Numerical simulation of entangled materials mechanical properties

A general approach to simulate the mechanical behaviour of entangled materials submitted to large deformations is described in this paper. The main part of this approach is the automatic creation of contact elements, with appropriate constitutive laws, to take into account the interactions between fibres. The construction of these elements at each increment, is based on the determination of intermediate geometries in each region where two parts of beams are sufficiently close to be likely to enter into contact. Numerical tests simulating a 90% compression of nine randomly generated samples of entangled materials are given. They allow the identification of power laws to represent the evolutions of the compressive load and of the number of contacts.     

A Micromechanical Approach to Simulate Rubberlike Materials with Damage

A damage approach based on a material model with microstructural evolution is presented. In contrast to phenomenological constitutive laws, the material response is given by mechanisms at the microscale. At first, a micromechanical substructure is chosen, which represents the overall material behaviour. Then the system is described using a micromechanical model. A geometrical modification of the microstructure is allowed to minimize the total energy. Consequently, the global stiffness is reduced. In this context, thermodynamical considerations are based on configurational forces. With the help of the discussed approach, void growth phenomena of materials, which lead to softening behaviour, can be taken into account numerically. In this article, the influence of the microstructure in hyperelastic materials is investigated. Hereby, we discuss evolution methods for small and finite strain problems. Finally, the implementation of this damage approach in an explicit finite element solver is described in detail.     

Rate constitutive equations for computational analyses of textile composite reinforcement mechanical behaviour during forming

Textile composite reinforcements are made up of fibres. Consequently, their mechanical behaviour is a result of the possible sliding and the interactions between the fibres. When they are formed on double curved shapes, these fabrics are submitted to large strains, in particular large in-plane shear. Among the mechanical behaviour models for these textile reinforcements, continuous models are most commonly used for forming simulations because they can be used with standard finite elements. The objective of the present paper is to propose a continuous approach for textile reinforcement deformation analysis based on a rate constitutive equation specific to materials made of fibres. The objective derivative of this constitutive model is defined by the fibre rotation. This constitutive model is implemented in ABAQUS and can be used in most commercial F.E. software. The approach is extended to materials with two-fibre directions in order to perform simulations of woven fabric forming processes. A set of simulations of large deformations of textile composite reinforcements at the mesoscopic scale (deformation of a woven unit cell) and at the macroscopic scale (deep drawing) is presented to show the efficiency of the proposed approach.     

Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms

Previous studies by the authors and their co‐workers show that the structure of equations representing shape Memory Alloy (SMA) constitutive behaviour can be very similar to those of rate‐independent plasticity models. For example, the Boyd–Lagoudas polynomial hardening model has a stress‐elastic strain constitutive relation that includes the transformation strain as an internal state variable, a transformation function determining the onset of phase transformation, and an evolution equation for the transformation strain. Such a structure allows techniques used in rate‐independent elastoplastic behaviour to be directly applicable to SMAs. In this paper, a comprehensive study on the numerical implementation of SMA thermomechanical constitutive response using return mapping (elastic predictor‐transformation corrector) algorithms is presented. The closest point projection return mapping algorithm which is an implicit scheme is given special attention together with the convex cutting plane return mapping algorithm, an explicit scheme already presented in an earlier work. The closest point algorithm involves relatively large number of tensorial operations than the cutting plane algorithm besides the evaluation of the gradient of the transformation tensor in the flow rule and the inversion of the algorithmic tangent tensor. A unified thermomechanical constitutive model, which does not take into account reorientation of martensitic variants but unifies several of the existing SMA constitutive models, is used for implementation. Remarks on numerical accuracy of both algorithms are given, and it is concluded that both algorithms are applicable for this class of SMA constitutive models and preference can only be given based on the computational cost. Copyright © 2000 John Wiley & Sons, Ltd.     

On Using a Dual Bound Approach to Characterize the Yield Behaviour of Porous Ductile Materials Containing Void Clusters

Two constitutive models for porous ductile materials are employed together to predict the yield behaviour of ductile materials containing void clusters. In this dual bound approach, the upper and lower bound constitutive models of Gurson (1977) and Sun and Wang (1989) are each evaluated in order to obtain upper and lower estimates for the material behaviour. By combining these two solutions, a predictive band can be created to capture the experimental variation in the yielding behaviour. Although these constitutive models have been derived with the assumption of a periodic void distribution, real materials contain void clusters that can significantly alter the onset of yielding and fracture. Therefore it is of great interest to determine if using dual constitutive models can produce an acceptable first-order approximation of the yielding behaviour in these materials. In the present work, the upper and lower bound yield loci are superimposed over numerical data available in the literature for the yielding of materials containing void clusters. It is shown that the dual bound approach is able to capture the material behaviour over a wide range of practically encountered stress triaxialities.     

弹性接触颗粒状周期性结构材料力学分析的均匀化方法(Ⅱ) ——宏观均匀化分析

基于文献[1]的工作,给出弹性接触颗粒状组成周期性结构材料宏观力学均匀化分析新方法。该方法的特点是在对材料进行微观分析的基础上建立宏观材料的均匀化非线性数值本构模型,并在此基础上构造宏观分析的一致性方法。给出了数值算例,说明了方法的正确性与有效性。      

On Constructing Retrospective ―X Control Chart Limits

In this paper, we address the issue of constructing retrospective ―X control chart limits so as to control the overall probability of a false alarm at a desired level. The standard approach for constructing limits is shown to result in a large overall probability of a false alarm. We propose that an established technique, the analysis of means (ANOM), be used for constructing the retrospective control limits, especially when the subgroup size is small. We compare the performance of the ANOM control limits with that of Bonferroni‐adjusted standard limits through Monte Carlo simulation experiments, and make recommendations as to when each approach can be used. Copyright © 2004 John Wiley & Sons, Ltd.     

