Related papers: Shape memory alloys as gradient-polyconvex materia…
In this article we discuss higher Sobolev regularity of convex integration solutions for the geometrically non-linear two-well problem. More precisely, we construct solutions to the differential inclusion $\nabla u\in K$ subject to suitable…
We work in a class of Sobolev $W^{1,p}$ maps, with $p > d-1$, from a bounded open set $\Omega \subset \mathbb{R}^{d}$ to $\mathbb{R}^{d}$ that do not exhibit cavitation and whose trace on $\partial \Omega$ is also $W^{1,p}$. Under the…
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…
This work presents a three-dimensional constitutive model for shape memory alloys considering the TRansformation-Induced Plasticity (TRIP) as well as the Two-Way Shape Memory Effect (TWSME) through a large deformation framework. The…
This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations…
Soft solids with surface energy exhibit complex mechanical behavior, necessitating advanced constitutive models to capture the interplay between bulk and surface mechanics. This interplay has profound implications for material design and…
The evolution of multivariant patterns in thin plates of magnetic shape memory materials with an applied magnetic field was studied theoretically. A geometrical domain-model is considered composed of straight stripe-like martensite variants…
Shape memory materials have gained considerable attention thanks to their ability to change physical properties when subjected to external stimuli such as temperature, pH, humidity, electromagnetic fields, etc. These materials are…
A flexible multi-parameter exactly solvable model of potential profile, containing an arbitrary number of continuous smoothly shaped barriers and wells, both equal or unequal, characterized by finite values and continuous profiles of the…
We consider the equation of motion for one-dimensional nonlinear viscoelasticity of strain-rate type under the assumption that the stored-energy function is $\lambda$-convex, which allows for solid phase transformations. We formulate this…
The deep energy method (DEM) has been used to solve the elastic deformation of structures with linear elasticity, hyperelasticity, and strain-gradient elasticity material models based on the principle of minimum potential energy. In this…
Shape memory alloys are a class of ferroic materials which undergo a structural (martensitic) transition where the associated ferroic property is a lattice distortion (strain). The sensitiveness of the transition to the conjugated external…
We present a well-posedness and stability result for a class of nondegenerate linear parabolic equations driven by rough paths. More precisely, we introduce a notion of weak solution that satisfies an intrinsic formulation of the equation…
We consider a class of models motivated by previous numerical studies of wrinkling in highly stretched, thin rectangular elastomer sheets. The model used is characterized by a finite-strain hyperelastic membrane energy perturbed by small…
We consider multi-gradient fluids endowed with a volumetric internal energy which is a function of mass density, volumetric entropy and their successive gradients. We obtained the thermodynamic forms of equation of motions and equation of…
Shape memory alloys that can deform and then spring back to their original shape, have found a wide range of applications in the medical field, from heart valves to stents. As we push the boundaries of technology creating smaller, more…
The concept of "multiplicity of solutions" was developed in arXiv:1509.02603v2 which is based on the theory of energy operators in the Schwartz space S^-(R) and some subspaces called energy spaces first defined in arXiv:1208.3385 and…
We consider different measure-valued solvability concepts from the literature and show that they could be simplified by using the energy-variational structure of the underlying system of partial differential equations. In the considered…
In this paper a Blaschke-Santal\'o diagram involving the area, the perimeter and the elastic energy of planar convex bodies is considered. More precisely we give a description of set $$\mathcal{E}:=\left\{(x,y)\in \R^2, x=\frac{4\pi…
Energy-based models (EBMs) implement inference as gradient descent on a learned Lyapunov function, yielding interpretable, structure-preserving alternatives to black-box neural ODEs and aligning naturally with physical AI. Yet their use in…