scholarly journals 2-D finite displacements and finite strain from PIV analysis of plane-strain tectonic analogue models

2019 ◽  
Author(s):  
David Boutelier ◽  
Christoph Schrank ◽  
Klaus Regenauer-Lieb
Keyword(s):  
Finite Strain ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Small Strain ◽  
Time Lapse ◽  
Complete Characterization ◽  
Image Correlation ◽  
Strain Rate Tensor ◽  
Analogue Models ◽  
Finite Displacements

Abstract. Image correlation techniques have provided new ways to analyze the distribution in space and time of deformation in analogue models of tectonics. Here we demonstrate how the correlation of successive time-lapse images of a deforming model allows not only to evaluate the components of the strain-rate tensor at any time in the model but also calculate the finite displacements and finite strain tensor. We illustrate, using synthetic images, the ability of the algorithm to produce maps of the velocity gradients, small-strain tensor components, but also incremental or instantaneous principal strains and maximum shear. The incremental displacements can then summed up using a Eulerian or a Lagrangian summation, and the components of the 2-D finite strain tensor can be calculated together with the finite principal strain and maximum finite shear. We benchmark the measures of finite displacements using specific synthetic tests for each summation mode. The deformation gradient tensor is calculated from the deformed state, and decomposed into the finite rigid-body rotation and left or right finite stretch tensors, allowing the deformation ellipsoids to be drawn. The finite strain has long been the only quantified measure of strain in analogue models. The presented software package allows producing these finite strain measures while also accessing incremental measures of strain. The more complete characterization of the deformation of tectonic analogue models will facilitate the comparison with numerical simulations and geological data, and help produce conceptual mechanical models.

scholarly journals 2-D finite displacements and strain from particle imaging velocimetry (PIV) analysis of tectonic analogue models with TecPIV

Solid Earth ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 1123-1139 ◽  
Author(s):  
David Boutelier ◽  
Christoph Schrank ◽  
Klaus Regenauer-Lieb
Keyword(s):  
Software Package ◽  
Finite Strain ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Small Strain ◽  
Time Lapse ◽  
Image Correlation ◽  
Strain Rate Tensor ◽  
Analogue Models ◽  
Finite Displacements

Abstract. Image correlation techniques have provided new ways to analyse the distribution of deformation in analogue models of tectonics in space and time. Here, we demonstrate, using a new version of our software package (TecPIV), how the correlation of successive time-lapse images of a deforming model allows not only to evaluate the components of the strain-rate tensor at any time in the model but also to calculate the finite displacements and finite strain tensor. We illustrate with synthetic images how the algorithm produces maps of the velocity gradients, small-strain tensor components, incremental or instantaneous principal strains and maximum shear. The incremental displacements can then be summed up with Eulerian or Lagrangian summation, and the components of the 2-D finite strain tensor can be calculated together with the finite principal strain and maximum finite shear. We benchmark the measures of finite displacements using specific synthetic tests for each summation mode. The deformation gradient tensor is calculated from the deformed state and decomposed into the finite rigid-body rotation and left or right finite-stretch tensors, allowing the deformation ellipsoids to be drawn. The finite strain has long been the only quantified measure of strain in analogue models. The presented software package allows producing these finite strain measures while also accessing incremental measures of strain. The more complete characterisation of the deformation of tectonic analogue models will facilitate the comparison with numerical simulations and geological data and help produce conceptual mechanical models.

A large deformation framework for shape memory polymers: Constitutive modeling and finite element implementation

2012 ◽  
Vol 24 (1) ◽  
pp. 21-32 ◽  
Author(s):  
Mostafa Baghani ◽  
Reza Naghdabadi ◽  
Jamal Arghavani
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Shape Memory ◽  
Finite Deformation ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Shape Memory Polymers ◽  
Small Strain ◽  
Internal Variables

Shape memory polymers commonly experience both finite deformations and arbitrary thermomechanical loading conditions in engineering applications. This motivates the development of three-dimensional constitutive models within the finite deformation regime. In the present study, based on the principles of continuum thermodynamics with internal variables, a three-dimensional finite deformation phenomenological constitutive model is proposed taking its basis from the recent model in the small strain regime proposed by Baghani et al. (2012). In the constitutive model derivation, a multiplicative decomposition of the deformation gradient into elastic and inelastic stored parts (in each phase) is adopted. Moreover, employing the mixture rule, the Green–Lagrange strain tensor is related to the rubbery and glassy parts. In the constitutive model, the evolution laws for internal variables are derived during both cooling and heating thermomechanical loadings. Furthermore, we present the time-discrete form of the proposed constitutive model in the implicit form. Using the finite element method, we solve several boundary value problems, that is, tension and compression of bars and a three-dimensional beam made of shape memory polymers, and investigate the model capabilities as well as its numerical counterpart. The model is validated by comparing the predicted results with experimental data reported in the literature that shows a good agreement.

