CONSISTENT INTEGRATION SCHEMES FOR ANALYSIS OF STRAIN GRADIENT ELASTICITY USING AI APPROACH

Strain gradient elasticity is a promising framework for modelling the mechanical behaviour of materials at small scales, where traditional continuum mechanics assumptions break down. Analysing the behaviour of materials under strain gradient elasticity requires the solution of complex partial differential equations, posing significant computational challenges. In this study, we propose a novel approach that combines consistent integration schemes with artificial intelligence (AI) techniques to efficiently analyse strain gradient elasticity. The key idea behind our approach is to leverage the power of AI algorithms, specifically deep learning, to approximate the solution of strain gradient elasticity equations. We train a neural network using a dataset of known solutions obtained from consistent integration schemes. The trained network is then capable of predicting the solution for a given set of input parameters, bypassing the need for computationally expensive numerical simulations. By utilizing AI techniques, our approach offers several advantages. It significantly reduces the computational cost associated with strain gradient elasticity analysis, enabling engineers and researchers to perform rapid and efficient analyses. This is particularly beneficial when dealing with complex material geometries or when exploring a wide range of input parameters. Our AI-based approach provides accurate and reliable solutions, as it learns from a dataset of consistent integration scheme solutions. The neural network captures the underlying relationships between input parameters and the corresponding strain gradient elasticity solutions, enabling it to generalize well to unseen cases. Our approach is flexible and adaptable, accommodating various material models and boundary conditions. The neural network can be trained on datasets generated from different consistent integration schemes or extended to handle more complex scenarios as new data becomes available. To evaluate the effectiveness of our approach, we conducted extensive numerical experiments on different material systems, comparing the results obtained using our AI-based approach with those obtained using traditional numerical methods. The results demonstrate that our approach achieves accurate solutions with significantly reduced computational effort. It offers a computationally efficient and accurate alternative to traditional numerical methods, enabling engineers and researchers to gain insights into the behaviour of materials at small scales. The integration of AI into strain gradient elasticity analysis