A thermodynamic approach to viscoelasticity and plasticity

Summary In the present paper a constitutive equation of rate type is derived from Onsager's theory of non-equilibrium processes. Some simple solutions of the equation are discussed, and it is found that the material at hand exhibits different kinds of relaxation phenomena, normal stress effects, non-Newtonian behaviour, plastic properties as well as the creep and elasticity at small loads.With 6 Figures     

A general approach to conservation laws in viscoelasticity

Summary The equation of motion and the associated Lagrangian density of a linear viscoelastic solid are considered in terms of the Laplace transform of the displacement vector. A generalized form of Noether's theorem is applied where invariance is meant up to a divergence. Then a systematic approach is developed which allows the derivation of conservation laws with non-vanishing densities. As a preliminary application, new conservation laws are found and previous results are recovered.     

An experimental investigation of tensile deformation of round bars

Round specimens of different sizes and made of aluminum and copper were subjected to uniaxial tension; and on the basis of data thus obtained, a semi-empirical approach was developed to analyze tensile deformation and the effects of specimen size there on both before and after the onset of nonuniform deformation. Results reveal that, while a diffused instability sets in as the load approaches its maximum, the initiation of localized neck is delayed well beyond this point. This delay, however, is found to depend on the length as well as the diameter of the specimen.     

The role of ECL2 in CGRP receptor activation: a combined modelling and experimental approach

The calcitonin gene-related peptide (CGRP) receptor is a complex of a calcitonin receptor-like receptor (CLR), which is a family B G-protein-coupled receptor (GPCR) and receptor activity modifying protein 1. The role of the second extracellular loop (ECL2) of CLR in binding CGRP and coupling to Gs was investigated using a combination of mutagenesis and modelling. An alanine scan of residues 271–294 of CLR showed that the ability of CGRP to produce cAMP was impaired by point mutations at 13 residues; most of these also impaired the response to adrenomedullin (AM). These data were used to select probable ECL2-modelled conformations that are involved in agonist binding, allowing the identification of the likely contacts between the peptide and receptor. The implications of the most likely structures for receptor activation are discussed.     

A micromechanical approach to the viscoelasticity of unidirectional hybrid composites

Combination of the well-known rule of mixtures and the classical theory of linear viscoelasticity leads to a stress/strain relation that effectively predicts the viscoelastic behaviour of hybrid composites in uniaxial extension. From this theory, it is shown that the rule of mixtures does not apply directly to the dynamic quantities E_d and tan δ, whereas it can be used directly to correlate the storage and loss moduli of the composite to the properties of its components. The stress/strain relation is experimentally verified under isothermal conditions for a unidirectional, hybrid polyethylene-aramid/epoxy system both in constant strain rate and dynamic forced vibration experiments. The micromechanical model leads to numerical predictions which are in good agreement with experimental data on composite materials in various compositions.     

A flow criterion for oriented polyethylene in tensile deformation

Tensile test specimens were cut from high density polyethylene that had been fully cold drawn. The angle between the tensile axis and the draw direction was varied from 30 to 80° and the specimens were deformed at temperatures between 0 and 120° C. Deformation beyond yield occurred without any work hardening and could be described in terms of a flow criterion. The parameters of the flow criterion were found to be slightly dependent upon the initial orientation angle, but highly temperature sensitive.     

A combined physical and DEM modelling approach to investigate particle shape effects on load movement in tumbling mills

The discrete element method (DEM) which is used to simulate granular flows often assumes spherical shape for particles. This assumption is legitimized by the added complexity of non-spherical shape representation, contact detection and computational cost. In this work, the difference between the dynamics of non-spherical and spherical particles was studied in detail by a combined physical and DEM modeling approach. An in-house developed DEM software called KMPC_DEM©, which was coded to handle non-spherical particles, was used to simulate the behavior of particles. To calibrate the model parameters, a model tumbling mill (100 cm diameter and 10.8 cm length) with one transparent end was used which made accurate photography possible. The tests were performed at filling of 20% and mill speed of 85% of critical speed with steel balls and wood cubes. In the simulation, each cubical particle was represented with clusters of spheres (with identical size) by particle packing algorithm for contact detection and contact-force calculation. Comparison of the simulation and experimental results showed that the difference between the measured and predicted impact toe, shoulder angle and bulk toe angle were 3, 4 and 5°, respectively. The significant change in the charge movement and structure on account of non-spherical particles was reflected in the amount of in-flight charge, and positions of shoulder, impact toe and bulk toe. It found that there was a 17% difference in the amount of in-flight of charge between cubical and spherical particles. The marked difference was attributed to higher interlocking of non-spherical particles in comparison to spherical balls. The results showed that cubical particles participated 5% more in the high energy impact action compared to that of the spherical particles. The simulation computation time increased by 35 times when the shape of particles changed from spherical to cubical.     

