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We assess the performance of EUCLID, Efficient Unsupervised Constitutive Law Identification and Discovery, a recently proposed framework for automated discovery of constitutive laws, on experimental data. Mechanical tests are performed on…

Within the scope of our recent approach for Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID), we propose an unsupervised Bayesian learning framework for discovery of parsimonious and interpretable constitutive…

Computational Engineering, Finance, and Science · Computer Science 2022-10-24 Akshay Joshi , Prakash Thakolkaran , Yiwen Zheng , Maxime Escande , Moritz Flaschel , Laura De Lorenzis , Siddhant Kumar

We extend the scope of our approach for unsupervised automated discovery of material laws (EUCLID) to the case of a material belonging to an unknown class of behavior. To this end, we leverage the theory of generalized standard materials,…

Materials Science · Physics 2023-01-18 Moritz Flaschel , Siddhant Kumar , Laura De Lorenzis

We propose a new approach for unsupervised learning of hyperelastic constitutive laws with physics-consistent deep neural networks. In contrast to supervised learning, which assumes the availability of stress-strain pairs, the approach only…

Machine Learning · Computer Science 2022-10-11 Prakash Thakolkaran , Akshay Joshi , Yiwen Zheng , Moritz Flaschel , Laura De Lorenzis , Siddhant Kumar

We propose a new approach for data-driven automated discovery of isotropic hyperelastic constitutive laws. The approach is unsupervised, i.e., it requires no stress data but only displacement and global force data, which are realistically…

Computational Engineering, Finance, and Science · Computer Science 2021-04-30 Moritz Flaschel , Siddhant Kumar , Laura De Lorenzis

We propose an automated computational algorithm for simultaneous model selection and parameter identification for the hyperelastic mechanical characterization of human brain tissue. Following the motive of the recently proposed…

Quantitative Methods · Quantitative Biology 2024-04-17 Moritz Flaschel , Huitian Yu , Nina Reiter , Jan Hinrichsen , Silvia Budday , Paul Steinmann , Siddhant Kumar , Laura De Lorenzis

We extend EUCLID, a computational strategy for automated material model discovery and identification, to linear viscoelasticity. For this case, we perform a priori model selection by adopting a generalized Maxwell model expressed by a Prony…

Materials Science · Physics 2024-04-17 Enzo Marino , Moritz Flaschel , Siddhant Kumar , Laura De Lorenzis

We propose a computational framework, Hetero-EUCLID, for segmentation and parameter identification to characterize the full hyperelastic behavior of all constituents of a heterogeneous material. In this work, we leverage the Bayesian-EUCLID…

Computational Engineering, Finance, and Science · Computer Science 2026-01-19 Kanhaiya Lal Chaurasiya , Saurav Dutta , Siddhant Kumar , Akshay Joshi

The automated discovery of constitutive laws forms an emerging research area, that focuses on automatically obtaining symbolic expressions describing the constitutive behavior of solid materials from experimental data. Existing…

Materials Science · Physics 2024-05-10 Georgios Kissas , Siddhartha Mishra , Eleni Chatzi , Laura De Lorenzis

Constitutive modeling lies at the core of mechanics, allowing us to map strains onto stresses for a material in a given mechanical setting. Historically, researchers relied on phenomenological modeling where simple mathematical…

Computational Engineering, Finance, and Science · Computer Science 2024-08-28 Asghar A. Jadoon , Knut A. Meyer , Jan N. Fuhg

Material Fingerprinting is a lookup table-based strategy to discover material models from experimental measurements, which completely avoids the need to solve an optimization problem. In an offline phase, a comprehensive database of…

Computational Engineering, Finance, and Science · Computer Science 2026-01-22 Moritz Flaschel , Miguel Angel Moreno-Mateos , Simon Wiesheier , Paul Steinmann , Ellen Kuhl

Machine learning approaches informed by physics have offered new insights into the discovery of constitutive models from data, helping overcome some limitations of traditional constitutive modelling while reducing the cost of otherwise…

Materials Science · Physics 2026-05-19 Filippo Masi

Cardiac muscle tissue exhibits highly non-linear hyperelastic and orthotropic material behavior during passive deformation. Traditional constitutive identification protocols therefore combine multiple loading modes and typically require…

Tissues and Organs · Quantitative Biology 2026-05-05 Rogier P. Krijnen , Akshay Joshi , Siddhant Kumar , Mathias Peirlinck

Unsupervised reinforcement learning (URL) poses a promising paradigm to learn useful behaviors in a task-agnostic environment without the guidance of extrinsic rewards to facilitate the fast adaptation of various downstream tasks. Previous…

Machine Learning · Computer Science 2023-02-23 Yifu Yuan , Jianye Hao , Fei Ni , Yao Mu , Yan Zheng , Yujing Hu , Jinyi Liu , Yingfeng Chen , Changjie Fan

The discovery of constitutive models for hyperelastic materials is essential yet challenging due to their nonlinear behavior and the limited availability of experimental data. Traditional methods typically require extensive stress-strain or…

Computational Physics · Physics 2025-12-22 Hyeonbin Moon , Donggeun Park , Hanbin Cho , Hong-Kyun Noh , Jae hyuk Lim , Seunghwa Ryu

The development of accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions…

Machine Learning · Computer Science 2023-02-22 Jan N. Fuhg , Craig M. Hamel , Kyle Johnson , Reese Jones , Nikolaos Bouklas

In computational materials science, predicting the yield strain of crosslinked polymers remains a challenging task. A common approach is to identify yield as the first critical point of stress-strain curves simulated by molecular dynamics…

Materials Science · Physics 2016-09-20 Paul N. Patrone , Samuel Tucker , Andrew Dienstfrey

Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains…

Numerical Analysis · Mathematics 2022-09-12 Xiaolong He , Qizhi He , Jiun-Shyan Chen

We propose Material Fingerprinting, a new method for the rapid discovery of mechanical material models from direct or indirect data that avoids solving potentially non-convex optimization problems. The core assumption of Material…

Computational Engineering, Finance, and Science · Computer Science 2025-12-09 Moritz Flaschel , Denisa Martonová , Carina Veil , Ellen Kuhl

In this work, we extend the existing framework of inelastic constitutive artificial neural networks (iCANNs) by incorporating plasticity to increase their applicability to model more complex material behavior. The proposed approach ensures…

Machine Learning · Computer Science 2025-06-10 Birte Boes , Jaan-Willem Simon , Hagen Holthusen
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