Model-Free Data-Driven inelasticity
We extend the Data-Driven formulation of problems in elasticity of Kirchdoerfer and Ortiz (2016) to inelasticity. This extension differs fundamentally from Data-Driven problems in elasticity in that the material data set evolves in time as a consequence of the history dependence of the material. We investigate three representational paradigms for the evolving material data sets: (i) materials with memory, i. e., conditioning the material data set to the past history of deformation; (ii) differential materials, i. e., conditioning the material data set to short histories of stress and strain; and (iii) history variables, i. e., conditioning the material data set to ad hoc variables encoding partial information about the history of stress and strain. We also consider combinations of the three paradigms thereof and investigate their ability to represent the evolving data sets of different classes of inelastic materials, including viscoelasticity, viscoplasticity and plasticity. We present selected numerical examples that demonstrate the range and scope of Data-Driven inelasticity and the numerical performance of implementations thereof.
© 2019 Elsevier. Received 9 September 2018, Revised 26 December 2018, Accepted 10 February 2019, Available online 1 March 2019. MO gratefully acknowledges the support of the Deutsche Forschungsgemeinschaft (DFG) through the Sonderforschungsbereich 1060 "The mathematics of emergent effects". SR and RE gratefully acknowledge the financial support of the Deutsche Forschungsgemeinschaft (DFG) through the project "Model order reduction in space and parameter dimension — towards damage-based modeling of polymorphic uncertainty in the context of robustness and reliability" within the priority programme SPP 1886 "Polymorphic uncertainty modelling for the numerical design of structures".
Submitted - 1808.10859.pdf