Efficient Deep Learning for Gradient-Enhanced Stress Dependent Damage Model

This manuscript introduces a computational approach to micro-damage problems using deep learning for the prediction of loading deflection curves. The location of applied forces, dimensions of the specimen and material parameters are used as inputs of the process. The micro-damage is modelled with a gradient-enhanced damage model which ensures the well-posedness of the boundary value and yields mesh-independent results in computational methods such as FEM. We employ the Adam optimizer and Rectified linear unit activation function for training processes and research into the deep neural network architecture. The performance of our approach is demonstrated through some numerical examples including the three-point bending specimen, shear bending on L-shaped specimen and different failure mechanisms.

[1]  Bernhard A. Schrefler,et al.  Artificial Neural Networks in numerical modelling of composites , 2009 .

[2]  Roham Rafiee,et al.  Evaluating mechanical performance of GFRP pipes subjected to transverse loading , 2018, Thin-Walled Structures.

[3]  A. Elnashai,et al.  Self-learning simulation method for inverse nonlinear modeling of cyclic behavior of connections , 2008 .

[4]  Hojjat Adeli,et al.  Neural Networks in Civil Engineering: 1989–2000 , 2001 .

[5]  K. Borgwardt,et al.  Machine Learning in Medicine , 2015, Mach. Learn. under Resour. Constraints Vol. 3.

[6]  Zhen Chen,et al.  One-Dimensional Softening With Localization , 1986 .

[7]  Gilles Pijaudier-Cabot,et al.  Measurement of Characteristic Length of Nonlocal Continuum , 1989 .

[8]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[9]  Timon Rabczuk,et al.  An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications , 2019, Computer Methods in Applied Mechanics and Engineering.

[10]  Gilles Pijaudier-Cabot,et al.  CONTINUUM DAMAGE THEORY - APPLICATION TO CONCRETE , 1989 .

[11]  Geoffrey E. Hinton,et al.  Deep Learning , 2015, Nature.

[12]  Manolis Kellis,et al.  Deep learning for regulatory genomics , 2015, Nature Biotechnology.

[13]  Roham Rafiee,et al.  Stochastic prediction of burst pressure in composite pressure vessels , 2018 .

[14]  Hyeonjoon Moon,et al.  Background Information of Deep Learning for Structural Engineering , 2017 .

[15]  Rhj Ron Peerlings,et al.  Gradient‐enhanced damage modelling of concrete fracture , 1998 .

[16]  O. Stegle,et al.  Deep learning for computational biology , 2016, Molecular systems biology.

[17]  Nicolas Triantafyllidis,et al.  A gradient approach to localization of deformation. I. Hyperelastic materials , 1986 .

[18]  Steffen Freitag,et al.  Modeling of materials with fading memory using neural networks , 2009 .

[19]  T. Belytschko,et al.  Localization limiters in transient problems , 1988 .

[20]  Jamshid Ghaboussi,et al.  Autoprogressive training of neural network constitutive models , 1998 .

[21]  Ryuusuke Kawamura,et al.  Optimization of material composition of nonhomogeneous hollow sphere for thermal stress relaxation making use of neural network , 1999 .

[22]  Rhj Ron Peerlings,et al.  Gradient enhanced damage for quasi-brittle materials , 1996 .

[23]  Roham Rafiee,et al.  Investigating structural failure of a filament-wound composite tube subjected to internal pressure: Experimental and theoretical evaluation , 2018 .

[24]  Yurii Nesterov,et al.  Gradient methods for minimizing composite functions , 2012, Mathematical Programming.

[25]  Genki Yagawa,et al.  Implicit constitutive modelling for viscoplasticity using neural networks , 1998 .

[26]  Nitish Srivastava,et al.  Improving neural networks by preventing co-adaptation of feature detectors , 2012, ArXiv.

[27]  Hans Muhlhaus,et al.  A variational principle for gradient plasticity , 1991 .

[28]  Guang-Zhong Yang,et al.  Deep Learning for Health Informatics , 2017, IEEE Journal of Biomedical and Health Informatics.

[29]  B. Schrefler,et al.  ANN approach to sorption hysteresis within a coupled hygro‐thermo‐mechanical FE analysis , 2001 .

[30]  Yee Whye Teh,et al.  A Fast Learning Algorithm for Deep Belief Nets , 2006, Neural Computation.

[31]  Abhinav Vishnu,et al.  Chemception: A Deep Neural Network with Minimal Chemistry Knowledge Matches the Performance of Expert-developed QSAR/QSPR Models , 2017, ArXiv.

[32]  René de Borst,et al.  Gradient-dependent plasticity: formulation and algorithmic aspects , 1992 .

[33]  Z. Bažant,et al.  Nonlocal Continuum Damage, Localization Instability and Convergence , 1988 .

[34]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[35]  Wam Marcel Brekelmans,et al.  Comparison of nonlocal approaches in continuum damage mechanics , 1995 .