Continuum Models for Phase Transitions and Twinning in Crystals

By M. Pitteri, G. Zanzotto. 2002

235 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/5230f3050573ea5329500f2c7c392683e44202b5

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Materials Chemistry

Citations in the corpus

Study of the cofactor conditions: Conditions of supercompatibility between phases (2013, methodology): “This energy density can be related to atomistic theory by the Cauchy-Born rule (Pitteri and Zanzotto, 2003).”
On the Cauchy—Born Rule (2008, background): “Conti and Zanzotto show that one can get a maximal PN by choosing some FD, picking some element in it to serve as a center, taking the orbit of FD under its lattice group, then discarding the boundary of the resulting set: by its definition, a PN is always an open set.”
Discontinuous Galerkin methods for non‐linear elasticity (2006, background): “Martensitic transformations in metals and metal alloys, such as shape memory alloys, are also well described within the non-linear elasticity framework [5, 6].”
A new approach to variational problems with multiple scales (2001, methodology): “As an illustration we study a one-dimensional model that describe the competition between formation of microstructure and highest gradient regularization.”
Interface Propagation and Microstructure Evolution in Phase Field Models of Stress-Induced Martensitic Phase Transformations (2010, background): “A list of components of transformation strain tensors for transformations between various crystal lattices are given, for exam- ple, in Bhattacharya (2004) and Pitteri and Zanzotto (2002).”
The structural performance of the periodic truss (2006, methodology): “The Cauchy–Born hypothesis (Bhattacharya, 2003; Born and Huang, 1954; Maugin, 1992; Pitteri and Zanzotto, 2003) states that the infinitesimal displacement fields of the periodic truss can be additively decomposed into an affine deformation field of the joints as dictated by the macroscopically homog”