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Related papers: Data-Driven Finite Elasticity

200 papers

Plasticity modelling has long been based on phenomenological models based on ad-hoc assuption of constitutive relations, which are then fitted to limited data. Other work is based on the consideration of physical mechanisms which seek to…

Materials Science · Physics 2022-06-06 Stefan Hiemer , Haidong Fan , Michael Zaiser

Conventional physics-based modeling techniques involve high effort, e.g., time and expert knowledge, while data-driven methods often lack interpretability, structure, and sometimes reliability. To mitigate this, we present a data-driven…

Dynamical Systems · Mathematics 2024-08-19 Johannes Rettberg , Jonas Kneifl , Julius Herb , Patrick Buchfink , Jörg Fehr , Bernard Haasdonk

We derive a hierarchy of plate theories for heterogeneous multilayers from three dimensional nonlinear elasticity by means of $\Gamma$-convergence. We allow for layers composed of different materials whose constitutive assumptions may vary…

Analysis of PDEs · Mathematics 2019-05-28 Miguel de Benito Delgado , Bernd Schmidt

The paper studies conical, convex, and affine models in the framework of behavioral systems theory. We investigate basic properties of such behaviors and address the problem of constructing models from measured data. We prove that closed,…

Optimization and Control · Mathematics 2023-10-25 Alberto Padoan , Florian Dörfler , John Lygeros

We study large deformations of hyperelastic membranes using a purely two-dimensional formulation derived from basic balance principles within a modern geometric setting, ensuring a framework that is independent of an underlying…

Soft Condensed Matter · Physics 2025-09-22 Claudia Grabs , Werner Wirges

Data-driven methods have become increasingly more prominent for musculoskeletal modelling due to their conceptually intuitive simple and fast implementation. However, the performance of a pre-trained data-driven model using the data from…

Signal Processing · Electrical Eng. & Systems 2022-11-23 Jie Zhang , Yihui Zhao , Tianzhe Bao , Zhenhong Li , Kun Qian , Alejandro F. Frangi , Sheng Quan Xie , Zhi-Qiang Zhang

Nonlinear bending phenomena of thin elastic structures arise in various modern and classical applications. Characterizing low energy states of elastic rods has been investigated by Bernoulli in 1738 and related models are used to determine…

Numerical Analysis · Mathematics 2024-12-20 Sören Bartels

This paper presents a detailed study on analytical solutions to a general nonlinear boundary-value problem in finite deformation theory. Based on canonical duality theory and the associated pure complementary energy principle in nonlinear…

Mathematical Physics · Physics 2015-04-14 David Yang Gao , Eldar Hajilarov

Driven elastic manifolds in random media exhibit a depinning transition to a state with non-vanishing velocity at a critical driving force. We study the depinning of stiff directed lines, which are governed by a bending rigidity rather than…

Statistical Mechanics · Physics 2015-05-12 Horst-Holger Boltz , Jan Kierfeld

Data-Driven Continuum Mechanics -- the continuous counterpart of Data-Driven Computational Mechanics -- is a modern paradigm that enhances classical continuum mechanics by incorporating finite sets of experimental material data directly,…

Analysis of PDEs · Mathematics 2026-05-21 Cristian G. Gebhardt , Kundan Kumar , Florin A. Radu

The problem of data-driven control is addressed here in the context of switched affine systems. This class of nonlinear systems is of particular importance when controlling many types of applications in electronic, biology, medicine, etc.…

Systems and Control · Electrical Eng. & Systems 2023-02-24 Alexandre Seuret , Carolina Albea , Francisco Gordillo

A wide variety of data can be represented using third-order tensors, spanning applications in chemometrics, psychometrics, and image processing. However, traditional data-driven frameworks are not naturally equipped to process tensors…

Systems and Control · Electrical Eng. & Systems 2024-10-29 Xin Mao , Anqi Dong , Ziqin He , Yidan Mei , Can Chen

The aim of this review is to highlight the connection between well-established physical and mathematical principles as they pertain to the theory of linear viscoelasticity. We begin by examining the physical foundations of Boltzmann and…

Mathematical Physics · Physics 2025-11-24 Michael Ortiz

We extend the model-free data-driven paradigm for rate-independent fracture mechanics proposed in Carrara et al. (2020), Data-driven Fracture Mechanics, Comp. Meth. App. Mech. Eng., 372 to rate-dependent fracture and sub-critical fatigue.…

Materials Science · Physics 2021-12-16 Pietro Carrara , Michael Ortiz , Laura De Lorenzis

Deep indentation of soft materials is ubiquitous across scales in nature and engineering, yet accurate predictions of contact behaviors under extreme deformations ($\delta/R > 1$) remain elusive due to geometric and material nonlinearities.…

Soft Condensed Matter · Physics 2026-03-10 Tong Mu , Changhong Linghu , Yanju Liu , Jinsong Leng , Huajian Gao , K. Jimmy Hsia

This work presents a shear elastoplasticity model for textile fabrics within the theoretical framework of anisotropic Kirchhoff-Love shells with bending of embedded fibers proposed by Duong et al. (2023). The plasticity model aims at…

Computational Engineering, Finance, and Science · Computer Science 2025-05-06 Thang Xuan Duong , Roger Andrew Sauer

We propose a generalized finite element method for linear elasticity equations with highly varying and oscillating coefficients. The method is formulated in the framework of localized orthogonal decomposition techniques introduced by…

Numerical Analysis · Mathematics 2016-08-24 Patrick Henning , Anna Persson

Fiber-reinforced soft biological tissues are typically modeled as hyperelastic, anisotropic, and nearly incompressible materials. To enforce incompressibility a multiplicative split of the deformation gradient into a volumetric and an…

Numerical Analysis · Mathematics 2022-04-13 Elias Karabelas , Matthias A. F. Gsell , Gundolf Haase , Gernot Plank , Christoph M. Augustin

This paper studies the discretization of a homogenization and dimension reduction model for the elastic deformation of microstructured thin plates proposed by Hornung, Neukamm, and Vel\v{c}i\'c in 2014. Thereby, a nonlinear bending energy…

Numerical Analysis · Mathematics 2024-06-19 Martin Rumpf , Stefan Simon , Christoph Smoch

In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…

Optimization and Control · Mathematics 2024-06-19 Yushuang Luo , Xiantao Li , Wenrui Hao