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We propose a dynamical theory of low-temperature shear deformation in amorphous solids. Our analysis is based on molecular-dynamics simulations of a two-dimensional, two-component noncrystalline system. These numerical simulations reveal…

Statistical Mechanics · Physics 2009-10-30 M. L. Falk , J. S. Langer

This study presents a novel physics informed, data-driven modeling framework for capturing the strongly nonlinear thermo-viscoelastic behavior of soft materials exhibiting stress softening, with emphasis on the Mullins effect. Unlike…

Soft Condensed Matter · Physics 2025-07-18 Alireza Ostadrahimi , Amir Teimouri , Kshitiz Upadhyay , Guoqiang Li

We develop a thermodynamically consistent, fractional visco-elasto-plastic model coupled with damage for anomalous materials. The model utilizes Scott-Blair rheological elements for both visco-elastic/plastic parts. The constitutive…

Numerical Analysis · Mathematics 2019-11-19 Jorge L. Suzuki , Yongtao Zhou , Marta D'Elia , Mohsen Zayernouri

We propose a complement to constitutive modeling that augments neural networks with material principles to capture anisotropy and inelasticity at finite strains. The key element is a dual potential that governs dissipation, consistently…

Computational Engineering, Finance, and Science · Computer Science 2025-12-09 Hagen Holthusen , Ellen Kuhl

The data-driven modeling of dynamical systems has become an essential tool for the construction of accurate computational models from real-world data. In this process, the inherent differential structures underlying the considered physical…

Numerical Analysis · Mathematics 2025-06-04 Michael S. Ackermann , Ion Victor Gosea , Serkan Gugercin , Steffen W. R. Werner

We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the polyconvex elastodynamics of hyperelastic bodies using…

Analysis of PDEs · Mathematics 2021-04-27 Sébastien Boyaval , Mark Dostalík

We present a hybrid model/model-free data-driven approach to solve poroelasticity problems. Extending the data-driven modeling framework originated from Kirchdoerfer and Ortiz (2016), we introduce one model-free and two hybrid…

Machine Learning · Computer Science 2021-07-27 Bahador Bahmani , WaiChing Sun

It is important to accurately model materials' properties at lower length scales (micro-level) while translating the effects to the components and/or system level (macro-level) can significantly reduce the amount of experimentation required…

Computers and Society · Computer Science 2022-11-08 Kazuma Kobayashi , Shoaib Usman , Carlos Castano , Dinesh Kumar , Syed Alam

Direct numerical simulation of hierarchical materials via homogenization-based concurrent multiscale models poses critical challenges for 3D large scale engineering applications, as the computation of highly nonlinear and path-dependent…

Computational Engineering, Finance, and Science · Computer Science 2022-12-29 Shiguang Deng

Exoskeleton locomotion must be robust while being adaptive to different users with and without payloads. To address these challenges, this work introduces a data-driven predictive control (DDPC) framework to synthesize walking gaits for…

Robotics · Computer Science 2024-10-28 Kejun Li , Jeeseop Kim , Xiaobin Xiong , Kaveh Akbari Hamed , Yisong Yue , Aaron D. Ames

One of the obstacles hindering the scaling-up of the initial successes of machine learning in practical engineering applications is the dependence of the accuracy on the size of the database that "drives" the algorithms. Incorporating the…

Computational Engineering, Finance, and Science · Computer Science 2021-06-09 Wei Li , Martin Z. Bazant , Juner Zhu

We propose and validate a data-driven approach for modeling large-amplitude flow-induced oscillations of elastically mounted pitching wings. We first train a neural networks regression model for the nonlinear aerodynamic moment using data…

Fluid Dynamics · Physics 2025-02-21 Yuanhang Zhu , Kenneth Breuer

Data-Driven Computational Mechanics is a novel computing paradigm that enables the transition from standard data-starved approaches to modern data-rich approaches. At this early stage of development, one can distinguish two mainstream…

Numerical Analysis · Mathematics 2019-10-29 Cristian Guillermo Gebhardt , Dominik Schillinger , Marc Christian Steinbach , Raimund Rolfes

In recent years, machine learning methods have been widely used to study physical systems that are challenging to solve with governing equations. Physicists and engineers are framing the data-driven paradigm as an alternative approach to…

Computational Physics · Physics 2020-07-02 Jong-Hoon Ahn

Recent work has shown that exoskeletons controlled through data-driven methods can dynamically adapt assistance to various tasks for healthy young adults. However, applying these methods to populations with neuromotor gait deficits, such as…

Robotics · Computer Science 2025-09-25 Fabian C. Weigend , Dabin K. Choe , Santiago Canete , Conor J. Walsh

Modeling living systems at the collective scale can be very challenging because the individual constituents can themselves be complex and the respective interactions between the constituents are not fully understood. With the advent of high…

Soft Condensed Matter · Physics 2021-10-27 Ahmad Borzou , Alison E. Patteson , J. M. Schwarz

We continue our investigation of finite deformation linear viscoelastodynamics by focusing on constructing accurate and reliable numerical schemes. The concrete thermomechanical foundation developed in the previous study paves the way for…

Numerical Analysis · Mathematics 2023-05-26 Ju Liu , Jiashen Guan

Recent advances in physics-augmented neural networks have enabled thermodynamically consistent data-driven constitutive modeling of complex inelastic materials. Most existing approaches, however, implicitly adopt a specific thermodynamic…

Materials Science · Physics 2026-05-28 Reese E. Jones , Jan N. Fuhg

We introduce a data-driven framework for identifying material behavior from full-field kinematics and force measurements in generalized (micromorphic) continua. Unlike traditional approaches that rely on constitutive assumptions or…

Numerical Analysis · Mathematics 2025-12-18 Jacinto Ulloa , Laurent Stainier

We consider a model of an elastic body immersed between two layers of incompressible viscous fluid. The elastic displacement $w$ is governed by the damped wave equation $w_{tt} + \alpha w_t + \Delta w =0$ without any stabilization terms,…

Analysis of PDEs · Mathematics 2023-09-06 Igor Kukavica , Wojciech S. Ożański