Superposition Of Strains Research Articles

Anisotropic elasticity studies of work hardening in epilayers

A force formalism is proposed to investigate the interactions between a semicoherent heterophase interface and free surfaces in anisotropic finite-thickness bilayers. The present approach enables the estimation of the mechanical forces acting on interfaces, which arise from inhomogeneous elastic fields between the neighboring materials. These short-range fields are produced by the superposition of coherency strains and the elastic strain fields of dislocation patterns, where the individual Burgers vectors are defined by requiring the global force balance on any internal plane perpendicular to the interfaces. Predictions in heterogeneous free-standing bilayers are compared to results for the homogeneous elasticity problem (i.e., both materials having the same stiffness) and the limiting case of infinite bicrystals. Examples of applications to pure misfit interfaces are given with controlled misfit dislocation spacings by continuously varying the alloy composition. The effect of dislocation density on the stability of semicoherent interfaces interacting with free surfaces is discussed in terms of the change in elastic strain energy of Pt/Pd bilayer systems.

Analytical and Measured Strains in Sunshine Skyway Bridge. II

This paper presents a methodology for the analysis of stage-constructed prestressed-concrete bridges. The method uses the step-by-step superposition of strains and accounts for time-dependent effects including creep, shrinkage, and hardening of concrete and relaxation of prestressing steel. This analytical model has been developed as a synthesis of structural analyses and computations of time-dependent deformations. The predicted strains in the pylons show reasonable agreement with the measured time-dependent strains. The magnitudes of the predicted time-dependent strains in the box-girder segments, including the thermal effects, closely agree with the measured values. Time-dependent deformation relationships are derived for the strain variations for the pylon and segment erection sequence. The analytical model can be used to predict the behavior at any specified time during the construction stages. The methodology is demonstrated with a 10-yr prediction of the time-dependent strains by superposition of t...

Strain analysis of the Ninemile fault zone, western Montana: insights into multiply deformed regions

By means of detailed field mapping and a systematic strain analysis we investigated the development of the Ninemile fault in western Montana. The fault has been considered to be either a Mesozoic or mid-Tertiary strike-slip fault, or a Late Eocene-Early Oligocene normal fault. The rock of the study area experienced a Mesozoic to early Tertiary NE-SW shortening expressed by thrusts, folds, and pervasive cleavage. We estimated total strain by measuring preferred orientation of chlorite grains in samples from within and near the Ninemile fault zone and by calculating the strain according to the March theory. Our goal was to explain how strain accumulated by successive superposition of strains during the two deformation events onto an early compaction strain. In all samples the minimum-elongation direction (= maximum shortening) is nearly vertical. The maximum-elongation directions of all the samples outside the Ninemile shear zone are subperpendicular to the strike of the shear zone, whereas in the shear zone they are either parallel to the strike of the shear zone or form an angle of about 45°. The systematic variation in the principal strain directions is the result of two deformational events expressed by local structures created by early NE-SW shortening and later NE-SW extension. The observed strain requires that the Ninemile fault, a normal fault during the Tertiary, had earlier been either a thrust or a zone of contractional shear deformation, along which there was fault-perpendicular shortening and fault-parallel extension. Although the average value of maximum elongation is greater within the Ninemile shear zone than outside, it varies significantly inside the fault zone, suggesting a highly inhomogeneous strain distribution created by a complex deformation history.

Reflectance anisotropy and syn-deformational coalification of the Jewel seam in the Cadomin area, Alberta, Canada

The Jewel seam of the Cadomin area is complexly folded and cut by several thrust faults. Vitrinite reflectance anisotropy was determined from twenty oriented coal blocks, collected from various structural positions. Five of the blocks have uniaxial anisotropies, five have biaxial positive anisotropies, the remaining ten are biaxial negative. The biaxial coals display maximum reflectance axes parallel to nearby fold axes, which suggests a relationship between vitrinite anisotropy and deformation. The biaxial vitrinite reflectance ellipsoids result from superposition of tectonic strains on a primary, sedimentary burial related, uniaxial anisotropy. A tectonic stress field was probably present during the later stages of sedimentary burial and subsequent deformation. Coalification resulted largely from pre-deformational, sedimentary burial, but the final coalification stage was syn-deformational, as illustrated by the intersection of isorank surfaces and the Jewel seam and the biaxial vitrinite reflectance anisotropy.

