Equilibrium Deformation Research Articles

Myriad Radial Cavitating Equilibria in Nonlinear Elasticity

It is shown that every bounded strictly increasing smooth positive function of sufficiently slow growth is the Jacobian of a radial hole creating equilibrium deformation for an appropriately constructed compressible nonlinearly elastic energy.

Theoretical description of dry laser cleaning

Dry laser cleaning (DLC) is considered as an escape from an adhesion potential under the forces induced by thermal expansion. Important temporal and spatial scales are: period of small oscillations τ 0, and equilibrium deformation h 0. Possible cleaning regimes are discussed. With laser pulse duration τ< τ 0 (large particles) removal is due to elastic energy. With τ> τ 0 (small particles) cleaning proceeds in the inefficient inertial force regime. If the fronts of the laser pulse are steep enough, t f⪡ τ 0, cleaning occurs when kinetic energy of the particle exceeds that of adhesion. Utilization of resonance effects by modulation of laser pulse or employing the train of pulses and influence of damping on these regimes are discussed. Effects of the near field focusing by dielectric spheres and decrease in cleaning threshold due to three-dimensional (3D) effects are analyzed and compared with the experimental results for SiO 2 particles on Si surface.

Actinide Neutron-Induced Fission up to 200 MeV

Neutron-induced fission cross sections of U, Np and Pu target nuclides are analyzed in fission/evaporation approximation up to 200 MeV excitation energy. Damping of collective modes contribution to the level density at excitation energies higher than ~20 MeV for saddle and equilibrium deformations is shown to be essential. Effective estimates of intrinsic level densities are obtained. Actinide first-chance fission cross sections of 238U(n, f) and 238U(p, f) reactions are found to be much different. Differences of measured proton- and neutron-induced fission cross sections of 238U are attributed to the influence of the isovector term of the nucleon-nucleus optical potential.

Quasifree electrofission of238U

We present the result of a theoretical study of the quasifree electrofission of ${}^{238}\mathrm{U}.$ The exclusive differential cross sections for the quasifree scattering reaction stage have been calculated in plane wave impulse approximation, using a macroscopic-microscopic approach for the description of the proton bound states. The nuclear shape was parametrized in terms of Cassinian ovoids. The equilibrium deformation parameters have been calculated by minimizing the total nuclear energy. In the calculation the axially deformed Woods-Saxon single-particle potential was used. The obtained single-particle momentum distributions were averaged over the nuclear symmetry axis direction. The occupation numbers were calculated in the BCS approach. The fissility for the single-hole excited states of the residual nucleus ${}^{237}\mathrm{Pa}$ was calculated on the statistical theory grounds, both without taking into account the preequilibrium emission of the particle and with preequilibrium emission in the framework of the exciton model.

Colloidal adhesion of phospholipid vesicles: high-resolution reflection interference contrast microscopy and theory

High-resolution reflection interference contrast microscopy (HR-RICM) was developed for probing the deformation and adhesion of phospholipid vesicles induced by colloidal forces on solid surfaces. The new technique raised the upper limit of the measured membrane–substrate separation from 1 to 4.5 μm and improved the spatial resolution of the heterogeneous contact zones. It was applied to elucidate the effects of wall thickness, pH and osmotic stress on the non-specific adhesion of giant unilamellar vesicles (ULV) and multilamellar vesicles (MLV) on fused silica substrates. By simultaneous cross-polarization light microscopy and HR-RICM measurements, it was observed that ULV with the wall thickness of a single bilayer would be significantly deformed in its equilibrium state on the substrate as the dimension of its adhesive–cohesive zone was 29% higher than the theoretical value of a rigid sphere with the same diameter. Besides, electrostatic interaction was shown as a significant driving force for vesicle adhesions since the reduction in pH significantly increased the degree of deformation of adhering ULV and heterogeneity of the adhesion discs. The degree of MLV deformation on the solid surfaces was significantly less than that of ULV. When the wall thickness of vesicle increased, the dimension of contact zone was reduced dramatically due to the increase of membrane bending modulus. Most important, the adhesion strength of colloidal adhesion approached that of specific adhesion. Finally, the increase of osmotic stress led to the collapse of adhering vesicles on the non-deformable substrate and raised the area of adhesive contact zone. To interpret these results better, the equilibrium deformation of adhering vesicle was modeled as a truncated sphere and the adhesion energy was calculated with a new theory.

