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Weichen Shi - One of the best experts on this subject based on the ideXlab platform.
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conservation laws from any conformal transformations and the parameters for a sharp v notch in plane elasticity
International Journal of Solids and Structures, 2013Co-Authors: Weichen ShiAbstract:Based on the well known complex Kolosov–Muskhelishvili potentials, two new independent Lagrangian functions are presented and their variational problems lead to two independent harmonic equations, which are also the Navier’s displacement equations in plane elasticity. By applying Noether’s theorem to these Lagrangian functions, it is found that their symmetry-transformation in Material Space is a conformal transformation in planar Euclidean Space. Since any analytic function is a conformal transformation in planar Euclidean Space, the conservation law obtained from this kind of symmetry-transformation possesses universality and leads to a path-independent integral. By adjusting the conformal transformation or analytic function, a finite value can be obtained from calculating this kind of path-independent integral around a Material point with any order singularity. By applying this path-independent integral to the tip of a sharp V-notch, unlike Rice’s J-integral, the parameters of Mode I and II problems are found, which remain invariant because of path independence for a fixed notch opening angle. That is, these two parameters are equivalent to the notch stress intensity factors (NSIFs), and two examples are presented to show the application.
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path independent integral for the sharp v notch in longitudinal shear problem
International Journal of Solids and Structures, 2011Co-Authors: Weichen ShiAbstract:Abstract By applying Noether’s theorem to the elastic energy density in longitudinal shear problem, it is shown that its symmetry-transformations of Material Space can be expressed by the real and imaginary parts of an analytic function. This kind of the symmetry-transformations leads to the existence of a conservation law in Material Space, which does not belong to trivial conservation laws and whose divergence-free expression gives a path-independent integral. It is found that by adjusting the analytic function, a finite value can be obtained from this path-independent integral calculated around the Material point with any order singularity. For a sharp V-notch placed on the edge of homogenous Materials and/or the interface of bi-Materials, application shows that the finite value obtained from this path-independent integral is directly related to the notch stress intensity factor (NSIF) and does not depend on the location of integral endpoints chosen respectively along two traction-free surfaces of which form a notch opening angle. Usability is presented in an example to estimate the NSIF of a bi-Material plate.
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Conservation laws of a decagonal quasicrystal in elastodynamics
European Journal of Mechanics - A Solids, 2005Co-Authors: Weichen ShiAbstract:A special version of Noether's theorem for the sake of absolute invariance on invariant variational principles is used to obtain conservation laws of a three-dimensional solid periodically stacked in a two-dimensional quasiperiodic structure with decagonal symmetry. By applying Lie's infinitesimal criterion on the invariance to the Lagrangian density function under a continuous transformation group, it is found that there exist fourteen conservation laws (nine in physical Space and five in Material Space). Conservation laws in physical Space correspond to the known physical facts. Influence of the phason displacement field on the conservation laws in Material Space is presented. The infinitesimal symmetry-transformations from scale change and translation of coordinates as well as one coordinate rotation are verified to be true. Especially, although the angular momentum conservation laws do not contain the physical quantities in phason field, and the conservation of angular momentum of the phason displacement field itself does not hold, the physical quantities in phason field play an important role in the conservation law in Material Space derived from an infinitesimal coordinate rotation.
Luann Wandsnider - One of the best experts on this subject based on the ideXlab platform.
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On complementarity of practice, scale and structure. Scalar aspects of social/Material Space in Anatolian peri-urban contexts in antiquity
Archaeological Dialogues, 2015Co-Authors: Luann WandsniderAbstract:In his illuminating article, Christophersen rethinks concepts in and approaches to the archaeological study of urban living, focusing especially on medieval urban towns in Scandinavia. He recruits various concepts – interaction, event, leakage and creativity – from a Materially imbued social-practice theory to explore the urban landscapes as a complex of dynamic social Spaces. Christophersen draws from scholars (Hodder 2012 ; Reckwitz 2002 ; Schatzki 1996 ; Shove, Pantzar and Watson 2012 ) who emphasize that practice is routinized behaviour through which actions and events are performed, that practices are tied to a place and timescape, that social actors live with and interact with Materials, and that Materials may be the media of interaction with others. Following Hodder ( 2012 ), he emphasizes that the nature and quality of social and Material relationships lead to the formation and stabilization of practices. In turn, this practice constitutes the town or city.
Chen Greif - One of the best experts on this subject based on the ideXlab platform.