Static analysis of thin-walled structures using polynomial and exact solutions. Application to thin-walled pipes

A new finite element procedure for the static analysis of beam thin-walled structures of open or closed cross-section is presented. The method is a combined or mixed one, based on the superposition of beam and shell strains and displacements. An essential part of this work is the development of new shape functions (which are either ‘exact’, or polynomial) for the interpolation of the shell displacements. The above method is applied to the thin-walled curved pipe problem and compared to the von Karman approach. Excellent results are obtained, as well as a drastic reduction of the total number of nodal variables.

Dynamic analysis of thin‐walled structures using polynomial and exact solutions: application to thin‐walled pipes

We present a combined or mixed method for the dynamic analysis of thin‐walled structures, based on the superposition of beam and shell strains and displacements. Polynomial or exact shape functions are used for the interpolation of the shell displacements, while discrete degrees of freedom are introduced instead of the generalized von Karman coefficients. Special attention has been given to the integration schemes, because of the combined beam and shell behaviour of the considered structures. The stability and accuracy of the four‐point integration scheme are studied by using the z‐transform. The method is applied to thin‐walled pipes and is also compared to the von Karman approach.

Superposition of small strains on large deformations as a probe of nonlinear response in polymers

AbstractThe incremental response ΔG(t) obtained by superposing a deformation, Δγ, on a large deformation, γ1, has been determined in step shear experiments for a polyisobutylene solution and for a poly(methylmethacrylate) glass in torsion. For both systems ΔG(t) at γ1 was found to be smaller than the linear viscoelastic modulus, G(t), at zero prestrain. ΔG(t) was found to increase with increasing time, te, after imposition of the large deformation. It was also observed that the “apparent relaxation spectrum” associated with ΔG(t) narrows and shifts to shorter times when compared to the spectrum associated with the linear viscoelastic modulus, ΔG(t). The results for the solution art‐well described by the nonlinear constitutive equation of the BKZ elastic fluid theory. It is found that ΔG(t) for the glass falls between the behavior predicted by the BKZ theory and the linear viscoelastic behavior.

Determination of finite strain from passive initially planar markers deflected in ductile rocks undergoing simultaneous superposition of heterogeneous strains

From an empirical model of strain in ductile heterogeneous shear zones simultaneously undergoing a bulk pure shear, we study the influence of the parameters of the deformation on the shape changes of passive initially planar markers and describe a method for determining the finite strain, and even sometimes the instantaneous strain, from these deflected markers.

Matrix computation of deformed lineation patterns

The superposition of distortional strains on originally small circle lineation loci leads to a range of lineation patterns. Such patterns can be calculated using matrix techniques. Matrix computation, together with modern computer graphics capabilities, greatly facilitate investigation of complex lineation loci. The computational scheme can be used to display the results of a range of geometric combinations of original small circles and superposed strains. The resultant patterns are similar to those found by recent field studies of lineations associated with individual mesoscopic folds. Such deformed loci appear to provide a useful data set for quantitative strain analyses.

Steady state creep in a microstructurally unstable steel

From recent microstructural examination of creep tested and service exposed Fe-0.5 Cr-0.5 Mo-0.25 V steels, it is concluded that they behave as a microstructurally unstable dispersion hardened material. In the absence of creep cavitation, this instability normally leads to pseudo tertiary creep behaviour where the creep rate continuously increases with time. However, under certain low stress testing conditions (30 MPa). extensive secondary creep periods are observed. This linear creep behaviour may be entirely fortuitous, relying on the superposition of strains from two independent creep mechanisms, namely: 1. (a) dislocation propagation in a degenerating material, leading to pseudo tertiary behaviour, and 2. (b) a decreasing strain contribution with time arising from a Nabarro-Herring creep mechanism in the presence of grain boundary particles, (N-H p). This paper critically examines and discusses this supposition. The conclusion reached is that a linear creep process is possible by the N-H p mechanism alone. The dislocation propagation mechanism is essentially suppressed at a strain value near the elastic strain level of the interphase matrix for long periods at engineering conditions.

Elastic and time-dependent effects of aggregate-matrix interaction

Secondary stresses arising from the interaction of the heterogeneous components of concrete are shown to influence the elastic and time-dependent strains in all directions, even under a uniaxial compression. The influence of creep of aggregate and the stress at the aggregate-matrix interface under sustained load are also considered. It is suggested that superposition of strains under multiaxial stress is not valid.