A Presentation and Comparison of Two Large Deformation Viscoelasticity Models

1997 ◽  
Vol 119 (3) ◽  
pp. 251-255 ◽  
Author(s):  
Sanjay Govindjee ◽  
Stefanie Reese
Keyword(s):  
Large Deformation ◽  
Plane Strain ◽  
Finite Deformation ◽  
Strain Relaxation ◽  
Elastic Equilibrium ◽  
Alternative Formulation ◽  
Small Perturbations ◽  
Elasto Plasticity

In this paper we present a theory of finite deformation viscoelasticity. The presentation is not restricted to small perturbations from the elastic equilibrium in contrast to many viscoelasticity theories. The fundamental hypothesis of our model is the multiplicative viscoelastic decomposition of Sidoroff (1974). This hypothesis is combined with the assumption of a viscoelastic potential to give a model that is formally similar to finite associative elasto-plasticity. Examples are given to compare the present proposal to an alternative formulation in the literature for the cases of uniaxial plane strain relaxation and creep.

scholarly journals Mapping and classifying large deformation from digital imagery: application to analogue models of lithosphere deformation

2021 ◽  
Author(s):  
Taco Broerse ◽  
Nemanja Krstekanić ◽  
Cor Kasbergen ◽  
Ernst Willingshofer
Keyword(s):  
Large Deformation ◽  
Finite Deformation ◽  
Large Strain ◽  
Shear Zones ◽  
Strike Slip ◽  
Strain Measure ◽  
Lithospheric Deformation ◽  
Analogue Models ◽  
Strain Tensors ◽  
Shape Changes

Summary Particle Image Velocimetry (PIV), a method based on image cross-correlation, is widely used for obtaining velocity fields from time series of images of deforming objects. Rather than instantaneous velocities, we are interested in reconstructing cumulative deformation, and use PIV-derived incremental displacements for this purpose. Our focus is on analogue models of tectonic processes, which can accumulate large deformation. Importantly, PIV provides incremental displacements during analogue model evolution in a spatial reference (Eulerian) frame, without the need for explicit markers in a model. We integrate the displacements in a material reference (Lagrangian) frame, such that displacements can be integrated to track the spatial accumulative deformation field as a function of time. To describe cumulative, finite deformation, various strain tensors have been developed, and we discuss what strain measure best describes large shape changes, as standard infinitesimal strain tensors no longer apply for large deformation. PIV or comparable techniques have become a common method to determine strain in analogue models. However, the qualitative interpretation of observed strain has remained problematic for complex settings. Hence, PIV-derived displacements have not been fully exploited before, as methods to qualitatively characterize cumulative, large strain have been lacking. Notably, in tectonic settings, different types of deformation - extension, shortening, strike-slip - can be superimposed. We demonstrate that when shape changes are described in terms of Hencky strains, a logarithmic strain measure, finite deformation can be qualitatively described based on the relative magnitude of the two principal Hencky strains. Thereby, our method introduces a physically meaningful classification of large 2D strains. We show that our strain type classification method allows for accurate mapping of tectonic structures in analogue models of lithospheric deformation, and complements visual inspection of fault geometries. Our method can easily discern complex strike-slip shear zones, thrust faults and extensional structures and its evolution in time. Our newly developed software to compute deformation is freely available and can be used to post-process incremental displacements from PIV or similar autocorrelation methods.

The Freestream Matching Condition for Stagnation Point Turbulent Flows: An Alternative Formulation

1996 ◽  
Vol 63 (1) ◽  
pp. 95-100 ◽  
Author(s):  
R. Abid ◽  
C. G. Speziale
Keyword(s):  
Plane Strain ◽  
Stagnation Point ◽  
Turbulent Flows ◽  
Ad Hoc ◽  
Matching Condition ◽  
Alternative Formulation ◽  
Mean Velocity ◽  
Turbulent Dissipation ◽  
Alternative Means ◽  
Homogeneous Plane

The problem of plane stagnation point flow with freestream turbulence is examined from a basic theoretical standpoint. It is argued that the singularity which arises in the standard K–ε model results from the use of an inconsistent freestream boundary condition. The inconsistency lies in the implementation of a production-equals-dissipation equilibrium hypothesis in conjunction with a freestream mean velocity field that corresponds to homogeneous plane strain—a turbulent flow for which the standard K–ε model does not predict such a simple equilibrium. The ad hoc adjustment that has been made in the constants of the ε-transport equation to eliminate this singularity is shown to be inconsistent for homogeneous plane-strain turbulence as well as other benchmark turbulent flows. An alternative means to eliminate this singularity—without compromising model predictions in more basic turbulent flows—is proposed based on the incorporation of nonequilibrium vortex stretching effects in the turbulent dissipation rate equation.

A Nonlinear Wound Roll Model Allowing for Large Deformation

1995 ◽  
Vol 62 (4) ◽  
pp. 853-859 ◽  
Author(s):  
R. C. Benson
Keyword(s):  
Numerical Solution ◽  
Large Deformation ◽  
Plane Strain ◽  
Constitutive Law ◽  
Symmetry Condition ◽  
Material Symmetry ◽  
Pressure Measurements ◽  
New Model ◽  
Orthotropic Plane ◽  
Principal Contribution

A new model is developed for predicting the internal loads in a wound roll. The principal contribution is the ability to account for large deformation. This is important for applications that require tightly packed rolls with large interlayer pressure and web compression. A nonlinear, orthotropic, plane-strain, pseudoelastic constitutive law is used. Arguments are made as to why the “material symmetry condition” does not apply to the wound roll. An efficient numerical solution scheme is developed, and a good correlation is achieved with interlayer pressure measurements available in the literature.

The Pattern of Plastic Deformation in a Deeply Notched Bar With Semicircular Roots

1956 ◽  
Vol 23 (1) ◽  
pp. 56-58
Author(s):  
L. Garr ◽  
E. H. Lee ◽  
A. J. Wang
Keyword(s):  
Plastic Deformation ◽  
Free Surface ◽  
Velocity Field ◽  
Plastic Strain ◽  
Plane Strain ◽  
Cross Section ◽  
Finite Deformation ◽  
Large Plastic Strain ◽  
Step Method ◽  
Square Grid

Abstract The plastic deformation in a notched bar with deep semicircular roots pulled in plane strain is determined theoretically. The finite deformation is analyzed according to plastic-rigid theory. The motion is unsteady, and the velocity field at any instant is given in terms of the current geometry of the deformed free surface. A graphical step-by-step method is used to determine the deformation of a square grid scribed on the undeformed cross section. The deformed pattern details the regions of large plastic strain, and may be useful in considering the initiation of fracture cracks.

A theory of minimum plastic spin in crystal mechanics

1989 ◽  
Vol 422 (1862) ◽  
pp. 193-239 ◽  
Keyword(s):  
Uniaxial Tension ◽  
Plane Strain ◽  
Finite Deformation ◽  
Relative Rate ◽  
Crystalline Material ◽  
Atomic Lattice ◽  
Multiple Slip ◽  
Plastic Spin ◽  
Free Extension ◽  
Observed Behaviour

A theory of minimum plastic spin (i. e. minimum relative rate-of-rotation of gross crystalline material and underlying atomic lattice) is proposed for the finite deformation of crystals, consistent with loading conditions and constraints. Three families of multiple-slip configurations of f. c. c. crystals are comprehensively investigated: (i) pure plane strain compression with a [100] axis of free extension; (ii) (110) loading in channel die compression; and (iii) all multiple-slip orientations in uniaxial tension. It is established that, in each case, minimum plastic spin uniquely predicts the experimentally observed behaviour.

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