Plasticity models of material variability based on uncertainty quantification techniques

The advent of fabrication techniques like additive manufacturing has focused attention on the considerable variability of material response due to defects and other micro-structural aspects. This variability motivates the development of an enhanced design methodology that incorporates inherent material variability to provide robust predictions of performance. In this work, we develop plasticity models capable of representing the distribution of mechanical responses observed in experiments using traditional plasticity models of the mean response and recently developed uncertainty quantification (UQ) techniques. We demonstrate that the new method provides predictive realizations that are superior to more traditional ones, and how these UQ techniques can be used in model selection and assessing the quality of calibrated physical parameters.

[1]  Qiushi Chen,et al.  ALBANY: USING COMPONENT-BASED DESIGN TO DEVELOP A FLEXIBLE, GENERIC MULTIPHYSICS ANALYSIS CODE , 2016 .

[2]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[3]  Mircea Grigoriu,et al.  On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems , 2015 .

[4]  H. Najm,et al.  On the Statistical Calibration of Physical Models: STATISTICAL CALIBRATION OF PHYSICAL MODELS , 2015 .

[5]  Jeremy A. Templeton,et al.  INFERENCE AND UNCERTAINTY PROPAGATION OF ATOMISTICALLY-INFORMED CONTINUUM CONSTITUTIVE LAWS, PART 1: BAYESIAN INFERENCE OF FIXED MODEL FORMS , 2014 .

[6]  Panayiotis Papadopoulos,et al.  A homogenization method for thermomechanical continua using extensive physical quantities , 2012, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[7]  Habib N. Najm,et al.  Stochastic spectral methods for efficient Bayesian solution of inverse problems , 2005, J. Comput. Phys..

[8]  Maher Salloum,et al.  INFERENCE AND UNCERTAINTY PROPAGATION OF ATOMISTICALLY INFORMED CONTINUUM CONSTITUTIVE LAWS, PART 2: GENERALIZED CONTINUUM MODELS BASED ON GAUSSIAN PROCESSES , 2014 .

[9]  R. Jones,et al.  Uncertainty quantification in MD simulations of concentration driven ionic flow through a silica nanopore. II. Uncertain potential parameters. , 2013, The Journal of chemical physics.

[10]  Brad Lee Boyce,et al.  Crystal plasticity simulations of microstructure-induced uncertainty in strain concentration near voids in brass , 2015 .

[11]  O. L. Maître,et al.  Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics , 2010 .

[12]  S. E. Ahmed,et al.  Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference , 2008, Technometrics.

[13]  W. T. Martin,et al.  The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals , 1947 .

[14]  F. RIZZI,et al.  Uncertainty Quantification in MD Simulations. Part I: Forward Propagation , 2012, Multiscale Model. Simul..

[15]  Elizabeth A. Holm,et al.  The effect of microstructural representation on simulations of microplastic ratcheting , 2010 .

[16]  Dongbin Xiu,et al.  The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations , 2002, SIAM J. Sci. Comput..

[17]  Omar M. Knio,et al.  Spectral Methods for Uncertainty Quantification , 2010 .

[18]  William E. Frazier,et al.  Metal Additive Manufacturing: A Review , 2014, Journal of Materials Engineering and Performance.

[19]  Sia Nemat-Nasser,et al.  Averaging theorems in finite deformation plasticity , 1999 .

[20]  Cosmin Safta,et al.  Uncertainty quantification in LES of channel flow , 2017 .

[21]  Mircea Grigoriu,et al.  Predicting laser weld reliability with stochastic reduced‐order models , 2015 .

[22]  J. C. Simo,et al.  A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. part II: computational aspects , 1988 .

[23]  John Skilling,et al.  Data analysis : a Bayesian tutorial , 1996 .

[24]  R. Hill.  Elastic properties of reinforced solids: some theoretical principles , 1963 .

[25]  Khachik Sargsyan,et al.  Uncertainty Quantification in MD Simulations. Part II: Bayesian Inference of Force-Field Parameters , 2012, Multiscale Model. Simul..

[26]  Bernd A. Berg,et al.  Markov Chain Monte Carlo Simulations , 2007, Wiley Encyclopedia of Computer Science and Engineering.

[27]  David L. McDowell,et al.  Representation and computational structure-property relations of random media , 2011 .

[28]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[29]  O. Knio,et al.  Uncertainty quantification in MD simulations of concentration driven ionic flow through a silica nanopore. I. Sensitivity to physical parameters of the pore. , 2013, The Journal of chemical physics.

[30]  Ralph C. Smith,et al.  Uncertainty Quantification: Theory, Implementation, and Applications , 2013 .

[31]  D. Xiu.  Numerical Methods for Stochastic Computations: A Spectral Method Approach , 2010 .