https://sam.ensam.eu:443 The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material. Thu, 18 Jun 2026 04:55:20 GMT 2026-06-18T04:55:20Z http://hdl.handle.net/10985/26841 Hybrid homogenization neural networks for periodic composites CHEN, Qiang; ZHAO, Wenhui; XIAO, Ce; YANG, Zhibo; CHATZIGEORGIOU, George; MERAGHNI, Fodil; CHEN, Xuefeng A new physics-informed deep homogenization neural network (DHN) framework is proposed to identify the homogenized and local behaviors in periodic heterogeneous microstructures. To achieve this, the displacement field is decomposed into averaged and fluctuating contributions, with the local unit cell solution obtained via neural networks subject to periodic boundary conditions. The periodic microstructures are divided into sub­domains representing the fiber and matrix phases, respectively. A key contribution of the proposed method is the marriage of elasticity solution and physics-informed neural network to each phase of the composite, namely, the fiber phase as a mesh-free component whose fluctuating displacements are expanded using a discrete Fourier transform, and the matrix phase using material points with fluctuating displacements handled through fully connected neural network layers. The interfacial continuity conditions are enforced by minimizing the traction and displacement differences at separate material points along the interface. Transfer learning is exploited further to facilitate training new microstructures from pre-trained geometry. This hybrid formulation inherently satisfies stress equilibrium equations within the fiber, while efficiently handling the periodic boundary conditions of hexagonal and square unit cells via a series of trainable sinusoidal functions. The innovative use of distinct neural network architectures enables accurate and efficient predictions of displacement and stress when discontinuities are present in the solution fields across the interface. We validate the proposed DHN with the finite-element predictions for unidirectional composites comprised of elastic fiber significantly stiffer than the matrix, under various volume fractions and loading conditions. Sat, 01 Nov 2025 00:00:00 GMT http://hdl.handle.net/10985/26841 2025-11-01T00:00:00Z CHEN, Qiang ZHAO, Wenhui XIAO, Ce YANG, Zhibo CHATZIGEORGIOU, George MERAGHNI, Fodil CHEN, Xuefeng A new physics-informed deep homogenization neural network (DHN) framework is proposed to identify the homogenized and local behaviors in periodic heterogeneous microstructures. To achieve this, the displacement field is decomposed into averaged and fluctuating contributions, with the local unit cell solution obtained via neural networks subject to periodic boundary conditions. The periodic microstructures are divided into sub­domains representing the fiber and matrix phases, respectively. A key contribution of the proposed method is the marriage of elasticity solution and physics-informed neural network to each phase of the composite, namely, the fiber phase as a mesh-free component whose fluctuating displacements are expanded using a discrete Fourier transform, and the matrix phase using material points with fluctuating displacements handled through fully connected neural network layers. The interfacial continuity conditions are enforced by minimizing the traction and displacement differences at separate material points along the interface. Transfer learning is exploited further to facilitate training new microstructures from pre-trained geometry. This hybrid formulation inherently satisfies stress equilibrium equations within the fiber, while efficiently handling the periodic boundary conditions of hexagonal and square unit cells via a series of trainable sinusoidal functions. The innovative use of distinct neural network architectures enables accurate and efficient predictions of displacement and stress when discontinuities are present in the solution fields across the interface. We validate the proposed DHN with the finite-element predictions for unidirectional composites comprised of elastic fiber significantly stiffer than the matrix, under various volume fractions and loading conditions. http://hdl.handle.net/10985/25589 Nitsche's method enhanced isogeometric homogenization of unidirectional composites with cylindrically orthotropic carbon/graphite fibers DU, Xiaoxiao; CHEN, Qiang; CHATZIGEORGIOU, George; MERAGHNI, Fodil; ZHAO, Gang; CHEN, Xuefeng An isogeometric homogenization (IGH) technique is constructed for the homogenization and localization of unidirectional composites with radially or circumferentially orthotropic carbon/graphite fibers. The proposed theory employs multiple non-conforming Non-Uniform Rational B-Splines (NURBS) patches to depict repeating unit cells (RUCs) representative of composite microstructures. Displacements are formulated using a two-scale expansion that integrates macroscopic and microscopic contributions, with the latter addressed through the isogeometric analysis technique. Nitsche’s method is utilized to apply the interfacial traction and displacement continuity and periodicity conditions. The capability and accuracy of the IGH theory were validated upon comparison with the elasticity solutions that take into account explicitly fiber morphologies, along with classical micromechanics solutions based on equivalent fiber moduli. A comparative analysis with conventional finite element techniques showcases the developed theory’s ability to accurately replicate the singular stress field at the fiber center and to capture smooth stress distributions