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