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Topic: Finite deformation tensors

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curvature tensor

tensor field

tensor algebra

tensor product of fields

Classical treatment of tensors

Tensor intrinsic definition

Tensor product of R algebras

Intermediate treatment of tensors

Component free treatment of tensors

Ricci tensor

rank of a tensor

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	Deformation - Wikipedia, the free encyclopedia
		In engineering mechanics, deformation is a change in shape due to an applied force.
		In the figure it can be seen that the compressive loading (indicated by the arrow) has caused deformation in the cylinder so that the original shape (dashed lines) has changed (deformed) into one with bulging sides.
		Perhaps the material with the largest plastic deformation range is wet chewing gum, which can be stretched dozens of times its original length.
	en.wikipedia.org /wiki/Deformation (695 words)

	Application of tensor theory in engineering s... - Wikipedia, the free encyclopedia
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	en.wikipedia.org /wiki/Application_of_tensor_theory_in_engineering_s... (184 words)

	From progressive to finite deformation and back
		It is widely accepted that any finite strain recorded in the field may be interpreted in terms of the simultaneous combination of a pure shear component with one or several simple shear components.
		The finite deformation tensor is given by D = exp (LΔt), where LΔt is the time-integrated velocity gradient tensor.
		Interestingly, certain deformation tensors, though geologically sensible, have no real logarithm and so cannot be explained by a deformation history implying strain rate components with a common time dependence.
	www.agu.org /pubs/crossref/2004/2001JB001734.shtml (374 words)

	BME 332: Strain/Deformation
		The first step in defining large deformation strain measures is to define the relationship between what is known as the reference, initial or undeformed configuration of a body, and the deformed configuration of the body.
		One way we can do this is to use the deformation gradient tensor, which gives the material vector dx in the deformed configuration in terms of the material vector dx' in the reference configuration.
		In addition to the finite strain tensor, other deformation tensors are oftern defined in terms of the deformation gradient tensor.
	www.engin.umich.edu /class/bme456/ch3strain/bme332straindef.htm (3457 words)

	Transformation Properties of the Lagrangian and Eulerian Strain Tensors - Storming Media
		Abstract: A coordinate independent derivation of the Eulerian and Lagrangian strain tensors of finite deformation theory is given based on the parallel propagator, the world function, and the displacement vector field as a three- point tensor.
		The Eulerian strain is a two-point tensor that transforms as a second rank tensor under transformation of spatial coordinates and transforms as a scalar under transformation of the material coordinates.
		The Lagrangian strain is a two-point tensor that transforms as a scalar under transformation of spatial coordinates and transforms as a second rank tensor under transformation of the material coordinates.
	www.stormingmedia.us /17/1760/A176004.html (180 words)

	deformation (Site not responding. Last check: 2007-10-11)
		Deformation is a change in shape due to an applied force.
		This can be a result of tensile (pulling forces) or of compressive (pushing forces) loads being applied.
		Israel's brutal aggressions, is the last one who has the right to throw out such accusations particularly that the US biased policies and deformation of facts...
	www.33beat.com /deformation.html (368 words)

	Nonlinear Finite Deformation Analysis of Beams and Columns (Site not responding. Last check: 2007-10-11)
		A method for solving the finite-displacement problem of a curved elastic beam with axial, shear, and flexural deformation subject to distributed and point loads is presented.
		In terms of three cross-sectional stress resultants, three Euler equations of equilibrium for the beam are derived with the aid of a variational principle for finite deformation.
		Upon linearization to small strains and the adoption of a linear elastic constitutive relation between the stress and strain tensors, it is shown that the problem is reducible to a single second-order nonlinear ordinary differential equation.
	www.pubs.asce.org /WWWdisplay.cgi?9404537 (190 words)

	references (Site not responding. Last check: 2007-10-11)
		Mesozoic And Cenozoic Deformation Inferred From Seismic Stratigraphy In The Southwestern Intracontinental Palmyride Fold-Thrust Belt, Syria.
		Structure And Deformation Of The Bitlis Suture Near Lake Hazar, Southeastern Turkey.
		Deformation Along The Yammuneh, The Restraining Bend Of The Dead Sea Transform: Paleomagnetic Data And Kinematic Implications.
	atlas.geo.cornell.edu /ctbt/references.html (14779 words)

	3D Image Matching Using a Finite Element Based Elastic Deformation Model (Site not responding. Last check: 2007-10-11)
		The finite element approach requires the different objects in the images to be meshed.
		This is achieved by embedding an image similarity constraint on the deformation field into the minimization scheme that leads to the constitutive equations of the deformation model.
		Within a finite element discretization framework, an elastic body can be approximated as an assemblage of discrete finite elements interconnected at nodal points on the element boundaries.
	www.tele.ucl.ac.be /PEOPLE/mat/Papers/MICCAI99/paper-91.html (2653 words)

	Oxford University Press
		Rheology is the study of the deformation and flow of materials.
		The plastic flow solids, such as molten rock, and the physical properties of complex fluids such as polymers, colloids, foams, gels are among the chief concerns of rheology.
		This text begins with refresher sections on tensor and vector operations and Newtonian fluid mechanics which the students may or may not have retained from their fluid mechanis course (a certain prerequesite to this course), but which are essential to comprehending the material in this subject.
	www.oup.com /ca/isbn/0-19-514166-0 (412 words)

	Seismological Software Library - ORFEUS
		FE programs for modelling deformation in the lithosphers, formulate tectonic hypotheses, fit geodetic data, estimate long-term seismic hazard, rheology.
		Calculates a single component of the displacement field due to a finite or point-source dislocation buried in an elastic half space.
		Computation of deformation induced by earthquakes in a multi-layered elastic crust.
	www.orfeus-eu.org /links/softwarelib.htm (2719 words)

