Peri-Net: Analysis of Crack Patterns Using Deep Neural Networks

Abstract

In this work, we introduce convolutional neural networks designed to predict and analyze damage patterns on a disk resulting from molecular dynamic (MD) collision simulations. The simulations under consideration are specifically designed to produce cracks on the disk and, accordingly, numerical methods which require partial derivative information, such as finite element analysis, are not applicable. These simulations can, however, be carried out using peridynamics, a nonlocal extension of classical continuum mechanics based on integral equations which overcome the difficulties in modeling deformation discontinuities. Although this nonlocal extension provides a highly accurate model for the MD simulations, the computational complexity and corresponding run times increase greatly as the simulations grow larger. We propose the use of neural network approximations to complement peridynamic simulations by providing quick estimates which maintain much of the accuracy of the full simulations while reducing simulation times by a factor of 1500. We propose two distinct convolutional neural networks: one trained to perform the forward problem of predicting the damage pattern on a disk provided the location of a colliding object's impact, and another trained to solve the inverse problem of identifying the collision location, angle, velocity, and size given the resulting damage pattern.

A peridynamic-based machine learning model for one-dimensional and two-dimensional structures

“…These data-driven models can be applicable for many scientific disciplines such as image recognition [44], natural language processing [45], cognitive science [46] and genomics [47]. In engineering, machine learning and artificial intelligence also show potential applications in many areas, including material science [48], fluid dynamics [49,50], structural health monitoring [51], additive manufacturing [52] and fracture mechanics and failure analysis [53][54][55].…”

“…The study in [55] proposed convolutional neural networks for predicting the damage patterns on a disk hit by an indenter. First, the PD simulations to predict crack patterns on a disk hit by an indenter are conducted to generate the data set.…”

“…As can be observed from [53,55], the neural networks are trained by using the crack propagation data predicted by trial numerical predictions, which can be very computationally expensive and limited. On the other hand, when available data are limited, the vast majority of recent machine learning techniques are lacking robustness and accuracy [56].…”

A physics-guided machine learning model for two-dimensional structures based on ordinary state-based peridynamics

“…In the recent two decades, with the availability of large datasets as well as the improvement in algorithms and computing power, machine learning (ML) and artificial intelligence (AI) have been providing an alternative solution for physics-based models of many engineering structures [1][2][3][4][5][6][7][8]. However, when available data are limited, machine learning techniques may lose robustness and accuracy [9].…”

Integrating Artificial Intelligence, Theory, Modeling and Experiments – Perspectives, Challenges, and Opportunities in Materials and Manufacturing

“…A convolutional encoder-decoder networks with quantified uncertainty (ConvPDE-UQ) [1] was developed to predict the solutions of partial differential equations on varied domains, which was much faster than the traditional finite element solver. A deep neural networks named Peri-Net [2] was designed for analysis of crack patterns, which is much faster than the peridynamics solver. A deep neural process with a quantified uncertainty capability named Peri-Net-Pro [3] was developed for analysis of crack patterns.…”