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NASA NTRS2013

A Leonard-Sanders-Budiansky-Koiter-Type Nonlinear Shell Theory with a Hierarchy of Transverse-Shearing Deformations

A detailed exposition on a refined nonlinear shell theory suitable for nonlinear buckling analyses of laminated-composite shell structures is presented. This shell theory includes the classical nonlinear shell theory attributed to Leonard, Sanders, Koiter, and Budiansky as an explicit proper subset. This approach is used in order to leverage the exisiting experience base and to make the theory attractive to industry. In addition, the formalism of general tensors is avoided in order to expose the details needed to fully understand and use the theory. The shell theory is based on "small" strains and "moderate" rotations, and no shell-thinness approximations are used. As a result, the strain-displacement relations are exact within the presumptions of "small" strains and "moderate" rotations. The effects of transverse-shearing deformations are included in the theory by using analyst-defined functions to describe the through-the-thickness distributions of transverse-shearing strains. Constitutive equations for laminated-composite shells are derived without using any shell-thinness approximations, and simplified forms and special cases are presented.

Nemeth, Michael P.↗

NASA NTRSDate not supplied

Higher-Order Approximations for Stabilizing Zero-Energy Modes in Peridynamics Crystal Plasticity Models with Large Horizon Interactions

The non-ordinary state-based peridynamics theory combines non-local dynamic techniques with a desirable correspondence material principle, allowing for the use of continuum mechanics constitutive models. Such an approach presents a unique capability for solving problems involving discontinuities (e.g., strain localization, fracture, and fragmentation). However, the correspondence-based peridynamics models often suffer from zero-energy mode instabilities in numerical implementation, primarily due to the approximations of the non-local deformation gradient tensor. This paper focuses on a computational scheme for eliminating the zero-energy mode oscillations using a choice of influence functions that improve the truncation error in a higher-order Taylor series expansion of the deformation gradient. The novelty here is a tensor-based derivation of the linear constraint equations, which can be used to systematically identify the particle interaction weight functions for various user-specified horizon radii. In this paper, the proposed higher-order stabilization scheme is demonstrated for multi-dimensional examples involving polycrystalline and composite microstructures, along with comparisons against conventional finite element methods. The proposed stabilization scheme is shown to be highly effective in suppressing the spurious zero-energy mode oscillations in all numerical examples while enabling efficient simulations of strain localizations across material interfaces.

Non-Ordinary State-Based Peridynamics↗

NASA NTRS1993

A Modeling Investigation of Thermal and Strain Induced Recovery and Nonlinear Hardening in Potential Based Viscoplasticity

Specific forms for both the Gibb's and the complementary dissipation potentials were chosen such that a complete potential based multiaxial, isothermal, viscoplastic model was obtained. This model in general possesses three internal state variables (two scalars associated with dislocation density and one tensor associated with dislocation motion) both thermal and dynamic recovery mechanisms, and nonlinear kinematic hardening. This general model, although possessing associated flow and evolutionary laws, is shown to emulate three distinct classes of theories found in the literature, by modification of the driving threshold function F. A parametric study was performed on a specialized nondimensional multiaxial form containing only a single tensorial internal state variable (i.e., internal stress). The study was conducted with the idea of examining the impact of including a strain-induced recovery mechanism and the compliance operator, derived from the Gibb's potential, on the uniaxial and multiaxial response. One important finding was that inclusion of strain recovery provided the needed flexibility in modeling stress-strain and creep response of metals at low homologous temperatures, without adversely affecting the high temperature response. Furthermore, for nonproportional loading paths, the inclusion of the compliance operator had a significant influence on the multiaxial response, but had no influence on either uniaxial or proportional load histories.

Arnold, S. M.↗

NASA NTRS1991

Polarized-cathodoluminescence study of uniaxial and biaxial stress in GaAs/Si

The strain-induced splitting of the heavy-hole (hh) and light-hole (lh) valence bands for 4-microns thick GaAs/Si is examined on a microscopic scale using linear polarized-cathodoluminescence imaging and spectroscopy. The energies and intensities of the hh- and lh-exciton luminescence are quantitatively analyzed to determine spatial variations in the stress tensor. The results indicate that regions near and far from the microcracks are primarily subject to uniaxial and biaxial tensile stresses, respectively. The transition region where biaxial stress gradually converts to uniaxial stress is analyzed, and reveals a mixing of lh and hh characters in the strain-split bands.

