Martinec-ContinuumMechanics.pdf

... may obtain a relatively simple description, just as in geometry one choice of coordinates may lead to a simple equation for a particular figure. However, the reference configuration itself has nothing to do with the motion it is used to describe, just as the coordinate system has nothing to do with ...

... may obtain a relatively simple description, just as in geometry one choice of coordinates may lead to a simple equation for a particular figure. However, the reference configuration itself has nothing to do with the motion it is used to describe, just as the coordinate system has nothing to do with ...

Dislocation density evolution upon plastic deformation of Al-Pd

... The behaviour at the yield point, described by equations (3)± (7), that is a stress drop accompanied by an increase in the mobile dislocation density, is well known from crystalline materials (Johnston 1962, Alexander and Haasen 1968). In crystals at higher strains the density of dislocations increa ...

... The behaviour at the yield point, described by equations (3)± (7), that is a stress drop accompanied by an increase in the mobile dislocation density, is well known from crystalline materials (Johnston 1962, Alexander and Haasen 1968). In crystals at higher strains the density of dislocations increa ...

Final program with abstracts - Laboratoire de Glaciologie et

... Keynote 1: Evolution of microstructures and textures during deformation and recrystallization Martyn Drury and Gill Pennock Department of Earth Sciences, Utrecht University, PO bus 80.021, 3508TA Utrecht, The Netherlands At elevated temperatures crystalline solids deform and recrystallize by a vari ...

... Keynote 1: Evolution of microstructures and textures during deformation and recrystallization Martyn Drury and Gill Pennock Department of Earth Sciences, Utrecht University, PO bus 80.021, 3508TA Utrecht, The Netherlands At elevated temperatures crystalline solids deform and recrystallize by a vari ...

4 Constitutive Equations

... The kinematic equations introduced in Chapter 2 are essential to describe motion and deformation of a body, whereas the local balance equations of Chapter 3 are the differential equations that determine the time evolution of the wanted fields. Altogether they are not yet a closed set of equations, s ...

... The kinematic equations introduced in Chapter 2 are essential to describe motion and deformation of a body, whereas the local balance equations of Chapter 3 are the differential equations that determine the time evolution of the wanted fields. Altogether they are not yet a closed set of equations, s ...

Engineering Mechanics

... Continuum mechanics is concerned with motion and deformation of material objects, called bodies, under the action of forces. If these objects are solid bodies, the respective subject area is termed solid mechanics, if they are fluids, it is fluid mechanics or fluid dynamics. The mathematical equatio ...

... Continuum mechanics is concerned with motion and deformation of material objects, called bodies, under the action of forces. If these objects are solid bodies, the respective subject area is termed solid mechanics, if they are fluids, it is fluid mechanics or fluid dynamics. The mathematical equatio ...

A QUASI-LINEAR VISCOELASTIC RHEOLOGICAL MODEL FOR

... components made of UHMWPE usually play the role of dampers which absorb the mechanical energy, thus making an implant less vulnerable to a failure. UHMWPE’s mechanical properties are representative for a class of nonlinear viscoelastic polymers, speciﬁcally thermoplastics and thermohardening polymer ...

... components made of UHMWPE usually play the role of dampers which absorb the mechanical energy, thus making an implant less vulnerable to a failure. UHMWPE’s mechanical properties are representative for a class of nonlinear viscoelastic polymers, speciﬁcally thermoplastics and thermohardening polymer ...

Dyadic Tensor Notation

... p in it. Under what conditions can we write (a) pi = ij Ej (b) pi = Ei? Write down the force in each case. Under what conditions can this be written F = grad(E 2=2) ? ...

... p in it. Under what conditions can we write (a) pi = ij Ej (b) pi = Ei? Write down the force in each case. Under what conditions can this be written F = grad(E 2=2) ? ...

Grav. o. Kosm. Exercises No. 5 Notes on the

... there are 20 of them that are independent. This saves some time, in D = 4 it is still a lot of them, and we will have to use tricks every time to make it manageable. But is is good to know how to identify these. Take D = 3, where we have to repeat at least one index (since there are 3 different ones ...

... there are 20 of them that are independent. This saves some time, in D = 4 it is still a lot of them, and we will have to use tricks every time to make it manageable. But is is good to know how to identify these. Take D = 3, where we have to repeat at least one index (since there are 3 different ones ...

212_khr.pdf

... [1] Bykovcev, G.I., & Ivlev, D.D., Plasticity Theory, Vladivostok, Russia, 1998. [2] Khromov, A.I., Localization of plastic strains and fracture of ideal rigid-plastic bodies. Doklady Physics, 43(9), pp. ...

... [1] Bykovcev, G.I., & Ivlev, D.D., Plasticity Theory, Vladivostok, Russia, 1998. [2] Khromov, A.I., Localization of plastic strains and fracture of ideal rigid-plastic bodies. Doklady Physics, 43(9), pp. ...

ON THE DEFINITION OF STRESS RATE1 = Dta"` (1) Since and

... in its instantaneous position, be considered functions of the material coordinates a" and of the time t. The partial derivative of a"'3 with respect to t is called "the convected derivative" by Oldroyd. The components Diaafl so defined form the contravariant components of a tensor, since the functio ...

... in its instantaneous position, be considered functions of the material coordinates a" and of the time t. The partial derivative of a"'3 with respect to t is called "the convected derivative" by Oldroyd. The components Diaafl so defined form the contravariant components of a tensor, since the functio ...

Stress, Strain, Virtual Power and Conservation Principles

... Scalars, vectors and tensors are mathematical entities that are used in applications to represent meaningful physical quantities. Consider two systems of coordinates ui and ui which are related by the coordinate transformation rules described above. Physical quantities of interest can be represente ...

... Scalars, vectors and tensors are mathematical entities that are used in applications to represent meaningful physical quantities. Consider two systems of coordinates ui and ui which are related by the coordinate transformation rules described above. Physical quantities of interest can be represente ...

Stress, Strain, Virtual Power and Conservation Principles

... Scalars, vectors and tensors are mathematical entities that are used in applications to represent meaningful physical quantities. Consider two systems of coordinates ui and ui∗ which are related by the coordinate transformation rules described above. Physical quantities of interest can be represente ...

... Scalars, vectors and tensors are mathematical entities that are used in applications to represent meaningful physical quantities. Consider two systems of coordinates ui and ui∗ which are related by the coordinate transformation rules described above. Physical quantities of interest can be represente ...

CTE3-Script.pdf

... The term on the left hand side is the product of mass times acceleration. The first three terms on the right hand side are the mutual interaction forces among particles of the body. Specifically, σxy is the component of the stress tensor representing force along the x direction acting on a plane who ...

... The term on the left hand side is the product of mass times acceleration. The first three terms on the right hand side are the mutual interaction forces among particles of the body. Specifically, σxy is the component of the stress tensor representing force along the x direction acting on a plane who ...

Suggested solutions to 2015 MEK2500 Mock Exam

... for real, positive constants κ1 , κ2 . Let the Frobenius norm of an n × n matrix A be denoted kAk with ...

... for real, positive constants κ1 , κ2 . Let the Frobenius norm of an n × n matrix A be denoted kAk with ...

# Finite strain theory

In continuum mechanics, the finite strain theory—also called large strain theory, or large deformation theory—deals with deformations in which both rotations and strains are arbitrarily large, i.e. invalidates the assumptions inherent in infinitesimal strain theory. In this case, the undeformed and deformed configurations of the continuum are significantly different and a clear distinction has to be made between them. This is commonly the case with elastomers, plastically-deforming materials and other fluids and biological soft tissue.