The results show that the mathematical model is able to qualitatively capture the atheroma plaque development observed in the intima layer.     

Mathematical model of delay in the secondary literature publishing process

In this paper, the internal law of delay in the secondary literature publishing process is presented. The process is demonstrated to abide by the partial differential equation of periodical literature publishing process. A definite solution of the publishing delay process is derived. Accordingly, the expression of average publication delay indicator based on the particular solution is deduced. Then the problem is studied that some information of primary literatures is missed in information retrieval, and the relationship is established between the average delay indicator and the miss ratio of primary literatures in the index periodicals or databases. Also it is proposed that the primary literature should be used as a supplemental tool in information retrieval to guarantee the recall ratio. This revised version was published online in June 2006 with corrections to the Cover Date.     

Quantification of the passive and active biaxial mechanical behaviour and microstructural organization of rat thoracic ducts

Mechanical loading conditions are likely to play a key role in passive and active (contractile) behaviour of lymphatic vessels. The development of a microstructurally motivated model of lymphatic tissue is necessary for quantification of mechanically mediated maladaptive remodelling in the lymphatic vasculature. Towards this end, we performed cylindrical biaxial testing of Sprague–Dawley rat thoracic ducts (n = 6) and constitutive modelling to characterize their mechanical behaviour. Spontaneous contraction was quantified at transmural pressures of 3, 6 and 9 cmH₂O. Cyclic inflation in calcium-free saline was performed at fixed axial stretches between 1.30 and 1.60, while recording pressure, outer diameter and axial force. A microstructurally motivated four-fibre family constitutive model originally proposed by Holzapfel et al. (Holzapfel et al. 2000 J. Elast. 61, 1–48. (doi:10.1023/A:1010835316564)) was used to quantify the passive mechanical response, and the model of Rachev and Hayashi was used to quantify the active (contractile) mechanical response. The average error between data and theory was 8.9 ± 0.8% for passive data and 6.6 ± 2.6% and 6.8 ± 3.4% for the systolic and basal conditions, respectively, for active data. Multi-photon microscopy was performed to quantify vessel wall thickness (32.2 ± 1.60 µm) and elastin and collagen organization for three loading conditions. Elastin exhibited structural ‘fibre families’ oriented nearly circumferentially and axially. Sample-to-sample variation was observed in collagen fibre distributions, which were often non-axisymmetric, suggesting material asymmetry. In closure, this paper presents a microstructurally motivated model that accurately captures the biaxial active and passive mechanical behaviour in lymphatics and offers potential for future research to identify parameters contributing to mechanically mediated disease development.