Abstract Prior to any numerical development, the paper objective is to answer first to a fundamental question: what is the mathematical form of the most general data-driven constitutive model for stable materials, taking maximum account of knowledge from physics and materials science? Here we restrict ourselves to elasto-(visco-)plastic materials under the small displacement assumption. The experimental data consists of full-field measurements from a family of tested mechanical structures. In this framework, a general data-driven approach is proposed to learn the constitutive model (in terms of thermodynamic potentials) from data. A key element that defines the proposed data-driven approach is a tool: the Constitutive Relation Error (CRE); the data-driven model is then the minimizer of the CRE. A notable aspect of this procedure is that it leads to quasi-explicit formulations of the optimal constitutive model. Eventually, a modified Constitutive Relation Error is introduced to take measurement noise into account.

Pierre Ladevèze

Ludovic Chamoin

Advanced Modeling and Simulation in Engineering Sciences

The research topics addressed by Advanced Modeling and Simulation in Engineering Sciences (AMSES) cover the vast domain of the advanced modeling and simulation of materials, processes and structures governed by the laws of mechanics. The emphasis is on advanced and innovative modeling approaches and numerical strategies. The main objective is to describe the actual physics of large mechanical systems with complicated geometries as accurately as possible using complex, highly nonlinear and coupled multiphysics and multiscale models, and then to carry out simulations with these complex models as rapidly as possible. In other words, this research revolves around efficient numerical modeling along with model verification and validation. Therefore, the corresponding papers deal with advanced modeling and simulation, efficient optimization, inverse analysis, data-driven computation and simulation-based control. These challenging issues require multidisciplinary efforts – particularly in modeling, numerical analysis and computer science – which are treated in this journal.

The journal "Advanced Modeling and Simulation in Engineering Sciences" addresses a wide range of topics related to the advanced modeling and simulation of materials, processes, and structures governed by the laws of mechanics. It emphasizes innovative modeling approaches and numerical strategies, aiming to accurately describe the actual physics of large mechanical systems with complex geometries. The core of this research revolves around efficient numerical modeling, along with model verification and validation. Consequently, the papers published in this journal cover advanced modeling and simulation, efficient optimization, inverse analysis, data-driven computation, and simulation-based control. These challenging issues require multidisciplinary collaboration, particularly in the fields of modeling, numerical analysis, and computer science, which are thoroughly explored in this journal.

《Advanced Modeling and Simulation in Engineering Sciences》期刊关注材料、过程和结构的先进建模与仿真，涉及力学规律下的广泛领域。期刊强调创新的建模方法和数值策略，旨在尽可能准确地描述复杂几何形状的大型机械系统的实际物理特性。研究的核心是高效的数值建模，以及模型的验证和确认。因此，相关论文涉及先进建模与仿真、高效优化、逆向分析、数据驱动计算和基于仿真的控制。这些具有挑战性的问题需要多学科的合作，特别是在建模、数值分析和计算机科学领域，这些内容在本期刊中得到了充分的探讨。

Data-driven material modeling based on the Constitutive Relation Error

ivySCI AI Smartly Parses PDF, Answers Researchers' Questions, and Helps You Understand Papers in Seconds

Journal Info

Category	Quartile
MECHANICS	3