where significant stress gradients are encountered. Thu, 01 Aug 2024 00:00:00 GMT http://hdl.handle.net/10985/25589 2024-08-01T00:00:00Z DU, Xiaoxiao CHEN, Qiang CHATZIGEORGIOU, George MERAGHNI, Fodil ZHAO, Gang CHEN, Xuefeng An isogeometric homogenization (IGH) technique is constructed for the homogenization and localization of unidirectional composites with radially or circumferentially orthotropic carbon/graphite fibers. The proposed theory employs multiple non-conforming Non-Uniform Rational B-Splines (NURBS) patches to depict repeating unit cells (RUCs) representative of composite microstructures. Displacements are formulated using a two-scale expansion that integrates macroscopic and microscopic contributions, with the latter addressed through the isogeometric analysis technique. Nitsche’s method is utilized to apply the interfacial traction and displacement continuity and periodicity conditions. The capability and accuracy of the IGH theory were validated upon comparison with the elasticity solutions that take into account explicitly fiber morphologies, along with classical micromechanics solutions based on equivalent fiber moduli. A comparative analysis with conventional finite element techniques showcases the developed theory’s ability to accurately replicate the singular stress field at the fiber center and to capture smooth stress distributions where significant stress gradients are encountered. http://hdl.handle.net/10985/25884 Physics-informed deep homogenization approach for random nanoporous composites with energetic interfaces CHEN, Qiang; CHATZIGEORGIOU, George; MERAGHNI, Fodil; CHEN, Xuefeng; YANG, Zhibo This contribution presents a new physics-informed deep homogenization neural network model for identifying local displacement and stress fields, as well as homogenized moduli, of nanocomposites with periodic arrays of porosities under general loading conditions. Notably, it accounts for the surface elasticity effect, utilizing the Gurtin-Murdoch interface theory. First of all, a fully connected neural network model is established that maps the spatial coordinates, passing first through several sinusoidal functions, to the microscopic displacements. The loss function is formulated as the weighted sum of residuals of Navier-Cauchy equations in the bulk domains and the Young-Laplace equations on the energetic surfaces, evaluated on separate sets of collocation points. To more effectively predict stress concentrations inside the microstructures, we introduce fully trainable weights to each collocation point. The capacity and effectiveness of the new homogenization technique for capturing the size-dependent local and global response of nanocomposites with distinct pore sizes and shapes are verified upon extensive comparisons with the finite-element benchmark results, under various loading conditions. New results showcase the proposed theory’s ability to model random distributions of nano-porosities with a high degree of accuracy, a task not easily achievable with alternative techniques except for the specialized finite-element method. Wed, 01 Jan 2025 00:00:00 GMT http://hdl.handle.net/10985/25884 2025-01-01T00:00:00Z CHEN, Qiang CHATZIGEORGIOU, George MERAGHNI, Fodil CHEN, Xuefeng YANG, Zhibo This contribution presents a new physics-informed deep homogenization neural network model for identifying local displacement and stress fields, as well as homogenized moduli, of nanocomposites with periodic arrays of porosities under general loading conditions. Notably, it accounts for the surface elasticity effect, utilizing the Gurtin-Murdoch interface theory. First of all, a fully connected neural network model is established that maps the spatial coordinates, passing first through several sinusoidal functions, to the microscopic displacements. The loss function is formulated as the weighted sum of residuals of Navier-Cauchy equations in the bulk domains and the Young-Laplace equations on the energetic surfaces, evaluated on separate sets of collocation points. To more effectively predict stress concentrations inside the microstructures, we introduce fully trainable weights to each collocation point. The capacity and effectiveness of the new homogenization technique for capturing the size-dependent local and global response of nanocomposites with distinct pore sizes and shapes are verified upon extensive comparisons with the finite-element benchmark results, under various loading conditions. New results showcase the proposed theory’s ability to model random distributions of nano-porosities with a high degree of accuracy, a task not easily achievable with alternative techniques except for the specialized finite-element method. http://hdl.handle.net/10985/25882 Elasticity-inspired data-driven micromechanics theory for unidirectional composites with interfacial damage CHEN, Qiang; TU, Wenqiong; WU, Jiajun; HE, Zhelong; CHATZIGEORGIOU, George; MERAGHNI, Fodil; YANG, Zhibo; CHEN, Xuefeng We present a novel elasticity-inspired data-driven Fourier homogenization network (FHN) theory for periodic heterogeneous microstructures with square or hexagonal arrays of cylindrical fibers. Towards this end, two custom-tailored networks are harnessed to construct microscopic displacement functions in each phase of composite materials, based on the exact Fourier series solutions of Navier’s displacement differential equations. The fiber and matrix networks are seamlessly connected through a common loss function by enforcing the continuity conditions, in conjunction with periodicity boundary conditions, of