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Modulated martensites play an important role in magnetic shape memory alloys, because all functional properties are closely connected to the twin microstructure and the phase boundary. The nature of the modulated martensites is still…
Magnetic shape-memory (MSM) Heuslers show a strong coupling between magnetic and structural characteristics, evidencing a correlation between magnetic, thermal, and mechanical properties through a magnetostructural martensitic…
Using reflection positivity techniques we prove the existence of minimizers for a class of mesoscopic free-energies representing 1D systems with competing interactions. All minimizers are either periodic, with zero average, or of constant…
We report a detailed numerical investigation of a recently introduced two dimensional model for square-to-rectangle martensitic transformation that explains several unusual features of the martensitic transformation. This model includes…
In a magnetic shape memory alloy system, we vary composition following phenomenological arguments to tune macroscopic properties. We achieve significantly higher shift in austenite to martensitic phase transition temperature with magnetic…
Additive manufacturing of Ti-6Al-4V alloy via laser powder-bed fusion leads to non-equilibrium $\alpha'$ martensitic microstructures, with high strength but poor ductility and toughness. These properties may be modified by heat treatments,…
Shape memory alloys (SMAs) exhibit hysteresis behaviors upon stress and temperature induced loadings. In this contribution, we focus on numerical simulations of microstructure evolution of cubic-to-tetragonal martensitic phase…
We present a practical algorithm for partially relaxing multiwell energy densities such as pertain to materials undergoing martensitic phase transitions. The algorithm is based on sequential lamination, but the evolution of the…
Direct experimental characterization of indentation-induced martensitic microstructures in pseudoelastic shape memory alloys (SMAs) is not possible, and thus there is a lack of evidence and understanding regarding the microstructure pattern…
Inspired by Lin-Pan-Wang (Comm. Pure Appl. Math., 65(6): 833-888, 2012), we continue to study the corresponding time-independent case of the Keller-Rubinstein-Sternberg problem. To be precise, we explore the asymptotic behavior of…
We aim to study the solutions of a fractional mesoscopic model of phase transitions in a periodic medium. After investigating the geometric properties of the interface of the associated minimal solutions, we construct minimal interfaces…
In a previous work a model was proposed for the phase transitions of crystals with localized magnetic moments which at low temperature have a "conical" arrangement that at higher T transforms into a more symmetrical structure (depending on…
We analyze generic sequences for which the geometrically linear energy \[E_\eta(u,\chi):= \eta^{-\frac{2}{3}}\int_{B_{0}(1)} \left| e(u)- \sum_{i=1}^3 \chi_ie_i\right|^2 d x+\eta^\frac{1}{3} \sum_{i=1}^3 |D\chi_i|(B_{0}(1))\] remains…
The large magnetocaloric effect in Heusler alloys showing martensite phase transformation puts them forward as efficient materials for magnetic refrigeration. However, irreversibility of the magnetocaloric cooling cycle is a major challenge…
We study the regularity of minimizers of a two-phase energy functional in periodic media. Our main result is a large scale Lipschitz estimate. We also establish improvement-of-flatness for non-degenerate minimizers, which is a key…
We study a system of classical particles in two dimensions interacting through an isotropic pair potential that displays a martensitic phase transition between a triangular and a rhomboidal structure upon the change of a single parameter.…
We consider a recently introduced 2-D square-to-rectangle martensite model that explains several unusual features of martensites to study ferromagnetic martensites. The strain order parameter is coupled to the magnetic order parameter…
A brief qualitative mapping is given between austenite, tweed and twinned phases of martensite alloys and corresponding paramagnetic, spin glass and periodic phases in spin glass alloys.
Materials exhibiting a martensitic phase transition are essential for applications in shape memory alloys, actuators and sensors. Hexamethylbenzene (HMB) has long been considered as a classical example of ferroelastic organic crystals since…
Using the delta correction to the standard free energy \cite{bc} in the elastic setting with a quadratic foundation term and some parameters, we introduce a one dimension only model for strong segregation in diblock copolymers, whose sharp…