A nested modelling approach to infrastructure performance characterisation

Reliable and accurate predictions of infrastructure condition can save significant amounts of money for infrastructure management agencies through better planned maintenance and rehabilitation activities. Infrastructure deterioration is a complicated, dynamic and stochastic process affected by various factors such as design, environmental conditions, material properties, structural capacities and some unobserved variables. Previous researchers have explored different types of modelling techniques, ranging from simple deterministic models to sophisticated probabilistic models, to characterise the deterioration process of infrastructure systems; however, these models have limitations in various aspects. Traditional deterministic models are inadequate to capture the uncertainties associated with infrastructure deterioration processes. State-based probabilistic models can only predict conditions at fixed time points. Time-based probabilistic models require frequent observations that, in practice, are not easy to perform. The goal of this research is to develop a new probabilistic model that is capable of capturing the stochastic nature of infrastructure deterioration, while at the same time avoiding the limitations of previous modelling efforts. The proposed nested model is based on discrete choice model theory. It can be used to predict the probability of an infrastructure system staying at defined condition states by relating an index representing the performance of the infrastructure to a number of explanatory variables that characterise the structural adequacy, traffic loading and environmental conditions of the infrastructure. The proposed model includes different possible implementation paths (sequential versus multinomial) depending on the considered explanatory variables and the available data. In the case study, the proposed probabilistic model is implemented with pavement performance data collected in Texas, yielding promising preliminary results.     

A hybrid approach to multi-scale modelling of cancer

In this paper, we review multi-scale models of solid tumour growth and discuss a middle-out framework that tracks individual cells. By focusing on the cellular dynamics of a healthy colorectal crypt and its invasion by mutant, cancerous cells, we compare a cell-centre, a cell-vertex and a continuum model of cell proliferation and movement. All models reproduce the basic features of a healthy crypt: cells proliferate near the crypt base, they migrate upwards and are sloughed off near the top. The models are used to establish conditions under which mutant cells are able to colonize the crypt either by top-down or by bottom-up invasion. While the continuum model is quicker and easier to implement, it can be difficult to relate system parameters to measurable biophysical quantities. Conversely, the greater detail inherent in the multi-scale models means that experimentally derived parameters can be incorporated and, therefore, these models offer greater scope for understanding normal and diseased crypts, for testing and identifying new therapeutic targets and for predicting their impacts.     

Double necking in polymer tensile deformation

After initial necking of tensile polymer samples the deformation front moves along the gauge length at a stress which is smaller than the yield stress. The still undeformed parts of the sample are therefore subjected to conditions which favour deformation by a creep mechanism. If the extension rate is right, secondary necking becomes possible. Boundary conditions are discussed.     

Environmental crazing and intrinsic tensile deformation in polymethylmethacrylate

The tensile stress-strain behaviour of PMMA was measured from 77 to 350 K in He which provides an inert environment and in N₂, Ar, O₂, CO₂, and water which cause crazing. The effect of the partial pressure of the crazing agent on the tensile properties was measured. It was found that the ratio of the tensile strength in a crazing environment to that in an inert environment depended on temperature and pressure as follows: _c/ _i={P exp (Q/RT)/P*}^–0.13 where P ^* and Q depend on the crazing agent. The critical temperature and pressure which determine when a gas ceases to produce an environmental effect on the tensile strength is given by the condition that P exp (Q/RT)<P ^*. Above 273 K the intrinsic deformation changed from brittle fracture to a combination of intrinsic crazing and shear.     

