This work investigated the thermal behavior of a series of thermoplastic poly(ether-urethane)s containing 36-71% by weight hard segments derived from 4,4'-methylene-bisphenylisocyanate and butane-1,4-diol, with poly(tetramethylene oxide) soft segments. In all materials studied, differential scanning calorimetry revealed the presence of a T-1 endotherm similar to 20-30 degrees C above the annealing temperature. Morphological changes during heating were observed using small-angle X-ray scattering; the data was analyzed using "globular" models based on a one-dimensional statistical lattice or the Percus-Yevick description of liquids, both of which appeared to provide good descriptions of these materials. The results indicated that the T-1 endotherm coincided with the onset of morphological changes during heating. Possible explanations are discussed, based on the melting of small hard-segment crystals or an activation energy associated with transient segmental mixing. (c) 2006 Wiley Periodicals, Inc.

SAXS was used to investigate the morphological responses of two commercial thermoplastic poly(ether-co-urethane) elastomers during repeated uniaxial extension and stress-relaxation at constant strain. Experimental data was analysed using a 'globular' morphological model, which has previously been shown to provide a good interpretation of the SAXS from these polymers. The results indicated that microdomain rotation and fragmentation coincided with and may have contributed to the strain-softening observed during the initial deformation cycles and stress relaxation. However, these morphological changes appeared to be largely reversed, when the material was allowed to retract; consequently, they appeared insufficient to account for the dramatic changes in mechanical properties and permanent set observed between the first and second extension cycles. One possible explanation is that the mechanical properties may have been dominated by a few, larger microdomains that were too large to be observed by SAXS. Alternatively, the considerable changes in scattering intensity suggested a mechanism based on the slippage of entanglements as a result of strain-induced segmental mixing.

Polyurethane net substrates (PNS) coupled with deferoxamine (DFO) have been studied to determine the extent of Fe2+ pick-up for use in chronic wound therapy. A m solution of ferrous sulphate (FeSO4) was used to generate ferrous ions similar to those found in chronic wounds. The concentration of Fe as a function of position through the dressings was evaluated using a variety of techniques. Atomic force microscopy (AFM) and energy-filtered transmission electron microscopy (EFTEM) revealed a rough precipitated layer at the surface of activated PNS exposed to FeSO4 solution. Optical microscopy (OM) and backscattered environmental scanning electron microscopy (ESEM) showed a clear layer of Fe3+-enriched material in the surface regions exposed to DFO. The penetration depth of DFO into activated dressings was found to be 20–30 μm. Energy-dispersive X-ray (EDX) analysis was used to approximate the distribution of bound- and unbound-Fe as a function of position within BPNS and DFO-activated dressings after immersing them in a FeSO4 solution for various times. These studies have shown the activity of iron with respect to ionic state in DFO-activated PNS for potential using as dressing for chronic wounds.

Thermoplastic polyurethanes, such as Pellethane 2363 80A™ (Pel80A) and Pellethane 2363 55D™ (Pel55D) are widely used in the medical device industry because of their biological and mechanical properties. However, premature failure in such devices has been observed and attributed to environmental stress cracking (ESC). The current work investigates the possibility of reducing ESC via bulk morphology manipulation. This can be achieved through various processing routes such as solvent-casting (SC) and hot-press quenching (HPQ). The effect of stress on the bulk morphology of Pel55D and Pel80A was evaluated using small-angle X-ray scattering (SAXS) in conjunction with tensile testing. SC samples exhibited greater phase separation compared with HPQ samples. Alignment of hard segment domains became apparent around the point of yield. Onset of ESC with respect to SC and HPQ routines was determined using the Zhao–Stokes glass-wool test with optical (OM) and environment scanning electron microscopy (ESEM). Improvement in biostability of Pel80A was found in HPQ samples compared to those that were SC. A secondary objective of this work was to investigate the effect of acetone pre-treatment on surface morphology. High resolution imaging of acetone treated and untreated SC Pel80A showed significant differences in surface morphology.

Uniaxial stress-strain behavior of a wide range of polyurethane elastomers was compared with current models of rubber-like elasticity. Although the data could be described well by a semi-empirical model, a systematic discrepancy was observed with more theoretically based models. This took the form of an additional energy term during deformation, which depended on the polyurethane composition. Microdomain fragmentation may provide a possible explanation. Alternatively, it may be due to the effects of segmental interactions on the relaxation of polymer chain entanglements during deformation.

