Mechanics in Material Space: With Applications to Defect and Fracture Mechanics

Kienzler, Reinhold; Herrmann, G.; Haslach, HW

doi:10.1115/1.1451102

Cited by 68 publications

(84 citation statements)

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“…In Reference [39], Eshelby showed that the forces acting on a defect in an elastic, homogeneous material can be calculated by integrating the energy-momentum tensor over a contour integral around the defect. These forces are known as 'material' [15,17] or 'configurational' [16] forces. As opposed to physical forces that act over physical space, material forces act on material space and do work in the evolution of defects in material structures; the duality between material and physical forces is presented by Steinmann [40].…”

Section: Materials Forcesmentioning

confidence: 99%

“…Residual-based error estimators measure the error by evaluating the local residual of the differential equation on the element domain and evaluating the flux jump across the element boundaries [13]. Material forces are associated with the Eshelby stress tensor [14][15][16][17], and have been recently used as an error indicator in finite element analysis [18,19].…”

Section: Introductionmentioning

confidence: 99%

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Adaptive computations using material forces and residual-based error estimators on quadtree meshes

Tabarraei

Sukumar

2007

Computer Methods in Applied Mechanics and Engineering

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Quadtree is a hierarchical data structure that is well-suited for h-adaptive mesh refinement. Due to the presence of hanging nodes, classical shape functions are non-conforming on quadtree meshes. In this paper, we use natural neighbor basis functions to construct conforming interpolants on quadtree meshes. To this end, the recently proposed construction of polygonal basis functions is adapted to quadtree elements. A fast technique for calculating stiffness matrix on quadtree meshes is introduced. Residual-based error estimators and material force technique are used to estimate the error on quadtree meshes. The performance of the adaptive technique is demonstrated through the solution of linear and nonlinear boundary-value problems.

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Section: Materials Forcesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive computations using material forces and residual-based error estimators on quadtree meshes

Tabarraei

Sukumar

2007

Computer Methods in Applied Mechanics and Engineering

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“…In material theories of modern mechanics -especially the ones based on the concept of material manifold (see e.g. [14,26]) -only the substantial time derivative appear. Experience shows that there is no need any of the objective derivatives of the deformation gradient χ t in finite strain mechanics with or without memory.…”

Section: Discussionmentioning

confidence: 99%

Absolute time derivatives

Matolcsi

Ván

2007

Journal of Mathematical Physics

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A four dimensional treatment of nonrelativistic space-time gives a natural frame to deal with objective time derivatives. In this framework some well known objective time derivatives of continuum mechanics appear as Lie-derivatives. Their coordinatized forms depends on the tensorial properties of the relevant physical quantities. We calculate the particular forms of objective time derivatives for scalars, vectors, covectors and different second order tensors from the point of view of a rotating observer. The relation of substantial, material and objective time derivatives is treated.

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“…Further information on configurational forces, stress intensity factors and their relation can be found in Müller et al (2002), Seelig (2011), Maugin (1993), Steinmann and Maugin (2010), Gurtin (1999) and Kienzler and Herrmann (2000).…”

Section: Interpretation Of Discrete Configurational Forcesmentioning

confidence: 99%

Evaluation of the criticality of cracks in ice shelves using finite element simulations

et al. 2012

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Abstract. The ongoing disintegration of large ice shelf parts in Antarctica raise the need for a better understanding of the physical processes that trigger critical crack growth in ice shelves. Finite elements in combination with configurational forces facilitate the analysis of single surface fractures in ice under various boundary conditions and material parameters. The principles of linear elastic fracture mechanics are applied to show the strong influence of different depth dependent functions for the density and the Young's modulus on the stress intensity factor K I at the crack tip. Ice, for this purpose, is treated as an elastically compressible solid and the consequences of this choice in comparison to the predominant incompressible approaches are discussed. The computed stress intensity factors K I for dry and water filled cracks are compared to critical values K Ic from measurements that can be found in literature.

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Mechanics in Material Space: With Applications to Defect and Fracture Mechanics

Abstract: The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and reguIations and therefore free general use.

Cited by 68 publications

References 0 publications

Adaptive computations using material forces and residual-based error estimators on quadtree meshes

Adaptive computations using material forces and residual-based error estimators on quadtree meshes

Absolute time derivatives

Evaluation of the criticality of cracks in ice shelves using finite element simulations

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