Data driven approach to f... - Pietro Car... - 德国科学基金(DFG)

Data driven approach to fatigue crack growth modeling

项目来源

德国科学基金(DFG)

项目主持人

Pietro Carrara

项目受资助机构

Eidgenössische Technische Hochschule Zürich,Departement Maschinenbau und Verfahrenstechnik

立项年度

2019

立项时间

未公开

项目编号

428299198

研究期限

未知 / 未知

项目级别

国家级

受资助金额

未知

学科

Applied Mechanics,Statics and Dynamics;Mechanics

学科代码

未公开

基金类别

Research Fellowships

关键词

未公开

参与者

Michael Ortiz

参与机构

未公开

项目标书摘要：Fatigue is a key phenomenon in mechanics,and is responsible for most structural failures.However,the inherent complexity of the problem makes the development of predictive models a non-trivial task and it greatly complicates the identification of the material fatigue constitutive behavior starting from experimental results.Hence,despite the relevance of the problem,a widely accepted model with truly predictive capabilities is still lacking.Aim of the present project is to develop a data driven approach to fatigue crack growth modeling.The adoption of data driven techniques allows to directly embed into the solution of the problem a discrete set of data of experimental or numerical nature.This has the advantage of overcoming the necessity of calibrating analytical fatigue constitutive material relationships.A recent variational phase-field approach to fatigue crack growth proposed by the applicant will be adopted as a reference mechanical model.Then,taking advantage of machine learning and data mining techniques,a data driven procedure will be proposed based on the identification of the numerical constitutive behavior.To this end,a technique involving the interpolation of the material behavior data within sub-clusters of the material space with limited extension will be used.This approach allows to determine a set of combination coefficients that parameterize the numerical(fatigue)constitutive manifold of the material.The procedure will be first studied for a 1D problem and based on a numerically generated material data set.Then,it will be extended to 2-3D and to the employment of experimental data sets.The initial adoption of numerical data allows to precisely estimate the accuracy of the procedure since a reference solution is available,i.e.the results of the numerical simulations adopting available constitutive relationships.The capability of the method will be investigated by simulating standard tests used to characterize the fatigue behavior,such as the compact tension or three-point-bending tests.Here,loading and boundary conditions different that those used to train the numerical manifold detection phase will be adopted.

Application Abstract: Fatigue is a key phenomenon in mechanics,and is responsible for most structural failures.However,the inherent complexity of the problem makes the development of predictive models a non-trivial task and it greatly complicates the identification of the material fatigue constitutive behavior starting from experimental results.Hence,despite the relevance of the problem,a widely accepted model with truly predictive capabilities is still lacking.Aim of the present project is to develop a data driven approach to fatigue crack growth modeling.The adoption of data driven techniques allows to directly embed into the solution of the problem a discrete set of data of experimental or numerical nature.This has the advantage of overcoming the necessity of calibrating analytical fatigue constitutive material relationships.A recent variational phase-field approach to fatigue crack growth proposed by the applicant will be adopted as a reference mechanical model.Then,taking advantage of machine learning and data mining techniques,a data driven procedure will be proposed based on the identification of the numerical constitutive behavior.To this end,a technique involving the interpolation of the material behavior data within sub-clusters of the material space with limited extension will be used.This approach allows to determine a set of combination coefficients that parameterize the numerical(fatigue)constitutive manifold of the material.The procedure will be first studied for a 1D problem and based on a numerically generated material data set.Then,it will be extended to 2-3D and to the employment of experimental data sets.The initial adoption of numerical data allows to precisely estimate the accuracy of the procedure since a reference solution is available,i.e.the results of the numerical simulations adopting available constitutive relationships.The capability of the method will be investigated by simulating standard tests used to characterize the fatigue behavior,such as the compact tension or three-point-bending tests.Here,loading and boundary conditions different that those used to train the numerical manifold detection phase will be adopted.

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1. Data driven fracture mechanics

2.2020 Final Report

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2020年
报告

In this joint German-Ukrainian project,the solvability and well-posedness of a large class of partial differential equations are studied.More precisely,we investigate elliptic equations in bounded domains with appropriate conditions on the boundary of the domain-this class of problems appearing in many applications from physics and engineering.Under standard assumptions,one can prove regularity properties of the solution and uniform estimates,showing continuous dependence of the solution on the data.While elliptic theory is a classical ﬁeld in partial differential equations,the novelty of this project lies in the choice of the spaces for the solution and the data:we consider so-called Hörmander spaces,which form a reﬁned scale of solution spaces compared to the more classical choice of Sobolev spaces.The focus of this project lies in Hormander spaces of low(and negative)regularity.In this way,one can include irregular source terms and random effects,in particular noise terms which affect the system on the boundary.The connection between Hörmander spaces and the regularity of white noise was surprising and could lead to a better understanding of the paths of white noise.This project also gives some contribution to the interpolation of Hilbert spaces,an abstract method from functional analysis which is useful in the investigation of partial differential equations.

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