Small-angle X-ray scattering data from several experimental and commercial poly(ether urethane) formulations was used to test various scattering models based on different morphologies. The best fits were generally found with 'globular' scattering models based on a distorted one-dimensional lattice or the Percus-Yevick model of liquid structure. Whilst this is not conclusive proof of the morphologies exhibited by the materials studied, these scattering models are roughly consistent with many AFM and TEM studies, which indicated discrete globular or elongated cylindrical microdomains. Moreover, reasons why meandering elongated or finite lamellar microdomains may behave more like globular scattering bodies are discussed. Hence, these models are proposed as a basis for interpreting scattering data from polyurethanes.Other models were unable to fit the observed scattering data adequately. A model based on the weak segregation of copolymers was rejected on the basis of deviations from the observed scattering behaviour in the Porod region. A model based on stacks of ideal (infinite, parallel, flat) lamellae was ruled out, since it was unable to reproduce the observed peak width. The Teubner-Strey model, based on microemulsion structure, was found to be incapable of fitting the data at low q, particularly for strained samples. However, this model appeared to be more successful at reproducing the scattering observed at elevated temperatures. One possible inference is that the morphologies became more akin to microemulsions during heating. (C) 2004 Elsevier Ltd. All rights reserved.

Boron segregation and precipitates were investigated using EFTEM. Chromium borides were identified. Comparison with published results suggests that segregation is mainly of non-equilibrium type. Non-uniform distribution of precipitates can be explained using nucleation theory if the segregation leads to grain-boundary boron concentration only slightly above the solubility limit.

The morphological behaviour of poly(ether-urethane)s undergoing deformation was studied using two-dimensional small-angle X-ray scattering (2D-SAXS). The data was analysed using the Zernike-Prins and Percus-Yevick models, which fitted the data well and indicated morphologies composed of discrete, elongated hard segment (HS) microdomains. Although the formulations contained relatively large HS weight fractions, relatively low volume fractions of scattering bodies were indicated, which implied limited segmental de-mixing. Possible explanations for this were discussed.Curve-fitting the 2D-SAXS data for deformation experiments using the Zernike-Prins model, indicated that HS microdomains initially became aligned with the applied strain and subsequently fragmented. This suggested a morphological basis for the observed mechanical properties of these materials, which will be explored in more detail, in subsequent publications. (C) 2004 Elsevier Ltd. All rights reserved.

The mechanical properties of thermoplastic polyurethanes (TPU) depend upon their composition and the complex two-phase morphologies, which originate from microphase separation of chains segments. In the present work, poly(ether-urethanes) were prepared with hard segment contents from 36% to 71% by weight, by systematically varying the length of the soft-segment macrodiol. Samples were prepared by hot pressing or solvent casting, and the resulting hard- and soft-segment morphologies were characterized by using small-angle x-ray scattering (SAXS) and transmission electron microscopy (TEM). Environmental scanning electron microscopy (ESEM) was used to study the fracture surfaces of TPU samples. The deformation behavior of the morphology was studied in real time, by using 2-dimensional SAXS (2D-SAXS) at the Daresbury synchrotron radiation source. Two distinct mechanisms were identified, with the dominant mechanism in a given material dependent on the copolymer composition and the extent of microphase separation, which developed during processing.

In situations outside those identified with routine elastic structural analysis, there is often a need for formulation in mixed form. Small-deformation elastostatics, expressed in terms of stress, strain, and displacement, is described here in the form of either of two complementary constrained-extremum problems. The set of governing equations and boundary conditions of elastostatics are obtained by an interpretation of the generalized “necessary conditions” for each of these fully mixed variational formulations. While the objectives in the problem statements are bilinear and therefore nonconvex, a simple proof is available to confirm that the solution to these conditions is an extremizer. Extensions of the basic formulation, obtained by the introduction of constraints or optimal relaxations, simulate constitutively nonlinear systems. The mixed formulations also provide a convenient representation of the mechanics requirements in connection with structural optimization.