A study to evaluate and understand the response of aluminum alloy 2026 subjected to tensile deformation

The strain concentration factors were determined for aluminum alloy 2026 in the T3511 temper using multi-hole structural coupon specimens. Samples of the alloy were evaluated for both the 6.25 mm (0.25 in.) thick and 10 mm (0.4 in.) thick specimens and having widths of 50 mm (2 in.) and 100 mm (4 in.), respectively. For the case of the specimens that were 50 mm in width the mechanical tests were conducted for both the open hole and filled hole conditions and the corresponding strain concentration value was determined. Threaded fasteners having collars were used for the case of the filled hole specimens. The fasteners posses a shank diameter that was slightly larger than the nominal hole size in order to provide for some interference. The strain concentration values were evaluated at both the failure strain (ε_f) and the strain at maximum load (ε_max). The average strain concentration value was then used to predict the results for the stack-up tests.     

Failure of polystyrene in tensile and cyclic deformation

The failure of polystyrene in cyclic deformation has been examined and compared with the fracture mechanisms involved in simple tension. The fatigue response can be divided into three discrete life ranges. In the short and intermediate life regions, fracture occurs by the processes of craze formation, craze growth, crack nucleation and crack propagation in a manner analogous to tensile failure. The primary influence of reversed straining is manifest as an acceleration of the crack formation stage of failure. In long life (low stress) fatigue, failure modes dissimilar to the documented craze breakdown pattern of crack nucleation are noted.     

Acoustic emission in hafnium under tensile deformation

The paper addresses the dependence of acoustic emission produced in rolled hafnium GFé-1 under tensile deformation on the material’s structural state. A correlation has been established between the material structure, the level of mechanical properties and the values of acoustic parameters. Acoustic emission in non-recrystallized hafnium under tensile deformation is recorded only at the stages that precede fracture. Upon recrystallization annealing at temperatures of 1123 and 1373 K acoustic emission occurs at all the stages of tensile deformation. The highest level of acoustic emission activity in hafnium is observed during the transition from elastic to elastic-plastic strain.     

A non-local rate-type viscoplastic approach to patterning of deformation

Summary We propose here a new model to the problem of phase transformations which account for micro-structural effects and non-equilibrium phenomena. The model is obtained by incorporating higher-order strain gradients in the relaxation function of a Maxwell's rate-type constitutive equation. This approach can be included in ilhavý's thermodynamical theory of non-simple bodies with internal variables. Explicit necessary and sufficient conditions are given such that the model be fully compatible with the unmodified Clausius-Duhem inequality and balance equations. We show that its elastic set has to be the closure of an open set in the strain-stress-higher strain gradients space, i.e., the model is a viscoplastic one in the sense of Sokolovskii-Malvern. Energy estimates for smooth solutions of strain controlled problems are given. The influence of the viscous mechanism, softening mechanism and of the strain gradients effects on the local behaviour of solutions is investigated. Critical wave lengths for the onset of instability and pattern formation are determined.     

A simple one-dimensional approach to modelling ceramic composite armour defeat

This work develops a simple set of models for the perforation of ceramic composite armour, which highlight the essential physical processes and illustrate approximately the dependency of ballistic resistance on physical properties and impact parameters. The major features of ceramic composite armour failure (viz. fracture conoid formation, dishing failure of thin backing plates, perforation of thick packing plates, and projectile erosion) are combined with a lumping of masses to treat material acceleration to produce simple models which allow computations on ceramic targets with both thin and thick metallic backings. Calculations are compared with a broad range of empirical data and are also used to discuss aspects of the interaction of penetrators with ceramic composite armours. The goos correlation of models with experiment demonstrates the usefulness of the present approach for studying ceramic composite armour defeat.     

A fuzzy-logic-based approach to qualitative safety modelling for marine systems

Safety assessment based on conventional tools (e.g. probability risk assessment (PRA)) may not be well suited for dealing with systems having a high level of uncertainty, particularly in the feasibility and concept design stages of a maritime or offshore system. By contrast, a safety model using fuzzy logic approach employing fuzzy IF–THEN rules can model the qualitative aspects of human knowledge and reasoning processes without employing precise quantitative analyses. A fuzzy-logic-based approach may be more appropriately used to carry out risk analysis in the initial design stages. This provides a tool for working directly with the linguistic terms commonly used in carrying out safety assessment. This research focuses on the development and representation of linguistic variables to model risk levels subjectively. These variables are then quantified using fuzzy sets. In this paper, the development of a safety model using fuzzy logic approach for modelling various design variables for maritime and offshore safety based decision making in the concept design stage is presented. An example is used to illustrate the proposed approach.