Generalized Continuum Mechanics and PINN-Based Modeling of Hyperelastic Materials

Generalized and higher-order continuum theories, such as micromorphic and gradient elasticity models, are essential for capturing size-dependent and microstructure-sensitive behavior in hyperelastic materials and metamaterials that classical continuum mechanics cannot describe. Solving the resulting nonlinear, thermodynamically consistent governing equations for real structures, such as functionally graded material (FGM) disks and inhomogeneous spheres, is analytically demanding, which has driven growing interest in physics-informed neural networks (PINNs) as a solver for these constitutive and thermodynamic formulations. Connecting these theoretical and PINN-based computational advances is a timely and active challenge.This Research Topic aims to bring together researchers advancing generalized continuum mechanics and thermodynamic modeling of hyperelastic and microstructured materials, together with physics-informed neural network approaches for solving their governing equations. It is intended to consolidate recent theoretical and PINN-based computational advances in higher-order continuum theories, showcase their application to functionally graded and inhomogeneous structures, and highlight emerging metamaterial designs, attracting contributions from continuum mechanics, condensed matter physics, and computational materials science communities.We invite contributions on generalized continuum mechanics, thermodynamics, and PINN-based modeling of nonlinear and microstructured materials, including but not limited to:• Generalized and higher-order continuum theories (micromorphic, gradient elasticity) for hyperelastic and nonlinear materials.• Physics-informed neural networks (PINNs) for solving nonlinear constitutive and thermodynamic equations in hyperelastic and complex media.• Thermodynamically consistent formulations for complex and microstructured media.• Applications to functionally graded material (FGM) disks, inhomogeneous spheres, and other nonlinear structural systems.• Metamaterial design and wave propagation, including mechanical, acoustic, and photonic metamaterials.• Complementary computational approaches, including finite element analysis, for validating PINN-based and analytical models.We welcome Original Research, Reviews, Mini-Reviews, and Technology and Code articles. Topic editors: Nasser Firouzi, Przemysław Podulka, Azhar Hamad Source: https://www.frontiersin.org/research-topics/85514/generalized-continuum-mechanics-and-pinn-based-modeling-of-hyperelastic-materials