Rich, D. H.↗

NASA NTRS1990

A simple nonlinear model for the return to isotropy in turbulence

A quadratic nonlinear generalization of the linear Rotta model for the slow pressure-strain correlation of turbulence is developed. The model is shown to satisfy realizability and to give rise to no stable nontrivial equilibrium solutions for the anisotropy tensor in the case of vanishing mean velocity gradients. The absence of stable nontrivial equilibrium solutions is a necessary condition to ensure that the model predicts a return to isotropy for all relaxational turbulent flows. Both the phase space dynamics and the temporal behavior of the model are examined and compared against experimental data for the return to isotropy problem. It is demonstrated that the quadratic model successfully captures the experimental trends which clearly exhibit nonlinear behavior. Direct comparisons are also made with the predictions of the Rotta model and the Lumley model.

Sarkar, Sutanu↗

NASA NTRS1992

Renormalization group analysis of the Reynolds stress transport equation

The pressure velocity correlation and return to isotropy term in the Reynolds stress transport equation are analyzed using the Yakhot-Orszag renormalization group. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a fast pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constant are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of driving higher order nonlinear models by approximating the sums more accurately.

Rubinstein, R.↗

NASA NTRS1992

Renormalization group methods for the Reynolds stress transport equations

The Yakhot-Orszag renormalization group is used to analyze the pressure gradient-velocity correlation and return to isotropy terms in the Reynolds stress transport equations. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a rapid pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constants are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of deriving higher order nonlinear models by approximating the sums more accurately. The Yakhot-Orszag renormalization group provides a systematic procedure for deriving turbulence models. Typical applications have included theoretical derivation of the universal constants of isotropic turbulence theory, such as the Kolmogorov constant, and derivation of two equation models, again with theoretically computed constants and low Reynolds number forms of the equations. Recent work has applied this formalism to Reynolds stress modeling, previously in the form of a nonlinear eddy viscosity representation of the Reynolds stresses, which can be used to model the simplest normal stress effects. The present work attempts to apply the Yakhot-Orszag formalism to Reynolds stress transport modeling.

Rubinstein, R.↗

NASA NTRS1989

A simple nonlinear model for the return to isotropy in turbulence

A quadratic nonlinear generalization of the linear Rotta model for the slow pressure-strain correlation of turbulence is developed. The model is shown to satisfy realizability and to give rise to no stable non-trivial equilibrium solutions for the anisotropy tensor in the case of vanishing mean velocity gradients. The absence of stable non-trivial equilibrium solutions is a necessary condition to ensure that the model predicts a return to isotropy for all relaxational turbulent flows. Both the phase space dynamics and the temporal behavior of the model are examined and compared against experimental data for the return to isotropy problem. It is demonstrated that the quadratic model successfully captures the experimental trends which clearly exhibit nonlinear behavior. Direct comparisons are also made with the predictions of the Rotta model and the Lumley model.

Sarkar, Sutanu↗

NASA NTRS1989

Reynolds stress development in pressure-driven three-dimensional turbulent boundary layers

The development of the Reynolds stress field was studied for flows in which an initially two-dimensional boundary layer was skewed sideways by a spanwise pressure gradient ahead of an upstream-facing wedge. Two different wedges were used, providing a variation in the boundary-layer skewing. Measurements of all components of the Reynolds stress tensor and all ten triple products were measured using a rotatable cross-wire anemometer. The results show the expected lag of the shear stress vector behind the strain rate. Comparison of the two present experiments with previous data suggests that the lag can be estimated if the radius of curvature of the free-stream streamline is known. The magnitude of the shear stress vector in the plane of the wall is seen to decrease rapidly as the boundary-layer skewing increases. The amount of decrease is apparently related to the skewing angle between the wall and the free stream. The triple products evolve rapidly and profiles in the three-dimensional boundary layer are considerably different than two-dimensional profiles, leaving little hope for gradient transport models for the Reynolds stresses. The simplified model presented by Rotta (1979) performs reasonably well providing that an appropriate value of the T-parameter is chosen.

Anderson, Shawn D.↗

NASA NTRS1993

Explicit robust schemes for implementation of general principal value-based constitutive models

The issue of developing effective and robust schemes to implement general hyperelastic constitutive models is addressed. To this end, special purpose functions are used to symbolically derive, evaluate, and automatically generate the associated FORTRAN code for the explicit forms of the corresponding stress function and material tangent stiffness tensors. These explicit forms are valid for the entire deformation range. The analytical form of these explicit expressions is given here for the case in which the strain-energy potential is taken as a nonseparable polynomial function of the principle stretches.