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simulating rigid body fracture with surface meshes
International Conference on Computer Graphics and Interactive Techniques, 2015Co-Authors: Robert Bridson, Chen GreifAbstract:We present a new brittle fracture simulation method based on a boundary integral formulation of elasticity and recent explicit surface mesh evolution algorithms. Unlike prior physically-based simulations in graphics, this avoids the need for volumetric sampling and calculations, which aren't reflected in the rendered output. We represent each quasi-rigid body by a closed triangle mesh of its boundary, on which we solve quasi-static linear elasticity via boundary integrals in response to boundary conditions and loads such as impact forces and gravity. A fracture condition based on maximum tensile stress is subsequently evaluated at mesh vertices, while crack initiation and propagation are formulated as an interface tracking procedure in Material Space. Existing explicit mesh tracking methods are modified to support evolving cracks directly in the triangle mesh representation, giving highly detailed fractures with sharp features, independent of any volumetric sampling (unlike tetrahedral mesh or level set approaches); the triangle mesh representation also allows simple integration into rigid body engines. We also give details on our well-conditioned integral equation treatment solved with a kernel-independent Fast Multipole Method for linear time summation. Various brittle fracture scenarios demonstrate the efficacy and robustness of our new method.
Johannes Schnepp - One of the best experts on this subject based on the ideXlab platform.
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On the Thermodynamic Coupling in the Continuum Theory of Defects
Volume 1: Advanced Computational Mechanics; Advanced Simulation-Based Engineering Sciences; Virtual and Augmented Reality; Applied Solid Mechanics and, 2012Co-Authors: Johannes SchneppAbstract:The well established continuum theory of lattice defects is usually formulated in a three-dimensional Material Space. The defects are represented by differential geometric properties of the Material manifold. Moving defects lead to differential geometric quantities changing with time. This motivates to augment the three Space-like coordinates in the Material Space by a time-like coordinate to a four-dimensional manifold. The lattice vectors of a crystalline solid represent three Space-like vectors in the Material manifold. They can be completed to a tetrad field by a fourth time-like vector. The additional components of the tetrad are related to temperature and heat flux. The derivatives of the Lagrangian density for a hyper-elastic solid with respect to the components of the tetrad can be arranged in a four-dimensional second-order tensor in which entropy density and current are coupled to Material momentum. The representation of entropy production leads to a Cattaneo type constitutive equation for heat transfer.Copyright © 2012 by ASME
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Thermodynamics in Material Space‐time
PAMM, 2011Co-Authors: Johannes SchneppAbstract:The concept of Material forces is well established in the continuum theory of defects. These forces are quantities in a three-dimensional Material manifold. The manifold can be augmented to a four-dimensional Material Space-time by a time-like coordinate. The inelastic phenomena caused by moving defects are highly dissipative. So a thermodynamic theory in Material Space-time seems to be indispensable. Some first steps towards such a theory are developed here. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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A fully covariant four‐dimensional formulation in Material Space‐time
PAMM, 2010Co-Authors: Johannes SchneppAbstract:A fully covariant formulation for a hyperelastic solid as a four-dimensional Space-time manifold is presented. It admits arbitrary coordinate transformations mixing Space and time. The geometrical structure of the manifold is represented by a tetrad field. A variational formulation is given which uses the tetrad field as extra dependent variables. This formulation is able to describe a homogeneous stress state in a defect-free crystal lattice. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
B. Verkin - One of the best experts on this subject based on the ideXlab platform.
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Material Space Motion Time - New Ideas and the Practical Results
2015Co-Authors: F. F. Mende, B. VerkinAbstract:In the article are examined the problems, connected with the determination of such concepts as Space, Material, time. Is introduced the concept of the point of united place, which is only in the Space. The concept of clustering Space, which presents the Space in the form is introduced of clusters with the intended sizes. It is shown that the time is not primary value, which are the length, mass and force, but it depends on the parameters indicated. Is introduced the new system of units, in which the time is expressed through the mass and the length. The concept of the global of counting and global time is introduced. Are given the conversions of electromagnetic pour on upon transfer from the global of counting into the inertial system.
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Material Space Motion Time Phenomenon of Kinetic Energy and Inertia of Material Bodies
2015Co-Authors: F. F. Mende, B. VerkinAbstract:In the article are examined the problems, connected with the determination of such concepts as Space, Material, time. Is introduced the concept of the point of united place, which is only in the Space. The concept of clustering Space, which presents the Space in the form is introduced of clusters with the intended sizes. It is shown that the time is not primary value, which are the length, mass and force, but it depends on the parameters indicated. Is introduced the new system of units, in which the time is expressed through the mass and the length. It is well known that for accelerating the Material bodies it is necessary to spend energy, in this case the executed work passes into the kinetic energy. With the braking the body returns this energy to the surrounding bodies, for which required the forces, the reverse facts, which accelerated body. This is the phenomenon of the inertia. However, nature of this phenomenon was up to now not clear. In the article it is shown that the inertia and kinetic energy of Material bodies are the consequence of the dependence of the scalar potential of charge on the speed.