Journal Article Characterization of Polyurethane Medical Materials Using Electron Microscopy Technique Get access J E Taylor, J E Taylor University of Cambridge, Dept. of Materials Science, Cambridge, UK CB2 3QZ Search for other works by this author on: Oxford Academic Google Scholar P R Laity, P R Laity University of Cambridge, Dept. of Materials Science, Cambridge, UK CB2 3QZ Search for other works by this author on: Oxford Academic Google Scholar S S Wong, S S Wong University of Leeds, IRC, School of Chemistry, Leeds, UK CB Search for other works by this author on: Oxford Academic Google Scholar K Norris, K Norris University of Leeds, IRC, School of Chemistry, Leeds, UK CB Search for other works by this author on: Oxford Academic Google Scholar P Khunkamchoo, P Khunkamchoo University of Leeds, IRC, School of Chemistry, Leeds, UK CB Search for other works by this author on: Oxford Academic Google Scholar A F Johnson, A F Johnson University of Leeds, IRC, School of Chemistry, Leeds, UK CB Search for other works by this author on: Oxford Academic Google Scholar M Cable, M Cable Ranier Technology, Greenhouse Park Innovation Centre, Cambridge, CB1 5AS Search for other works by this author on: Oxford Academic Google Scholar V Chohan, V Chohan Ranier Technology, Greenhouse Park Innovation Centre, Cambridge, CB1 5AS Search for other works by this author on: Oxford Academic Google Scholar G Andrews, G Andrews Ranier Technology, Greenhouse Park Innovation Centre, Cambridge, CB1 5AS Search for other works by this author on: Oxford Academic Google Scholar R E Cameron R E Cameron Ranier Technology, Greenhouse Park Innovation Centre, Cambridge, CB1 5AS Search for other works by this author on: Oxford Academic Google Scholar Microscopy and Microanalysis, Volume 9, Issue S02, 1 August 2003, Pages 18–19, https://doi.org/10.1017/S1431927603440877 Published: 06 August 2003

This note investigates the role of problem formulation in avoiding conputal difficulties. The proposed notion is applied to trusses with stress constraints and to an alternative general approach to topology design.

This paper describes an implementation of recent developments in modelling for the design of continuum structures into a general program for computational solution of such problems. In the basic model, the unrestricted material tensor appears as the design variable. The algorithm for this program is presented and the method of solution is described. The approach is applicable to predict both the optimal unrestricted material design and as well for design with a specified material. In either case, the distributions (fields) of all designable components of the material tensor are predicted. Results are given for 2D and 3D examples, in the form of continuously varying material properties and for various values of volume fraction. The associated zero-one or topology designs are obtained by application of an additional procedure to these results. Comparison against results from earlier approaches indicates that optimization of the material may lead to considerable improvement in structural performance.

This paper presents a variational formulation for the design of elastic structures where the function to be minimized by the optimal design, i.e. the objective, is expressed in abstract form. The resulting statement of necessary conditions is uniformly applicable for all admissible objectives. Both state and adjoint state variables appear directly in the problem statement, and all objectives and the arguments of constraints are scalars. The adjoint pair of state variables appear in symmetric roles via the expression termed “mutual energy". Application of the generalized formulation is demonstrated by treatment of the following examples: design to minimize the maximum value of displacement or to minimize a global measure of stress, design for generalized compliance, design where self-weight is taken into account, and multicriterion design.

An analytical model is presented for the optimal design of linearly elastic continuum structures. To facilitate the expression of the combined analysis and design problem in general form, a basis is introduced covering a general set of energy invariants. Both internal (strain) energy and the expression of generalized cost are represented conveniently in terms of this basis, and as a result the optimality conditions for the design problem have a particularly simple form. Present developments comprise a reinterpretation and an extension of existing models where the design variable is the material modulus tensor, and where “cost” is represented in a general form. The conventional potential energy statement for linear continuum elastostatics is restated in the form of an isoperimetric problem, as a preliminary step. This interpretation of the mechanics is then incorporated in a max-min formulation applicable for the general design of linear continuum structures. To exemplify its application, the model is interpreted as it would apply for certain materials with particular geometric structure, e.g. crystalline forms. Also problems treated earlier where optimal material properties are predicted for the case where unit cost is proportional to the trace of the modulus tensor are identified as examples within the generalized formulation. The application of a recently developed technique to predict optimal black-white structures, i.e. designs having sharp topological features, is considered in the setting of the present generalized model.