Arnold, S. M.↗

DOE OSTI2023

High-throughput ab initio design of atomic interfaces using InterMatch

Forming a hetero-interface is a materials-design strategy that can access an astronomically large phase space. However, the immense phase space necessitates a high-throughput approach for an optimal interface design. Here we introduce a high-throughput computational framework, InterMatch, for efficiently predicting charge transfer, strain, and superlattice structure of an interface by leveraging the databases of individual bulk materials. Specifically, the algorithm reads in the lattice vectors, density of states, and the stiffness tensors for each material in their isolated form from the Materials Project. From these bulk properties, InterMatch estimates the interfacial properties. We benchmark InterMatch predictions for the charge transfer against experimental measurements and supercell density-functional theory calculations. We then use InterMatch to predict promising interface candidates for doping transition metal dichalcogenide MoSe 2 . Finally, we explain experimental observation of factor of 10 variation in the supercell periodicity within a few microns in graphene/α-RuCl 3 by exploring low energy superlattice structures as a function of twist angle using InterMatch. We anticipate our open-source InterMatch algorithm accelerating and guiding ever-growing interfacial design efforts. Moreover, the interface database resulting from the InterMatch searches presented in this paper can be readily accessed online.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2013

An Exposition on the Nonlinear Kinematics of Shells, Including Transverse Shearing Deformations

An in-depth exposition on the nonlinear deformations of shells with "small" initial geometric imperfections, is presented without the use of tensors. First, the mathematical descriptions of an undeformed-shell reference surface, and its deformed image, are given in general nonorthogonal coordinates. The two-dimensional Green-Lagrange strains of the reference surface derived and simplified for the case of "small" strains. Linearized reference-surface strains, rotations, curvatures, and torsions are then derived and used to obtain the "small" Green-Lagrange strains in terms of linear deformation measures. Next, the geometry of the deformed shell is described mathematically and the "small" three-dimensional Green-Lagrange strains are given. The deformations of the shell and its reference surface are related by introducing a kinematic hypothesis that includes transverse shearing deformations and contains the classical Love-Kirchhoff kinematic hypothesis as a proper, explicit subset. Lastly, summaries of the essential equations are given for general nonorthogonal and orthogonal coordinates, and the basis for further simplification of the equations is discussed.

Nemeth, Michael P.↗

NASA NTRS1987

A nonlinear viscoelastic constitutive equation - Yield predictions in multiaxial deformations

Yield stress predictions of a nonlinear viscoelastic constitutive equation for amorphous polymer solids have been obtained and are compared with the phenomenological von Mises yield criterion. Linear viscoelasticity theory has been extended to include finite strains and a material timescale that depends on the instantaneous temperature, volume, and pressure. Results are presented for yield and the correct temperature and strain-rate dependence in a variety of multiaxial deformations. The present nonlinear viscoelastic constitutive equation can be formulated in terms of either a Cauchy or second Piola-Kirchhoff stress tensor, and in terms of either atmospheric or hydrostatic pressure.

Shay, R. M., Jr.↗

NASA NTRS1989

Viscoplasticity: A thermodynamic formulation

A thermodynamic foundation using the concept of internal state variables is given for a general theory of viscoplasticity, as it applies to initially isotropic materials. Three fundamental internal state variables are admitted. They are: a tensor valued back stress for kinematic effects, and the scalar valued drag and yield strengths for isotropic effects. All three are considered to phenomenologically evolve according to competitive processes between strain hardening, strain induced dynamic recovery, and time induced static recovery. Within this phenomenological framework, a thermodynamically admissible set of evolution equations is put forth. This theory allows each of the three fundamental internal variables to be composed as a sum of independently evolving constituents.

Freed, A. D.↗

NASA NTRS2014

Multi-Scale Computational Modeling of Two-Phased Metal Using GMC Method

A multi-scale computational model for determining plastic behavior in two-phased CMSX-4 Ni-based superalloys is developed on a finite element analysis (FEA) framework employing crystal plasticity constitutive model that can capture the microstructural scale stress field. The generalized method of cells (GMC) micromechanics model is used for homogenizing the local field quantities. At first, GMC as stand-alone is validated by analyzing a repeating unit cell (RUC) as a two-phased sample with 72.9% volume fraction of gamma'-precipitate in the gamma-matrix phase and comparing the results with those predicted by finite element analysis (FEA) models incorporating the same crystal plasticity constitutive model. The global stress-strain behavior and the local field quantity distributions predicted by GMC demonstrated good agreement with FEA. High computational saving, at the expense of some accuracy in the components of local tensor field quantities, was obtained with GMC. Finally, the capability of the developed multi-scale model linking FEA and GMC to solve real life sized structures is demonstrated by analyzing an engine disc component and determining the microstructural scale details of the field quantities.

