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The present paper proposes a novel Bayesian, computational strategy in the context of model-based inverse problems in elastostatics. On one hand we attempt to provide probabilistic estimates of the material properties and their spatial…

Computation · Statistics 2015-12-21 P. S. Koutsourelakis

We propose a novel approach to model viscoelasticity materials using neural networks, which capture rate-dependent and nonlinear constitutive relations. However, inputs and outputs of the neural networks are not directly observable, and…

Numerical Analysis · Mathematics 2020-05-12 Kailai Xu , Alexandre M. Tartakovsky , Jeff Burghardt , Eric Darve

In material science, models are derived to predict emergent material properties (e.g. elasticity, strength, conductivity) and their relations to processing conditions. A major drawback is the calibration of model parameters that depend on…

Neural and Evolutionary Computing · Computer Science 2021-11-22 Gabriel Kronberger , Evgeniya Kabliman , Johannes Kronsteiner , Michael Kommenda

A key problem of solid mechanics is the identification of the constitutive law of a material, that is, the relation between strain and stress. Machine learning has lead to considerable advances in this field lately. Here we introduce…

Materials Science · Physics 2026-02-23 Chenyi Ji , Kian P. Abdolazizi , Hagen Holthusen , Christian J. Cyron , Kevin Linka

Data-driven models based on deep learning algorithms intend to overcome the limitations of traditional constitutive modelling by directly learning from data. However, the need for extensive data that collate the full state of the material…

Materials Science · Physics 2023-12-27 Filippo Masi , Itai Einav

This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this…

Classical Physics · Physics 2019-09-12 Roger A. Sauer , Reza Ghaffari , Anurag Gupta

We propose a sampling method based on an ensemble approximation of second order Langevin dynamics. The log target density is appended with a quadratic term in an auxiliary momentum variable and damped-driven Hamiltonian dynamics introduced;…

Dynamical Systems · Mathematics 2025-06-06 Ziming Liu , Andrew M. Stuart , Yixuan Wang

In this two part series, we present a contact model able to capture the response of interacting adhesive elastic-perfectly plastic particles under a variety of loadings. In Part I, we focus on elastic through fully-plastic contact with and…

Soft Condensed Matter · Physics 2023-09-15 William Zunker , Ken Kamrin

We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…

Statistics Theory · Mathematics 2020-07-31 Fei Lu , Mauro Maggioni , Sui Tang

Manipulation of deformable objects is a challenging task for a robot. It will be problematic to use a single sensory input to track the behaviour of such objects: vision can be subjected to occlusions, whereas tactile inputs cannot capture…

Robotics · Computer Science 2023-05-01 Leszek Pecyna , Siyuan Dong , Shan Luo

Efficient and accurate learning of constitutive laws is crucial for accurately predicting the mechanical behavior of materials under complex loading conditions. Accurate model calibration hinges on a delicate interplay between the…

Computational Engineering, Finance, and Science · Computer Science 2025-06-24 Royal C. Ihuaenyi , Wei Li , Martin Z. Bazant , Juner Zhu

The main purpose of this work is to address the question of the utility of "effective constitutive relations" for problems in dynamics. This is done in the context of longitudinal shear waves in an elastic medium that is periodically…

Materials Science · Physics 2013-11-18 John Willis

This article deals with a viscoplastic material model of overstress type. The model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part. An additional multiplicative decomposition of…

Numerical Analysis · Mathematics 2015-05-13 A. V. Shutov , R. Kreissig

We experimentally characterize the impact response of concentrated suspensions consisting of cornstarch and water. We observe that the suspensions support a large normal stress -- on the order of MPa -- with a delay after the impactor hits…

Soft Condensed Matter · Physics 2018-05-09 Rijan Maharjan , Shomeek Mukhopadhyay , Benjamin Allen , Tobias Storz , Eric Brown

This paper consists of two parts. In the first part we prove the unique solvability for the abstract variational-hemivariational inequality with history-dependent operator. The proof is based on the existing result for the static…

Analysis of PDEs · Mathematics 2016-08-17 Justyna Ogorzaly

The problem of acquiring elastic properties of a composite material from the data of the vibrational testing is considered. The specimen is considered to abide by the linear elasticity laws and subject to viscoelastic damping. The BVP for…

Numerical Analysis · Mathematics 2024-01-22 Vitalii Aksenov , Aleksey Vasyukov , Katerina Beklemysheva

We consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of visco-acoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is…

Analysis of PDEs · Mathematics 2022-09-20 Florian Faucher , Otmar Scherzer

Humans leverage the dynamics of the environment and their own bodies to accomplish challenging tasks such as grasping an object while walking past it or pushing off a wall to turn a corner. Such tasks often involve switching dynamics as the…

Robotics · Computer Science 2021-03-29 Saumya Saxena , Alex LaGrassa , Oliver Kroemer

Recent research has made the surprising finding that state-of-the-art deep learning models sometimes fail to generalize to small variations of the input. Adversarial training has been shown to be an effective approach to overcome this…

Machine Learning · Computer Science 2020-03-26 Sven Gowal , Chongli Qin , Po-Sen Huang , Taylan Cemgil , Krishnamurthy Dvijotham , Timothy Mann , Pushmeet Kohli

In this work, we analyze a non-clamped dynamic viscoelastic contact problem involving thermal effect. The friction law is described by a non-monotone relation between the tangential stress and the tangential velocity. This leads to a system…

Numerical Analysis · Mathematics 2024-01-02 Piotr Bartman , Krzysztof Bartosz , Michał Jureczka , Paweł Szafraniec