The developments reported in this paper relate to the concept of optimal evolutionary remodelling. A variational formulation is presented for the problem of optimal remodel of an arbitrary, given continuum structure, where the modification may be interpreted to represent a strengthening (growth) of or diminishing (resorbtion) from the starting structure. Modification variables have the form of an unrestricted material modulus tensor or a set (mixture) of such tensors. The argument of the isoperimetric constraint is expressed in generalized form, as is the objective. Evolution is simulated as a stepwise process, where each step is determined as an optimal remodel. Both local material properties and load configuration may vary with the process. Necessary and sufficient conditions for the optimal stepwise remodel are identified. Interpretations of the simulation model are compared to known methods for application to growth or degradation in bone.

Problem formulations are presented for the evaluation of upper and lower bounds on the effect of progressive structural degradation. For the purposes of this study, degradation effect is measured by an increase in global structural compliance (flexibility). Thus the stated bounds are given simply by the maximum and minimum values, respectively, of the increase in compliance corresponding to a specified global interval of degradation. Solutions to these optimization problems identify the particular patterns of local degradation associated with the respective “worst case” and “least degrading” interpretations. Several formulations for extremal “loss of stiffness”, each with one or another form of model for local degradation, are compared and evaluated. An isoperimetric constraint controls the degree of loss in overall structural stiffness. Results obtained sequentially for a set of specified, increasing values for the bound in this constraint track the evolution of local degradation. While the full exposition of the paper is written specifically for trussed structures, analogues for the more useful formulations are described as well for the treatment of continuum systems. Implementation of methods for computational solution are described in detail, and computational results are given for the bound solutions corresponding to evolution from a starting structure through to its fully degraded form.

Extremum problem formulations are presented that are applicable for the equilibrium analysis of continuum structures made up of a non-specific, aeleotropic and inhomogeneous, constitutively non-linear material. The formulations are described for linear deformation kinematics, and they amount to generalizations of the classical characterization in terms of potentials for elastostatics with non-linear materials. In one case, a generalized version of the classical minimum potential energy formulation is obtained using a representation of total strain expressed as a linear composition of independent fields. Each such constituent field is to have a separate potential, and the contribution of each constituent is limited by specified constraint. The resulting generalized potential energy formulation for non-linear elasticity provides for the simulation of overall properties for an arbitrary material, in terms of the set of individually specified potential functions. A second formulation provides a generalized model of the classical complementary energy principle. Here total stress is expressed as a composition of independent fields, and there is a separate potential associated with each of these constituent fields. These two problem statements are complementary in concept and in their structure. The net constitutive properites, which are implicit in the models, generally may be non-smooth. In both formulations, load path is represented in terms of a load path (or process) parameter, and this provides for interpretation of the dependence of evolution of response on the form of loading.

A new formulation is presented for mathematical modelling to predict the distribution of material, material properties, and topology for the optimal design of trussed structures. The design problem is cast in a form to minimize a measure ofgeneralized compliance, which is calculated as a sum over the structure of weighted displacement. Member stiffnesses appear as design variables and, starting with a given ground structure, the solution predicts the optimal layout and distribution of stiffness. The isoperimetric constraint in the reformulated problem measures totalcost in generalized form, based on independently specified unit relative cost factors for each truss element. One or another form of optimal design is generated via a process where designated elements in the unit relative cost field are adjusted systematically at each cycle. The generalized cost feature provides as well for the introduction of certain technical constraints into the design problem, e.g. the facility to design around obstacles. Results for each cycle of an algorithm for computational treatment are identified as the solution to a properly posed optimization problem. Computational procedures are demonstrated by the prediction of optimal designs for a variety of truss problems in 2D.

Finite strain elastostatics is expressed for general anisotropic, piecewise linear stiffening materials, in the form of a constrained minimization problem. The corresponding boundary value problem statement is identified with the associated necessary conditions. Total strain is represented as a superposition of variationally independent constituent fields. Net stress-strain properties in the model are implicit in terms of the parameters that define the constituents. The model accommodates specification of load fields as functions of a process parameter.