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Needle-like twins are observed experimentally within the transition layer at the martensite-twinned martensite interface. We utilize a phase-field approach to investigate this microstructure. Our goal is to simulate the morphology of the…
Shape memory alloys inherit their macroscopic properties from their mesoscale microstructure originated from the martensitic phase transformation. In a cubic to orthorhombic transition, a single variant of marten- site can have a compatible…
We study a simplified two-dimensional model for a cubic-to-orthorhombic phase transition occuring in certain shape-memory-alloys. In the low temperature regime the linear theory of elasticity predicts various possible patterns of martensite…
A three-dimensional phase-field model is proposed for simulating the magnetic martensitic phase transformation. The model considers a paramagnetic cubic austenite to ferromagnetic tetragonal martensite transition, as it occurs in magnetic…
Martensites are metastable phases, possessing a characteristic morphology, usually formed during a fast quench accross a structural transition. We attempt to understand these morphological features using a coarsegrained free energy…
A family of integral functionals F which, in a simplified way, model material microstructure occupying a two-dimensional domain D and which take account of surface energy and a variable well-depth is studied. It is shown that there is a…
We present a unifying description for the martensitic transformation of steel that accounts for important experimentally observable features of the transformation namely, the Neumann bands, the interfacial (habit) plane between the…
Diffusionless phase transitions are at the core of the multifunctionality of (magnetic) shape memory alloys, ferroelectrics and multiferroics. Giant strain effects under external fields are obtained in low symmetric modulated martensitic…
In this paper we introduce a 3D phenomenological model for shape memory behavior, accounting for: martensite reorientation, asymmetric response of the material to tension/compression, different kinetics between forward and reverse phase…
In materials that undergo martensitic phase transformation, macroscopic loading often leads to the creation and/or rearrangement of elastic domains. This paper considers an example {involving} a single-crystal slab made from two martensite…
We study microstructure formation in two nonconvex singularly-perturbed variational problems from materials science, one modeling austenite-martensite interfaces in shape-memory alloys, the other one slip structures in the plastic…
We present systematic temperature-quench Monte Carlo simulations on discrete-strain pseudospin model Hamiltonians to study microstructural evolutions in 2D ferroelastic transitions with two-component vector order parameters ($N_{OP}=2$).…
Cofactor Conditions (CCs) are geometric compatibility conditions mathematically derived from the crystallographic theory of martensitic phase transformation. The CCs guarantee compatible interfaces between the austenite and the parallelled…
This paper investigates the conditions necessary for the elimination of transition layers at interfaces involving compound domains, extending the classical framework of cofactor conditions. Although cofactor conditions enable stress-free…
We use the phase-field method to study the martensitic transformation at the nanoscale. For nanosystems such as nanowires and nanograins embedded in a stiff matrix, the geometric constraints and boundary conditions have an impact on…
We propose a mesh-free method to solve nonconvex energy minimization problems for martensitic phase transitions and twinning in crystals, using the deep learning approach. These problems pose multiple challenges to both analysis and…
Branching can be observed at the austenite-martensite interface of martensitic phase transformations. For a model problem, Kohn and M\"uller studied a branching pattern with optimal scaling of the energy with respect to its parameters.…
In the setting of continuum elasticity martensitic phase transformations are characterized by a non-convex free energy density function that possesses multiple wells in strain space and includes higher-order gradient terms for…
The martensitic transformation in NiTi-based Shape Memory Alloys (SMAs) provides a basis for shape memory effect and superelasticity, thereby enabling applications requiring solid-state actuation and large recoverable shape changes upon…
To study martensitic phase transformation we use a micromechanical model based on statistical mechanics. Employing lattice Monte-Carlo simulations and realistic material properties for shape-memory alloys (SMA), we investigate the combined…