The monodromic Galois groups of the sextic equation of anisotropic elasticity

Anisotropic Elasticity offers for the first time a comprehensive survey of the analysis of anisotropic materials that can have up to twenty-one elastic constants. Focusing on the mathematically elegant and technically powerful Stroh formalism as a means to understanding the subject, the author tackles a broad range of key topics, including antiplane deformations, Green's functions, stress singularities in composite materials, elliptic inclusions, cracks, thermo-elasticity, and piezoelectric materials, among many others. Well written, theoretically rigorous, and practically oriented, the book will be welcomed by students and researchers alike.

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Free pro- $p$ product decompositions of Galois groups

Mathematische Zeitschrift ◽

10.1007/pl00004310 ◽

1997 ◽

Vol 225 (2) ◽

pp. 245-261 ◽

Cited By ~ 7

Author(s):

Ido Efrat

Keyword(s):

Galois Groups

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Anisotropic Elasticity with Matlab

10.1007/978-3-030-66676-7 ◽

2021 ◽

Author(s):

Chyanbin Hwu

Keyword(s):

Anisotropic Elasticity

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First-principles calculations to investigate the anisotropic elasticity and thermodynamic properties of FeAl3 under pressure effect

Results in Physics ◽

10.1016/j.rinp.2021.104361 ◽

2021 ◽

pp. 104361

Author(s):

H.J. Wang ◽

X.P. Su ◽

S.P. Sun ◽

J.H. Wang ◽

Y. Jiang

Keyword(s):

Thermodynamic Properties ◽

First Principles ◽

Pressure Effect ◽

Anisotropic Elasticity ◽

First Principles Calculations

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Viscoelastic phase-field fracture using the framework of representative crack elements

International Journal of Fracture ◽

10.1007/s10704-021-00522-1 ◽

2021 ◽

Author(s):

Bo Yin ◽

Johannes Storm ◽

Michael Kaliske

Keyword(s):

Phase Field ◽

Consistency Condition ◽

Field Method ◽

Anisotropic Elasticity ◽

Phase Field Method ◽

Internal Variables ◽

Crack Model ◽

Material Degradation ◽

Discrete Crack ◽

Deformation State

AbstractThe promising phase-field method has been intensively studied for crack approximation in brittle materials. The realistic representation of material degradation at a fully evolved crack is still one of the main challenges. Several energy split formulations have been postulated to describe the crack evolution physically. A recent approach based on the concept of representative crack elements (RCE) in Storm et al. (The concept of representative crack elements (RCE) for phase-field fracture: anisotropic elasticity and thermo-elasticity. Int J Numer Methods Eng 121:779–805, 2020) introduces a variational framework to derive the kinematically consistent material degradation. The realistic material degradation is further tested using the self-consistency condition, which is particularly compared to a discrete crack model. This work extends the brittle RCE phase-field modeling towards rate-dependent fracture evolution in a viscoelastic continuum. The novelty of this paper is taking internal variables due to viscoelasticity into account to determine the crack deformation state. Meanwhile, a transient extension from Storm et al. (The concept of representative crack elements (RCE) for phase-field fracture: anisotropic elasticity and thermo-elasticity. Int J Numer Methods Eng 121:779–805, 2020) is also considered. The model is derived thermodynamic-consistently and implemented into the FE framework. Several representative numerical examples are investigated, and consequently, the according findings and potential perspectives are discussed to close this paper.

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