Fields of a Finite Strain Tensor in the Neighborhood of Discontinuity of the Velocity Field of Displacements under Axisymmetric Strain

2019 ◽  
Vol 945 ◽  
pp. 873-878
Author(s):  
O.V. Kozlova ◽  
E.P. Zharikova ◽  
A.I. Khromov
Keyword(s):  
Free Surface ◽  
Velocity Field ◽  
Finite Strain ◽  
Strain Tensor ◽  
Discontinuity Point ◽  
Axisymmetric Deformation ◽  
Displacement Velocity ◽  
Strain Rate Tensor ◽  
System Of Equations ◽  
Rigid Plastic

The problem of the distribution fields of a finite strain tensor in the neighborhood of points of discontinuities of speeds of movements under axisymmetric strain conditions is considered. The Almansi finite strain tensor is a measure of deformation, the motion of points of discontinuities is assumed to be given from the solution of the problems strain bodies taking into account change geometry of the free surface. The relations defining fields of a tensor the finite strains are obtained by integrating the system of equations, binding components of The Almansi finite strain tensor and strain rate tensor along the trajectory of the movement of the material particles. At the same time features of the displacement velocity field are considered in the form of cross points of characteristics of indicial equations which define displacement velocity field (center of the fan of characteristics for a deformation case in axisymmetric deformation of ideal rigid-plastic bodies conditions). The limiting trajectories of the motion of particles contracting to the discontinuity point are considered.

scholarly journals A study of the progression of damage in an axially loaded Branta leucopsis femur using X-ray computed tomography and digital image correlation

PeerJ ◽  
2017 ◽  
Vol 5 ◽  
pp. e3416 ◽  
Author(s):  
Zartasha Mustansar ◽  
Samuel A. McDonald ◽  
William Irvin Sellers ◽  
Phillip Lars Manning ◽  
Tristan Lowe ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Digital Image Correlation ◽  
Digital Image ◽  
Time Lapse ◽  
Image Correlation ◽  
Long Bone ◽  
Barnacle Goose ◽  
3D Images ◽  
X Ray ◽  
X Ray Computed

This paper uses X-ray computed tomography to track the mechanical response of a vertebrate (Barnacle goose) long bone subjected to an axial compressive load, which is increased gradually until failure. A loading rig was mounted in an X-ray computed tomography system so that a time-lapse sequence of three-dimensional (3D) images of the bone’s internal (cancellous or trabecular) structure could be recorded during loading. Five distinct types of deformation mechanism were observed in the cancellous part of the bone. These were (i) cracking, (ii) thinning (iii) tearing of cell walls and struts, (iv) notch formation, (v) necking and (vi) buckling. The results highlight that bone experiences brittle (notch formation and cracking), ductile (thinning, tearing and necking) and elastic (buckling) modes of deformation. Progressive deformation, leading to cracking was studied in detail using digital image correlation. The resulting strain maps were consistent with mechanisms occurring at a finer-length scale. This paper is the first to capture time-lapse 3D images of a whole long bone subject to loading until failure. The results serve as a unique reference for researchers interested in how bone responds to loading. For those using computer modelling, the study not only provides qualitative information for verification and validation of their simulations but also highlights that constitutive models for bone need to take into account a number of different deformation mechanisms.

scholarly journals Kinematics and Timing Constraints in a Transpressive Tectonic Regime: The Example of the Posada-Asinara Shear Zone (NE Sardinia, Italy)

Geosciences ◽  
2020 ◽  
Vol 10 (8) ◽  
pp. 288
Author(s):  
Rodolfo Carosi ◽  
Alessandro Petroccia ◽  
Salvatore Iaccarino ◽  
Matteo Simonetti ◽  
Antonio Langone ◽  
...  
Keyword(s):  
Shear Zone ◽  
Finite Strain ◽  
Pure Shear ◽  
Deformation Gradient ◽  
Shear Zones ◽  
Temperature Deformation ◽  
Timing Constraints ◽  
Important Variation ◽  
Deformation Phase ◽  
First Time

Detailed geological field mapping, integrated with meso- and microstructural investigations, kinematic of the flow and finite strain analyses, combined with geochronology, are fundamental tools to obtain information on the temperature–deformation–timing path of crystalline rocks and shear zone. The Posada-Asinara shear zone (PASZ) in northern Sardinia (Italy) is a steeply dipping km-thick transpressive shear zone. In the study area, located in the Baronie region (NE Sardinia), the presence of mylonites within the PASZ, affecting high- and medium-grade metamorphic rocks, provides an opportunity to quantify finite strain and kinematic vorticity. The main structures of the study area are controlled by a D2 deformation phase, linked to the PASZ activity, in which the strain is partitioned into folds and shear zone domains. Applying two independent vorticity methods, we detected an important variation in the percentage of pure shear and simple shear along the deformation gradient, that increases from south to north. We constrained, for the first time in this sector, the timing of the transpressive deformation by U–(Th)–Pb analysis on monazite. Results indicate that the shear zone has been active at ~325–300 Ma in a transpressive setting, in agreement with the ages of the other dextral transpressive shear zones in the southern Variscan belt.