Implementation of a constitutive micromechanical model for damage analysis in glass mat reinforced composite structures

A micromechanical model based on a probabilistic approach is implemented in the finite element code CASTEM 2000 to develop numerical simulations that efficiently predict the overall damaged behaviour of random oriented fibre composites. The proposed damage constitutive model is based upon the generalised Mori and Tanaka scheme and Eshelby's equivalence theory. Damage mechanisms occurring at each composite constituent (fibres, matrix and interface) are associated to Weibull probabilistic functions to model their onset and progressive growth at the microscopic scale level. It is obvious that the damaged behaviour of the composite material depends widely on the microscopic material parameters (fibre length, fibre volume fraction, fibre orientation, …). On one hand, the micromechanical model uses homogenisation techniques which enabled us to link these microscopic parameters to the material behaviour and to evaluate explicitly their influences. On the other hand, the implementation of the derived behaviour law into a finite element code enabled us to reflect on the effect of these microscopic parameters on the overall response of a simple composite structure presenting heterogeneous stress fields. In fact, the damage evolution in each constituent (local scale) and the related stiffness reduction are estimated at any material point (integration point) or node of the considered structure subject to a specific loading. Numerical simulations of a composite plate with a hole under in-plane tension were performed to validate the implementation of the behaviour law. Numerical results have been compared to experimental curves and damage evolutions monitored by acoustic emission techniques. Simulations agree well with experimental results in terms of damage onset and growth.     

A spreadsheet method for calculating work completion time probability distributions of paced or linked assembly lines

This study presents a spreadsheet method for computing the work completion time probability distribution of a linked assembly line with variable station service times. Once developed, this distribution can be used to analyse the probability of completing all work at all stations within a given cycle time on either a linked or mechanically paced assembly line. The method can be used to determine what cycle time to set on a paced line, given a desired workload at each station. Alternately, given a desired cycle time and probability that all work has been completed at each station within the cycle time, the method can be used to determine how much work to allocate to each station on the paced line. The method is simple, easy to use, and works with any continuous or discrete station service time distribution that can be specified in a spreadsheet. Comparisons between the output of the spreadsheet method and simulations of the same system indicate the spreadsheet method is quite accurate. Hence, the method can be useful to both researchers and practitioners working with the design and/or behaviour of linked or paced lines, and it provides an easy-to-use teaching tool for illustrating characteristics of linked or paced assembly lines.     

Analysis of behaviour transitions in tumour growth using a cellular automaton simulation

The authors used computational biology as an approach for analysing the emergent dynamics of tumour growth at cellular level. They applied cellular automata for modelling the behaviour of cells when the main cancer cell hallmarks are present. Their model is oriented to mimic the development of multicellular spheroids of tumour cells. In their modelling, cells have a genome associated with the different cancer hallmarks, indicating if those are acquired as a consequence of mutations. The presence of the cancer hallmarks defines cell states and cell mitotic behaviours. These hallmarks are associated with a series of parameters, and depending on their values and the activation of the hallmarks in each of the cells, the system can evolve to different dynamics. With the simulation tool the authors performed an analysis of the first phases of cancer growth, using different and alternative strategies: firstly, studying the evolution of cancer cells and hallmarks in different representative situations regarding initial conditions and parameters, analysing the relative importance of the hallmarks for tumour progression; secondly, being the focus of this work, inspecting the behaviour transitions when the cancer cells are killed with a given probability during the cellular system progression.Inspec keywords: tumours, cellular biophysics, cancer, cellular automata, probabilityOther keywords: behaviour transition analysis, tumour growth, cellular automaton simulation, computational biology, cellular level, cellular automata, cancer cell hallmarks, multicellular spheroids, tumour cells, cell mitotic behaviours, tumour progression, probability, cellular system progression     

Spread of infectious disease through clustered populations

Networks of person-to-person contacts form the substrate along which infectious diseases spread. Most network-based studies of this spread focus on the impact of variations in degree (the number of contacts an individual has). However, other effects such as clustering, variations in infectiousness or susceptibility, or variations in closeness of contacts may play a significant role. We develop analytic techniques to predict how these effects alter the growth rate, probability and size of epidemics, and validate the predictions with a realistic social network. We find that (for a given degree distribution and average transmissibility) clustering is the dominant factor controlling the growth rate, heterogeneity in infectiousness is the dominant factor controlling the probability of an epidemic and heterogeneity in susceptibility is the dominant factor controlling the size of an epidemic. Edge weights (measuring closeness or duration of contacts) have impact only if correlations exist between different edges. Combined, these effects can play a minor role in reinforcing one another, with the impact of clustering the largest when the population is maximally heterogeneous or if the closer contacts are also strongly clustered. Our most significant contribution is a systematic way to address clustering in infectious disease models, and our results have a number of implications for the design of interventions.