	References
		Gay N C 1968 :The determination of total finite strain in a rock using objects such as deformed pebbles.
		Mukhopadhyay, D 1973: Strain measurements from deformed quartz grains in the slaty rocks from the Ardennes and the Northern Eifel.
		P.F. Williams, D. Jiang: 2000 :The role of initial perturbations in the development of folds in a rock-analogue J Struct Geol, pp 845-856 Wilson, Gilbert, 1961, Tectonic significance of small scale structures and their important to the geologist in the field: Annales de la Société Géologique de Belgique, v.
	www.structural-geology-portal.com /references.html (7675 words)

	Amazon.com: Understanding Rheology (Topics in Chemical Engineering): Books: Faith A. Morrison (Site not responding. Last check: 2007-10-11)
		Rheology--the study of the deformation and flow of matter--deals primarily with the stresses generated during the flow of complex materials including polymers, colloids, foams, and gels.
		Designed as a main text for advanced undergraduate- or graduate-level courses in rheology or polymer rheology, Understanding Rheology is also an ideal self-teaching guide for practicing engineers and scientists who find rheological principles applicable to their work.
		Rheology is the study of the deformation and flow of matter.
	www.amazon.com /exec/obidos/tg/detail/-/0195141660?v=glance (833 words)

	3D Image Matching Using a Finite Element Based Elastic Deformation Model (ResearchIndex)
		If your firewall is blocking outgoing connections to port 3125, you can use these links to download local copies.
		We present a new approach for the computation of the deformation field between three dimensional (3D) images.
		The deformation field minimizes the sum of the squared differences between the images to be matched and is constrained by the physical properties of the different objects represented by the image.
	citeseer.ist.psu.edu /238056.html (485 words)

	GraSMech 2005-2006 : Course #1 (Site not responding. Last check: 2007-10-11)
		Strain; rate of strain; rotation; rate of deformation; polar decomposition; composed transformations; superposition principle; volume changes; incompressibility
		Tensor calculus in curvilinear coordinates; covariant derivatives; curvature; Riemann tensor...
		Particular topics (finite elasticity, plasticity, viscoelastic media, crystals, surface tension and interfacial phenomena,...)
	www.mech.kuleuven.be /GraSMech/adconmec.htm (184 words)

	description (Site not responding. Last check: 2007-10-11)
		Course Objectives: The course will introduce the fundamental principles of mechanics applied to study the physiology of biological systems.
		An introduction to the basic concepts of continuum mechanics will be provided, including index and direct notation, tensors, finite deformation kinematics, stress, the constitutive equation, and the governing conservation laws of mass, momentum and energy applied to deformable continua.
		Rigid body kinematics and dynamics will be introduced in the context of applications in biomechanics.
	www.sci.utah.edu /~weiss/classes/bioen5201_f01/description.html (154 words)

	Ca-Cm
		The goal of this project is to create an integrated framework for creating generalized cellular automata using the object oriented features of C++.
		The CASE tool consists of a classical finite state machine and a visualization system or presentation manager.
		A finite state machine is an abstract system which can exist in any of a discrete set of states or conditions, with the state at any instant characterized by the collective state of all of the individual cells which comprise the machine.
	stommel.tamu.edu /~baum/linuxlist/linuxlist/node11.html (10664 words)

	Micromechanical Modeling of the Finite Deformation of Thermoelastic Multiphase Composites (Site not responding. Last check: 2007-10-11)
		A micromechanical model is proposed for the prediction of nonlinearly thermoelastic, multiphase particulate and/or continuous reinforced composites in which any or all constituents exhibit large strain (finite deformation).
		The analysis provides closed-form representations for the instantaneous mechanical and thermal concentration tensors as well as the effective tangent mechanical and thermal properties of the composite.
		The micromechanical model predictions are assessed by a comparison with an analytical spherical composite model, valid for hydrostatic loadings only.
	gltrs.grc.nasa.gov /cgi-bin/GLTRS/browse.pl?1997/TM-107531.html (228 words)

	Computer Animation Information Page
		Terzopoulos and K. Fleischer, Deformable Models, Visual Computer, 4:306-331, 1988.
		Versatile and efficient techniques for simulating cloth and other deformable objects, Computer Graphics (Proc.
		S. Natsupakpong, Numerical Integration Method in Deformable Object Simulation, Case Western Reserve, 2004.
	www.cse.ohio-state.edu /~parent/animation/index1.html (1825 words)

	D Image Matching Using a Finite Element Based Elastic Deformation Model (ResearchIndex)
		D Image Matching Using a Finite Element Based Elastic Deformation Model (ResearchIndex)
		D Image Matching Using a Finite Element Based Elastic Deformation Model
		@inproceedings{ ferrant99image, author = "Matthieu Ferrant and Simon K. Warfield and Charles R. Guttmann and Robert V. Mulkern and Ferenc A. Jolesz and Ron Kikinis", title = "3D Image Matching Using a Finite Element Based Elastic Deformation Model", booktitle = "{MICCAI}", pages = "202-209", year = "1999", url = "citeseer.ist.psu.edu/387830.html" }
	citeseer.ist.psu.edu /387830.html (220 words)

	ELA Mathematics Directory
		On-Line Tutorials for Finite Mathematics Applied Calculus Finite Mathematics & Applied Calculus
		SOLID 2.0 collision detection library, 3D objects rigid motion & deformation, VRML
		Finite Element Heat and Mass Transfer Code (FEHM) Los Alamos National Laboratory
	www.elapro.net /math.htm (3232 words)

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