A Physics-Informed Assembly of Feed-Forward Neural Network Engines to Predict Inelasticity in Cross-Linked Polymers

Abstract

In solid mechanics, data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and accuracy. However, the implementation of machine-learned approaches in material modeling has been modest due to the high-dimensionality of the data space, the significant size of missing data, and limited convergence. This work proposes a framework to hire concepts from polymer science, statistical physics, and continuum mechanics to provide super-constrained machine-learning techniques of reduced-order to partly overcome the existing difficulties. Using a sequential order-reduction, we have simplified the 3D stress–strain tensor mapping problem into a limited number of super-constrained 1D mapping problems. Next, we introduce an assembly of multiple replicated neural network learning agents (L-agents) to systematically classify those mapping problems into a few categories, each of which were described by a distinct agent type. By capturing all loading modes through a simplified set of dispersed experimental data, the proposed hybrid assembly of L-agents provides a new generation of machine-learned approaches that simply outperform most constitutive laws in training speed, and accuracy even in complicated loading scenarios. Interestingly, the physics-based nature of the proposed model avoids the low interpretability of conventional machine-learned models.

Application of Ultrasonic Measurements for the Evaluation of Steel Fiber Reinforced Concrete

“…Fibers used in concrete [18][19][20][21] can be made of steel, glass, and polymer. Authors in [22][23] investigated the mechanical behavior of polymers by infusing machine learning algorithms and asserted the advantages of using polymers on concrete's characteristics which is applicable to real-world problems [12,18]. The random and closely spaced distribution of steel fibers enabled them to control the development of cracks better than continuous bars.…”

Hand Gesture Recognition Based on Auto-Landmark Localization and Reweighted Genetic Algorithm for Healthcare Muscle Activities

“…SONG is an unsupervised learning model used in applications in which it is important to maintain the topology between input and output spaces. The clustering of input data is achieved so that the distance of the data item in inter-cluster variance is small, and in different classes, inter-cluster variance is large [72][73][74]. A typical SONG training starts with the first two output neurons (n = 2).…”

Adaptive prescribed‐time disturbance observer using nonsingular terminal sliding mode control: Extended Kalman filter and particle swarm optimization

“…where 𝐼 is the inertia moment of the cross-section, 𝑘 0 = √𝐼 𝐴 ⁄ is the radius gyration, and 𝐸, 𝜌, and 𝐴 represent the Young's modulus, mass density, and cross-sectional area, respectively. Substituting (37) into (34), the dimensionless form of the governing equation is expressed as "(see (38)) Substituting ( 41) and ( 42) into (38), multiplying both sides by 𝜙(𝑥̅ ), and integrating the obtained equation over the beam length ( 𝑥̅ = 0 to 𝑥̅ = 1 ), the following dimensionless ordinary differential equation is achieved as 𝑄 ̈(𝑡 ̅ ) + 𝐾 1 𝑄(𝑡 ̅ ) + 𝐾 2 𝑄 3 (𝑡̅ ) = −𝑔𝑃 0 (𝑡̅ ) (43) where the coefficients 𝐾 1 , 𝐾 2 , and 𝑔 are "(see (44)(45)(46))"…”