相关论文: Rigidity of branching microstructures in shape mem…

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.

We are interested in the energetic cost of a martensitic inclusion of volume $V$ in austenite for the cubic-to-tetragonal phase transformation. In contrast with the work of [Kn\"upfer, Kohn, Otto: Comm. Pure Appl. Math. 66 (2013), no. 6,…

We study the symmetrised rank-one convex hull of monoclinic-I martensite (a twelve-variant material) in the context of geometrically-linear elasticity. We construct sets of T3s, which are (non-trivial) symmetrised rank-one convex hulls of…

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…

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…

Employing the Ginzburg-Landau phase-field theory, a new coupled dynamic thermo-mechanical 3D model has been proposed for modeling the cubic-to-tetragonal martensitic transformations in shape memory alloy (SMA) nanostructures. The…

The large magnetocaloric effect (MCE) observed in Ni-Mn based shape-memory Heusler alloys put them forward to use in magnetic refrigeration technology. It is associated with a first-order magnetostructural (martensitic) phase transition. We…

Modulated phases occur in numerous functional materials like giant ferroelectrics and magnetic shape memory alloys. To understand the origin of these phases, we review and generalize the concept of adaptive martensite. As a starting point,…

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 derive the quasiconvex relaxation of the Biot-type energy density $\lVert\sqrt{\operatorname{D}\varphi^T \operatorname{D}\varphi}-I_2\rVert^2$ for planar mappings $\varphi\colon\mathbb{R}^2\to \mathbb{R}^2$ in two different scenarios.…

We present a continuum model for symmetry-breaking phase transformations in intercalation compounds, based on Ericksen's multi-well energy formulation. The model predicts the nucleation and growth of crystallographic microstructures in…

We explore the possibilities and limitations of using a coherent second phase to engineer the thermo-mechanical properties of a martensitic alloy by modifying the underlying free energy landscape that controls the transformation. We use…

Motivated by complex microstructures in the modelling of shape-memory alloys and by rigidity and flexibility considerations for the associated differential inclusions, in this article we study the energy scaling behaviour of a simplified…

The paper is devoted to the study of a mathematical model for the thermomechanical evolution of metallic shape memory alloys. The main novelty of our approach consists in the fact that we include the possibility for these materials to…

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…

Using a variational model based on non-linear elasticity we investigate whether in a cubic-to-tetragonal phase transformation it is energetically preferable to nucleate martensite within austenite. Under minimal growth assumptions on the…

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,…

We consider the Moore-Gibson-Thompson equation with memory of type II $$ \partial_{ttt} u(t) + \alpha \partial_{tt} u(t) + \beta A \partial_t u(t) + \gamma Au(t)-\int_0^t g(t-s) A \partial_t u(s){\rm d} s=0 $$ where $A$ is a strictly…

We present here a model for instantaneous collisions in a solid made of shape memory alloys (SMA) by means of a predictive theory which is based on the introduction not only of macroscopic velocities and temperature, but also of microscopic…

We exploit the intrinsic structural instability of the Fe70Pd30 magnetic shape memory alloy to obtain functional epitaxial films exhibiting a self-organized nanostructure. We demonstrate that coherent epitaxial straining by 54% is possible.…