nickel alloys↗

NASA NTRS1990

Tidal disruption of solid bodies

The problem of stress, strain, and breakup in solid satellites and stray bodies subject to tidal perturbations is presently addressed in view of three novel considerations. After presenting a new analytic solution for the stress tensor in a homogeneous and compressible elastic sphere, where the inclusion of compressibility alters stresses by several percent, realistic failure criteria are noted to demonstrate the general failure of such ductile bodies as iron meteoroids by plastic shear, while brittle ice bodies fail by either tensile or shear fracture. A reexamination of crack propagation after initial failure allows the diverse breakup criteria to be reconciled.

Dobrovolskis, Anthony R.↗

NASA NTRS1997

Mechanical signals in plant development: a new method for single cell studies

Cell division, which is critical to plant development and morphology, requires the orchestration of hundreds of intracellular processes. In the end, however, cells must make critical decisions, based on a discrete set of mechanical signals such as stress, strain, and shear, to divide in such a way that they will survive the mechanical loads generated by turgor pressure and cell enlargement within the growing tissues. Here we report on a method whereby tobacco protoplasts swirled into a 1.5% agarose entrapment medium will survive and divide. The application of a controlled mechanical load to agarose blocks containing protoplasts orients the primary division plane of the embedded cells. Photoelastic analysis of the agarose entrapment medium can identify the lines of principal stress within the agarose, confirming the hypothesis that cells divide either parallel or perpendicular to the principal stress tensors. The coincidence between the orientation of the new division wall and the orientation of the principal stress tensors suggests that the perception of mechanical stress is a characteristic of individual plant cells. The ability of a cell to determine a shear-free orientation for a new partition wall may be related to the applied load through the deformation of the matrix material. In an isotropic matrix a uniaxial load will produce a rotationally symmetric strain field, which will define a shear-free plane. Where high stress intensities combine with the loading geometry to produce multiaxial loads there will be no axis of rotational symmetry and hence no shear free plane. This suggests that two mechanisms may be orienting the division plane, one a mechanism that works in rotationally symmetrical fields, yielding divisions perpendicular to the compressive tensor, parallel to the long axis of the cell, and one in asymmetric fields, yielding divisions parallel to the short axis of the cell and the compressive tensor.

NASA Discipline Number 40-50↗

DOE OSTI2024

The effects of thickness, polarization, and strain on vibrational modes of 2D Fe 3 GeTe 2

In this study, we investigated the effects of thickness, light polarization, and strain on the Raman spectra of two-dimensional (2D) Fe 3 GeTe 2 (FGT) crystals synthesized via chemical vapor transport. The crystals are thoroughly characterized using a combination of microscopic, diffraction, and spectroscopic techniques. Particularly, a systematic angle-resolved polarized Raman spectroscopy study reveals a clear polarization dependence of the Raman intensity in both parallel and crossed polarization directions, with the $A$$^{1}_{g}$ mode completely disappearing in the crossed polarization direction. The angle-dependent intensity of both the $A$$^{1}_{g}$ and $E$$^{2}_{2g}$ modes in parallel polarization and the intensity of the $E$$^{2}_{2g}$ mode in the crossed polarization remain constant at all angles. These findings align with predictions from Raman tensor analysis, providing compelling evidence for the unambiguous assignment of the $A$$^{1}_{g}$ and $E$$^{2}_{2g}$ modes to specific peaks observed in the Raman spectrum of FGT, resolving existing confusion in the literature regarding their assignment. Furthermore, we examine the effect of strain on the Raman spectrum of 2D FGT in-situ using a bending device. Our study, conducted on a monolayer to few-layer 2D FGT deposited onto polyethylene terephthalate and subjected to outward (inward), i.e., tensile (compressive) bending, demonstrates appreciable downshifting (upshifting) of the Raman peak position of both $A$$^{1}_{g}$ and $E$$^{2}_{2g}$ modes. Furthermore, these findings are particularly significant given that strain engineering represents an effective approach to modulate the magnetic properties of FGT and other 2D magnetic materials.

2D materials↗