Data-Oriented Constitutive Modeling of Plasticity in Metals

Abstract

Constitutive models for plastic deformation of metals are typically based on flow rules determining the transition from elastic to plastic response of a material as function of the applied mechanical load. These flow rules are commonly formulated as a yield function, based on the equivalent stress and the yield strength of the material, and its derivatives. In this work, a novel mathematical formulation is developed that allows the efficient use of machine learning algorithms describing the elastic-plastic deformation of a solid under arbitrary mechanical loads and that can replace the standard yield functions with more flexible algorithms. By exploiting basic physical principles of elastic-plastic deformation, the dimensionality of the problem is reduced without loss of generality. The data-oriented approach inherently offers a great flexibility to handle different kinds of material anisotropy without the need for explicitly calculating a large number of model parameters. The applicability of this formulation in finite element analysis is demonstrated, and the results are compared to formulations based on Hill-like anisotropic plasticity as reference model. In future applications, the machine learning algorithm can be trained by hybrid experimental and numerical data, as for example obtained from fundamental micromechanical simulations based on crystal plasticity models. In this way, data-oriented constitutive modeling will also provide a new way to homogenize numerical results in a scale-bridging approach.

Multiphysics Modeling and Numerical Simulation in Computer-Aided Manufacturing Processes

“…Constitutive models of plasticity at the micro-and macroscales are able to describe the elastic and plastic behavior of metallic materials [35][36][37][38][39], ceramic materials [40], porous media [41], fibered sheets [42][43][44][45], gradient materials [46,47], composites [48][49][50][51], and forms [52]. Novel constitutive modeling approaches take into account the change in flow stress depending on such parameters as deformation, deformation speed, the strain hardening phenomenon, the change of orientation of strain state components, temperature, deformation history, and the hardening rule [53][54][55]. The advantages of FEM include the ease of discretization of complex shapes, the ease of determining the boundary conditions, and the ease of adaptive compaction and coarsening of the mesh [56].…”

Empowering engineering with data, machine learning and artificial intelligence: a short introductive review

“…Other works address multi-scale problems and the use of the so-called Deep Material Network [38,39,83,84], micro and macrostructural analysis [82], learning constitutive equations from indirect observations or the plasticity modeling [41,47,52,53,93,133].…”

Discovering plasticity models without stress data

“…Also in this context, the idea of constitutive-model-free approaches is to bypass the formulation of a path-dependent constitutive law and hence any assumptions on the material behavior, by solving forward problems that are directly informed by the given data [16][17][18][19][20][21] . The other stream of approaches describes the pathdependent constitutive behavior based on ANNs 7,22-27 , support vector machines 28 , symbolic regression 29 , or use the information gained from the data to correct material models known from traditional theories 30 . Being supervised, all these methods require for the training process a tremendous amount of labeled data in form of stress-strain paths, i.e.…”