Incompressible Elastic Bodies with Non-Convex Energy under Dead-Load Surface Tractions

In this paper we study the equilibrium deformations of an incompressible elastic body with a non-convex strain energy function which is subjected to a homogeneous distribution of dead-load tractions. To determine the stable solutions we consider the mixtures of the phases which minimize the total energy density. In the special case of a trilinear material we discuss the stability of the equilibrium phases in detail. Finally, we show that multiphase solutions are possible when the surface loads correspond to a critical simple shear and we sketch their possible forms.

Transient response of a capsule subjected to varying flow conditions: Effect of internal fluid viscosity and membrane elasticity

The transient deformation of an axisymmetric capsule freely suspended in a pure straining flow is studied, for sudden or periodic variations of the intensity of the rate of strain. The particle Reynolds number is supposed to be very small and the problem is solved numerically by means of the boundary integral method. In the case of a sudden start of flow, the time response of the capsule can be approximated by an exponential function, and is thus characterized by only two parameters: the equilibrium deformation D∞ and the characteristic response time τs. The respective influence of viscosity ratio, membrane elasticity, and initial particle geometry is analyzed. The dynamic response of the capsule subjected to periodic variations of the rate of strain is also studied. The response time τs appears to be an appropriate parameter to estimate the capsule adaptability to changing flow conditions.

A quartz-crystal-embedded split Hopkinson pressure bar for soft materials

A dynamic experimental technique that is three orders of magnitude as sensitive in stress measurement as a conventional split Hopkinson pressure bar (SHPB) has been developed. Experimental results show that this new method is effective and reliable for determining the dynamic compressive stress-strain responses of materials with low mechanical impedance and low compressive strengths, such as elastomeric materials and foams at high strain rates. The technique is based on a conventional SHPB. Instead of a surface strain gage mounted on the transmission bar, a piezoelectric force transducer was embedded in the middle of the transmission bar of a high-strength aluminum alloy to directly measure the weakly transmitted force profile from a soft specimen. In addition, a pulse-shape technique was used for increasing the rise time of the incident pulse to ensure stress equilibrium and homogeneous deformation in the low-impedance and low-strength specimen.

Measurement of the Electric Quadrupole Moment of the 9/2− and 21/2− Isomers in 173Ta

The electric quadrupole moments of the 9/2− and 21/2− isomeric states of 173Ta at 165.8 keV and 1713.2 keV, respectively, were measured as Q(9/2−)=2.92(15) b and Q(21/2−)=6.23(18) b for the first time using the TDPAD technique. A 66 MeV pulsed 12C ion beam from the 15UD pelletron accelerator facility of the Nuclear Science Centre at New Delhi was used in the reaction 165Ho(12C, 4nγ)173Ta. The experimental values of equilibrium deformations β2(9/2−)=0.251(7) and β2(21/2−)=0.391(7) were extracted.

Nonlinear Analysis of Uniform Pantographic Columns in Compression

The linear analysis of a uniform pantographic deployable column shows that, in bending, its behavior is very similar to that of an equivalent solid column, whereas under axial loading the two columns display distinct differences in their force and deformation distributions. The total change in the height of a particular pantographic unit in the deployable structure consists of two parts, one due to relative rotation of bars in the unit and the other to their bending. To account for configuration changes, the internal forces must satisfy the equilibrium of each unit after rotation. The additional pantographic unit deformation due to bending of bars is found to be based on these forces. The set of equilibrium and nonlinear deformation equations is solved iteratively. The deformation-controlled approach for solving this system of equations shows the load maximum in the equilibrium paths that corresponds to the snap-through buckling of the top pantographic unit. It is found that the change in the number of units in the column introduces only minor differences in the equilibrium paths as long as the column height and degree of deployment are kept constant. The axial stiffness of the pantographic column is greatly increased and the snap-through buckling considerably postponed if just one additional constraint is introduced, namely the horizontal link between the two nodes at a particular unit interface. The optimal location of the link is found.

