Application of material forces to hyperelastostatic fracture mechanics. II. Computational setting

Steinmann, Paul; Ackermann, Dimitri; Barth, Franz Josef

doi:10.1016/s0020-7683(00)00381-4

Cited by 154 publications

(115 citation statements)

References 17 publications

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“…It should be noted that the definitions (29) and (32) can be employed to satisfy the balance equation (16), and therefore the governing equations (21) and (22), or equivalently the system (33), of the material motion problem, but for the computation of the configurational energy these definitions are normally not sufficient. In order to compute the configurational energy or the released energy δ x w mec con , the value of the configurational forces B con t and T con t must be evaluated separately.…”

Section: Formulation In the Deformed Configurationmentioning

confidence: 99%

“…In order to compute the configurational energy or the released energy δ x w mec con , the value of the configurational forces B con t and T con t must be evaluated separately. The definitions (29) and (32) offer us only some assumed but not computed values of these forces and therefore can only be used to evaluate δ x w mec con under some certain conditions. An example of these conditions is the case in which there is no body force b mec t = 0 and the surface force t mec t does not perform work with respect to a change in the undeformed configuration t mec t · δ x � � � = 0, for example in the case the body is loaded by some constant displacement (fixed grip condition).…”

Section: Formulation In the Deformed Configurationmentioning

confidence: 99%

“…Next we use the same approach to extend the formulations of these two problems into nonlinear electro-elastostatics by taking into account both Maxwell's traction and the electric flux on the boundary of the material body. For more details on the material motion problem, its formulation and application, the readers are referred to, for example, [29][30][31][32][33][34][35][36].…”

mentioning

confidence: 99%

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On the spatial and material motion problems in nonlinear electro-elastostatics with consideration of free space

Steinmann

2012

Mathematics and Mechanics of Solids

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In this work the formulation of spatial and material motion problems in nonlinear electro-elastostatics is considered using an energy approach, which takes into account the contribution of the free space surrounding a nonlinearly polarized body undergoing large deformation. The free space can have a huge impact on the electric field and on the deformation field inside a body made of materials with low electric permittivity such as the so-called electronic electroactive polymers (EEAPs). The contribution of the free space can be taken into account by using the electric flux and the Maxwell's traction acting on the boundary of the body. These two quantities can be expressed in terms of a stored energy density function. By using a stored energy density function for both the material body and the (finite or infinite) free space, the governing equations of both spatial and material motion problems are derived by considering the change of energy with respect to a change in the spatial or material configuration. In the spatial motion problem, well-known definitions for electric and mechanical quantities are derived. In the material motion problem, in addition to the derivation of configurational forces, this approach reveals the formulas for the part of energy that is released from the system material body, applied forces in response to a change in the material configuration, which are particularly useful in the study of defects such as crack propagation. The same approach can be used in the case of nonlinear electro-thermo-mechanical coupling and constitutes the direction for future works.

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Section: Formulation In the Deformed Configurationmentioning

confidence: 99%

Section: Formulation In the Deformed Configurationmentioning

confidence: 99%

mentioning

confidence: 99%

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On the spatial and material motion problems in nonlinear electro-elastostatics with consideration of free space

Steinmann

2012

Mathematics and Mechanics of Solids

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“…In this section, the concept of material forces and a finite element-based technique to evaluate material forces is reviewed. For a detailed discussion on material forces, we point to References [14][15][16][17] and to see its application within finite elements the interested reader can refer to References [18,41,42]. …”

Section: Materials Forcesmentioning

confidence: 99%

“…[40,41]. The accuracy of the J-integral hinges on the accuracy of the energy-momentum tensor in the elements connected to the crack-tip.…”

Section: Evaluating the J-integralmentioning

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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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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Fracture Mechanics

Kolednik

2012

Wiley Encyclopedia of Composites

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Fracture mechanics is a continuum mechanics tool for the description of the behavior of cracks in materials and components. The text concentrates on the fundamental understanding of the various parameters that are applied to characterize the crack driving force and the fracture resistance and outlines their physical meanings and their limitations. Then a few important topics are presented, such as the influence of geometry and size on the crack growth resistance, the conditions for unstable crack growth, and the prediction of the crack path. The final focus is the behavior of cracks in inhomogeneous materials, such as composites. Especially interesting here is the understanding, how spatial material property variations influence the crack driving force, since this opens the door for materials and components design, that is, to optimize materials by intentional variations of the material properties so that the fracture resistance increases.

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Application of material forces to hyperelastostatic fracture mechanics. II. Computational setting

Cited by 154 publications

References 17 publications

On the spatial and material motion problems in nonlinear electro-elastostatics with consideration of free space

On the spatial and material motion problems in nonlinear electro-elastostatics with consideration of free space

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

Fracture Mechanics

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