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Related papers: Shape memory alloys as gradient-polyconvex materia…

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We consider problems of dynamic viscoelasticity taking into account the coupling of elastic and thermal fields. Efficient approximate models are developed and computational results on thermomechanical behaviour of shape-memory-alloy…

Numerical Analysis · Mathematics 2025-10-20 R. V. N. Melnik , A. J. Roberts

In the present work, a machine learning based constitutive model for electro-mechanically coupled material behavior at finite deformations is proposed. Using different sets of invariants as inputs, an internal energy density is formulated…

Computational Engineering, Finance, and Science · Computer Science 2022-08-30 Dominik K. Klein , Rogelio Ortigosa , Jesús Martínez-Frutos , Oliver Weeger

We study the geometry of needle-shaped domains in shape-memory alloys. Needle-shaped domains are ubiquitously found in martensites around macroscopic interfaces between regions which are laminated in different directions, or close to…

Computational Physics · Physics 2019-12-06 Sergio Conti , Martin Lenz , Nora Lüthen , Martin Rumpf , Barbara Zwicknagl

This work presents a three-dimensional constitutive model for the martensitic transformation in polycrystalline Shape Memory Alloys (SMAs) under large deformation. By utilizing the logarithmic strain and rate, the model is able to account…

Materials Science · Physics 2019-09-04 Lei Xu , Theocharis Baxevanis , Dimitris Lagoudas

We develop a theory of existence of minimizers of energy functionals in vectorial problems based on a nonlocal gradient under Dirichlet boundary conditions. The model shares many features with the peridynamics model and is also applicable…

Analysis of PDEs · Mathematics 2022-11-07 José C. Bellido , Javier Cueto , Carlos Mora-Corral

Randomly crumpled sheets have shape memory. In order to understand the basis of this form of memory, we simulate triangular lattices of springs whose lengths are altered to create a topography with multiple potential energy minima. We then…

Soft Condensed Matter · Physics 2015-11-18 Naomi Oppenheimer , Thomas A. Witten

Shape Memory Alloys (SMAs) has been widely aware of working as actuators for active/smart morphing structures in the engineering industry. Because of the high actuation energy density of SMAs, compared to other active materials, structures…

Materials Science · Physics 2020-01-16 Lei Xu , Theocharis Baxevanis , Dimitris Lagoudas

We show that memory can be encoded in a model amorphous solid subjected to athermal oscillatory shear deformations, and in an analogous spin model with disordered interactions, sharing the feature of a deformable energy landscape. When…

Statistical Mechanics · Physics 2014-01-17 D. Fiocco , G. Foffi , S. Sastry

Isothermal visco-elastodynamics in the Kelvin-Voigt rheology is formulated in the spatial Eulerian coordinates in terms of velocity and deformation gradient. A generally nonconvex (possibly also frame-indifferent) stored energy is admitted.…

Analysis of PDEs · Mathematics 2022-04-13 Tomáš Roubíček

Data-driven methods are becoming an essential part of computational mechanics due to their unique advantages over traditional material modeling. Deep neural networks are able to learn complex material response without the constraints of…

Computational Engineering, Finance, and Science · Computer Science 2022-07-27 Vahidullah Tac , Francisco S. Costabal , Adrian Buganza Tepole

Shape memory alloys (SMAs) have been intensively investigated as actuators for the past several decades. Due to their high actuation energy density compared to other active materials, their current and potential applications in engineering…

Materials Science · Physics 2018-12-31 Lei Xu , Alexandros Solomou , Dimitris Lagoudas

Additive manufacturing has been adopted to process nickel-titanium shape memory alloys due to its advantages of flexibility and minimal defects. The current layer-by-layer method is accompanied by a complex temperature history, which is not…

Materials Science · Physics 2021-10-05 Shiming Gao , Fei Weng , Ojo Philip Bodunde , Mian Qin , Wei-Hsin Liao , Ping Guo

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…

Analysis of PDEs · Mathematics 2014-01-10 Michel Fremond , Elisabetta Rocca

We consider a singularly-perturbed two-well problem in the context of planar geometrically linear elasticity to model a rectangular martensitic nucleus in an austenitic matrix. We derive the scaling regimes for the minimal energy in terms…

Analysis of PDEs · Mathematics 2020-03-10 Sergio Conti , Johannes Diermeier , David Melching , Barbara Zwicknagl

This paper is concerned with the energy decay of a viscoelastic variable coefficient wave equation with nonlocality in time as well as nonlinear damping and polynomial nonlinear terms. Using the Lyapunov method, we establish a polynomial…

Analysis of PDEs · Mathematics 2025-12-03 Qingqing Peng , Yikan Liu

This article is about hyperelastic deformations of plates (planar domains) which minimize a neohookean type energy. Particularly, we investigate a stored energy functional introduced by J.M. Ball in his seminal paper "Global invertibility…

Analysis of PDEs · Mathematics 2020-04-08 Tadeusz Iwaniec , Jani Onninen , Pekka Pankka , Teresa Radice

A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane…

Optimization and Control · Mathematics 2021-06-09 José A. Iglesias , Martin Rumpf , Otmar Scherzer

We develop a 1D model of twin branching in shape memory alloys. The free energy of the branched microstructure comprises the interfacial and elastic strain energy contributions, both expressed in terms of the average twin spacing treated as…

Materials Science · Physics 2025-04-25 Stanislaw Stupkiewicz , Seyedshoja Amini , Mohsen Rezaee-Hajidehi

We derive a class of two-dimensional shell energies for thin elastic bodies exhibiting small-length scale effects modeled via strain-gradient elasticity. Building on the final author's earlier work on plate models, the kinetic and stored…

Mathematical Physics · Physics 2025-08-08 C. Balitactac , Y. Canzani , R. S. Hallyburton , J. Mott , C. Rodriguez

In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…

Analysis of PDEs · Mathematics 2023-10-23 Abramo Agosti , Robert Lasarzik , Elisabetta Rocca