A split Hopkinson bar technique for low-impedance materials

An experimental technique that modifies the conventional split Hopkinson pressure bar has been developed for measuring the compressive stress-strain responses of materials with low mechanical impedance and low compressive strengths such as elastomers at high strain rates. A high-strength aluminum alloy was used for the bar materials instead of steel, and the transmission bar was hollow. The lower Young's modulus of the aluminum alloy and the smaller cross-sectional area of the hollow bar increased the amplitude of the transmitted strain signal by an order of magnitude as compared to a conventional steel bar. In addition, a pulse shaper lengthened the rise time of the incident pulse to ensure stress equilibrium and homogeneous deformation in the low-impedance specimen. Experimental results show that the high strain rate, compressive stress-strain behavior of an elastomeric material can be determined accurately and reliably using this technique.

Steady motions of translating, twisted webs

The literature on thin, narrow axially moving materials is diverse and mature. However, few investigators have studied the behavior of thin, wide translating continua. This paper evaluates the effect of twist on the equilibrium of wide, axially moving webs. A fully non-linear shell theory that incorporates transverse shear strains is developed and used to determine the equilibrium deformation. This model allows for consideration of large, possibly intentional, twist from effects like roller misalignment. The equations of steady motion are reduced by assuming that the twisted web deforms into a right helicoid. The resulting non-linear, ordinary, differential equations are solved both numerically and analytically. The longitudinal, membrane stress increases with the twist. However, in a web with free lateral edges, the lateral, membrane stress is compressive for any twist of its ends. The translation speed acts, by way of centrifugal tensioning, to increase the lateral, membrane stress. Example results highlight the steady response of translating webs with twisted ends.

Elastic surface—substrate interactions

A theory for three–dimensional finite deformations of elastic solids with conforming elastic films attached to their bounding surfaces is described. The Gurtin–Murdoch theory incorporating elastic resistance of the film to strain is generalized to account for the effects of intrinsic flexural resistance. This modification yields a model that can be used to describe equilibrium deformations in the presence of compressive–surface stress fields. An associated variational theory is given and material symmetry considerations are discussed. The theory is illustrated by examples.

Study of the molecular structure of PET films obtained by an inverse stretching process Part 2: crystalline reorganization during longitudinal drawing

The transverse stretching, under a constant drawing force, of a one-way drawn poly(ethylene terephtalate) film has been studied. This type of stretching leads to an equilibrium deformation under load which increases mainly with the applied stress and to a lesser degree with temperature. The crystalline phase of such samples has been characterized using wide-angle X-ray diffraction. The orientation of the chain axis and the normal to the phenylene ring have been analysed as well as the crystalline size, as a function of the draw ratio and the stretching temperature. The crystallinity is constant during stretching. The orientation distribution of the chain axes as well as the length of the crystals shows that the crystals which were preferentially oriented with their c-axes along the first stretching direction rotate rapidly towards the actual draw direction and grow up in length as the stretching proceeds. At the same time, the length of the crystals aligned along the other direction of the film plane decreases rapidly, indicating a break-down of some of these crystals. The orientation in the crystalline phase is uniquely controlled by the draw ratio. No relaxation with temperature is observed. This stretching method is compared with the constant speed drawing of one-way drawn films, where no rotation of large crystallites can be detected.

Relative properties of smooth terminating bands

The relative properties of smooth terminating bands observed in the A ∼ 110 mass region are studied within the effective alignment approach. Theoretical values of ietf are calculated using the configuration-dependent shell-correction model with the cranked Nilsson potential. Reasonable agreement with experiment shows that previous interpretations of these bands are consistent with the present study. Contrary to the case of superdeformed bands, the effective alignments of these bands deviate significantly from the pure single-particle alignments 〈jx〉 of the corresponding orbitals. This indicates that in the case of smooth terminating bands, the effects associated with changes in equilibrium deformations contribute significantly to the effective alignment.