A Corotational Elastoplastic Formulation With Subloading Surface Model for Hardening Materials

Volume 1 ◽  
2004 ◽  
Author(s):  
Ali Reza Saidi ◽  
Koichi Hashiguchi
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Simple Shear ◽  
Deformation Theory ◽  
Elastoplastic Deformation ◽  
Strain Tensor ◽  
Surface Model ◽  
Strain Rate Tensor ◽  
Hencky Strain ◽  
Stress Components

In this paper a corotational constitutive model for the large elastoplastic deformation of hardening materials using subloading surface model is formulated. This formulation is obtained by refining the large deformation theory of Naghdabadi and Saidi (2002) adopting the corotational logarithmic (Hencky) strain rate tensor and incorporating it into the subloading surface model of Hashiguchi (1980, 2003) falling within the framework of the unconventional plasticity. As an application of the proposed constitutive model, the large Elastoplastic deformation of simple shear example has been solved and the results have been compared with classical elasto-plastic model using the Hencky strain tensor. Also the effect of the choice of corotational rates on stress components has been studied.

scholarly journals An advanced shell model for the analysis of geometrical and material nonlinear shells

2020 ◽  
Vol 66 (6) ◽  
pp. 1353-1376
Author(s):  
F. Gruttmann ◽  
W. Wagner
Keyword(s):  
Shell Model ◽  
Geometrical Nonlinearity ◽  
Local Equilibrium ◽  
Deformation Gradient ◽  
Computing Time ◽  
Strain Tensor ◽  
Shell Element ◽  
Field Equations ◽  
Residual Vector ◽  
Layered Shells

AbstractIn this paper layered shells subjected to static loading are considered. The displacements of the Reissner–Mindlin theory are enriched by a an additional part. These so-called fluctuation displacements include warping displacements and thickness changes. They lead to additional terms for the material deformation gradient and the Green–Lagrangian strain tensor. Within a nonlinear multi-field variational formulation the weak form of the boundary value problem accounts for the equilibrium of stress resultants and couple resultants, the local equilibrium of stresses, the geometrical field equations and the constitutive equations. For the independent shell strains an ansatz with quadratic shape functions is chosen. This leads to a significant improved convergence behaviour especially for distorted meshes. Elimination of a set of parameters on element level by static condensation yields an element stiffness matrix and residual vector of a quadrilateral shell element with the usual 5 or 6 nodal degrees of freedom. The developed model yields the complicated three-dimensional stress state in layered shells for elasticity and elasto-plasticity considering geometrical nonlinearity. In comparison with fully 3D solutions present 2D shell model requires only a fractional amount of computing time.

FINITE DISPLACEMENTS IN RHEOLOGICAL BODIES

1956 ◽  
Vol 34 (5) ◽  
pp. 498-509 ◽  
Author(s):  
A. E. Scheidegger
Keyword(s):  
Boundary Conditions ◽  
Parameter Space ◽  
Continuous Medium ◽  
Finite Strain ◽  
Equations Of Motion ◽  
Mathematical Formalism ◽  
Mathematical Representations ◽  
Finite Displacements ◽  
Earth’S Interior ◽  
Earth's Interior

The study of the behavior of continuous matter is basic in many disciplines, such as in various branches of engineering and in the study of the Earth's interior. Herein, it is evidently necessary to have a sufficiently general mathematical formalism to encompass the behavior of any type of material under any mechanical conditions. Customary "rheological" theories suffer from various drawbacks; they are either (i) restricted to too specialized "ideal" materials, or (ii) restricted to too special displacements, or (iii) restricted to too specialized mathematical representations. The present paper attempts to fill the need for a summary of the representations of the dynamics of arbitrary materials. The displacement within the continuous medium is described by three "co-ordinate" functions as functions of three "parameters" and of time. Extensive use is made of the fact that, insofar as the expression of any physical statement is concerned, "co-ordinates" and "parameters" are entirely equivalent. Formulas are deduced which enable one to express the boundary conditions, the equations of motion, and any chosen rheological condition in either parameter space or co-ordinate space. The notion of finite strain is scrutinized.

Improvement of heterogeneous deformation measurement in digital image correlation

2017 ◽  
Vol 31 (19-21) ◽  
pp. 1740032
Author(s):  
Huan Shen ◽  
Zhonghan Liang ◽  
Baishun Cheng
Keyword(s):  
Digital Image Correlation ◽  
Digital Image ◽  
Displacement Field ◽  
Large Strain ◽  
Small Strain ◽  
Deformation Measurement ◽  
Image Correlation ◽  
Subset Size ◽  
Information Reduction ◽  
Heterogeneous Deformation

Heterogeneous deformation measurement using traditional digital image correlation (DIC) has times error of homogeneous deformation due to localized complexity. In case of small strain window, displacement field error will substantially corrupt the derived strain. On the contrary, large strain window will induce a reasonable information reduction in particular of heterogeneous deformation. In this paper, a novel parameter was put forward to correct displacement field and select strain subset size dynamically. This parameter was determined by localized displacement field that is called the localized displacement non-uniform intensity [Formula: see text]. In addition, there is a simple and effective method to eliminate the rigid body rotation impact on strain measurement. A series of speckle images containing different heterogeneous deformation are simulated finally. Results show that the accuracy on the displacement and strain field can be substantially improved especially in heterogeneous deformation fields.

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