Masses and shapes of heaviest nuclei

Shell effects in the masses of heaviest nuclei, most of which are well deformed, are studied. The main attention is paid to the study of the high-multipolarity components, β 6 0 and β 8 0, of the equilibrium deformation of these nuclei, and of the contribution of these components to the masses of the nuclei. Even-even nuclides with proton numbers Z = 82 – 120 and neutron numbers N = 126 – 190 are considered.

Role of Effective Distance in the Fission Mechanism Study by the Double-energy Measurement for Uranium Isotopes

Fission product kinetic energies were measured by the double-energy method for thermal-neutron fission of 235,233U and proton-induced fission of 238U at the 15.8-MeV excitation. From the obtained energy-mass correlation data, the kinetic-energy distribution was constructed from each mass bin to evaluate the first moment of the kinetic energy for a given fragment mass. The resulting kinetic energy was then converted to the effective distance between the charge centers at the moment of scission. The effective distances deduced for the proton-induced fission was concluded to be classified into two constant values, one for asymmetric and the other for symmetric mode, irrespective of the mass though an additional component was further extracted in the asymmetric mass region. This indicates that the fission takes place via two well-defined saddles, followed by the random neck rupture. On the contrary, the effective distances obtained for thermal-neutron induced fission turned out to lie along the contour line at the same level as the equilibrium deformation in the two-dimensional potential map. This strongly suggests that it is essentially a barrier-penetrating type of fission rather than the over-barrier fission.

Properties of the hypothetical spherical superheavy nuclei

Theoretical results on the ground-state properties of the hypothetical spherical superheavy atomic nuclei are presented and discussed. Even-even isotopes of elements Z=104{minus}120 are considered. Certain conclusions are also drawn for odd-A and odd-odd superheavy nuclei. Results obtained earlier for even-even deformed superheavy nuclei with Z=104{minus}114 are given for completeness. Equilibrium deformation, nuclear mass, {alpha}-decay energy, {alpha}-decay half-life, dynamical fission barrier, as well as spontaneous-fission half-life are considered. {beta}-stability of superheavy nuclei is also discussed. The calculations are based on the macroscopic-microscopic model. A multidimensional deformation space describing axially symmetric nuclear shapes is used in the analysis of masses and decay properties of superheavy nuclei. We determined the boundaries of the region of superheavy nuclei which are expected to live long enough to be detected after the synthesis in a present-day experimental setup. {copyright} {ital 1997} {ital The American Physical Society}

Uniaxial deformation of bridging polymer systems: A Monte Carlo study

A new approach for the equilibrium deformation of three-dimensional chains, that are bigrafted to parallel planes is presented. The underlying lattice Monte Carlo algorithm is the bond fluctuation model. In addition to the excluded-volume interaction of this a priori athermal algorithm, we incorporated external potentials in order to enable direct detection of forces. The whole deformation process is split up into a series of separate steps. Each step consists of a generation process and subsequent relaxation procedures. Stress and strain are simultaneously calculated as time-averaged quantities of sufficiently equilibrated systems. Stress–strain relations ranging from compression to the highly stretched regime were simulated by variation of both chain length, N, and grafting density, σ. In the high-density limit the simulation data agree perfectly with a simple one-dimensional theory. The N and σ dependency of the distance, h0(N,σ), of grafting planes at vanishing force is in qualitative agreement with theoretical predictions for an intermediate regime of σ. The simulated force–length relations are in satisfactory agreement with current scaling predictions.

SMALL OSCILLATIONS OF FINITELY DEFORMED ELASTIC NETWORKS

Linearized equations describing small motions superimposed on finitely deformed equilibrium configurations of elastic networks are derived. The theory is based on the so-called membrane model in which the fibres of the network are assumed to be continuously distributed to form a surface. A consistent linearization method is used to obtain equations of motion valid for arbitrary underlying equilibrium deformations. Modal analysis is performed for a sector of a one-parameter family of hyperbolic paraboloids with non-linearly elastic fibres, and the effect of geometric and material non-linearity on the frequency response of the network is quantified.