both tractions and displacements. These conditions are evaluated on a set of weighted collocation points located on the fiber/matrix interface and the exterior faces of the unit cell, respectively. The partial derivatives of displacements are computed effortlessly through the automatic differentiation functionality. During the training of the FHN model, the total loss function is minimized with respect to the Fourier series parameters using gradient descent and concurrently maximized with respect to the adaptive weights using gradient ascent. The transfer learning technique is employed to speed up the training of new geometries by leveraging a pre-trained model. Comparison with finite-element/volume-based unit cell solutions under various loading scenarios showcases the computational capability of the proposed method. The utility of the proposed technique is further demonstrated by capturing the interfacial debonding in unidirectional composites via a cohesive interface model. Fri, 01 Nov 2024 00:00:00 GMT http://hdl.handle.net/10985/25882 2024-11-01T00:00:00Z CHEN, Qiang TU, Wenqiong WU, Jiajun HE, Zhelong CHATZIGEORGIOU, George MERAGHNI, Fodil YANG, Zhibo CHEN, Xuefeng We present a novel elasticity-inspired data-driven Fourier homogenization network (FHN) theory for periodic heterogeneous microstructures with square or hexagonal arrays of cylindrical fibers. Towards this end, two custom-tailored networks are harnessed to construct microscopic displacement functions in each phase of composite materials, based on the exact Fourier series solutions of Navier’s displacement differential equations. The fiber and matrix networks are seamlessly connected through a common loss function by enforcing the continuity conditions, in conjunction with periodicity boundary conditions, of both tractions and displacements. These conditions are evaluated on a set of weighted collocation points located on the fiber/matrix interface and the exterior faces of the unit cell, respectively. The partial derivatives of displacements are computed effortlessly through the automatic differentiation functionality. During the training of the FHN model, the total loss function is minimized with respect to the Fourier series parameters using gradient descent and concurrently maximized with respect to the adaptive weights using gradient ascent. The transfer learning technique is employed to speed up the training of new geometries by leveraging a pre-trained model. Comparison with finite-element/volume-based unit cell solutions under various loading scenarios showcases the computational capability of the proposed method. The utility of the proposed technique is further demonstrated by capturing the interfacial debonding in unidirectional composites via a cohesive interface model. http://hdl.handle.net/10985/27122 Micromechanics-Informed Neural Networks for Periodic Homogenization of Thermocondcutive Behavior in Unidirectional Composites with Cylindrically Orthotropic Graphite Fibers XIAO, Ce; CHEN, Qiang; EL FALLAKI IDRISSI, Mohammed; YANG, Zhibo; CHEN, Xuefeng; CHATZIGEORGIOU, George; MERAGHNI, Fodil A micromechanics-informed neural network framework is developed for homogenization of periodic unidirectional thermoconductive composites with cylindrically orthotropic fibers. The framework hard-imposes the steady-state governing heat conduction equations within the network architecture, enabling accurate capture of singular heat flux fields at the fiber center that are challenging for conventional approaches. In contrast, continuity and periodicity conditions are enforced via boundary collocation points in the loss function. Validation against finite element simulations across a wide range of fiber volume fractions shows that accurate and converged temperature distributions can be achieved after 9000 training epochs using 8-16 harmonic terms. Additional higher-order harmonics are difficult to train reliably and may degrade predictions. While strong agreement is observed in the matrix heat flux distributions, noticeable discrepancies persist in the fiber phase due to varying ability to capture the singular heat flux fields. Furthermore, uniform collocation points converge faster than random points during solution refinement. Finally, transfer learning is employed to accelerate training for new configurations, allowing the network to achieve comparable accuracy after only 2000 training epochs, which is substantially fewer than the 9,000 epochs required when training from scratch. Sat, 01 Nov 2025 00:00:00 GMT http://hdl.handle.net/10985/27122 2025-11-01T00:00:00Z XIAO, Ce CHEN, Qiang EL FALLAKI IDRISSI, Mohammed YANG, Zhibo CHEN, Xuefeng CHATZIGEORGIOU, George MERAGHNI, Fodil A micromechanics-informed neural network framework is developed for homogenization of periodic unidirectional thermoconductive composites with cylindrically orthotropic fibers. The framework hard-imposes the steady-state governing heat conduction equations within the network architecture, enabling accurate capture of singular heat flux fields at the fiber center that are challenging for conventional approaches. In contrast, continuity and periodicity conditions are enforced via boundary collocation points in the loss function. Validation against finite element simulations across a wide range of fiber volume fractions shows that accurate and converged temperature distributions can be achieved after 9000 training epochs using 8-16 harmonic terms. Additional higher-order harmonics are difficult to train reliably and may degrade predictions. While strong agreement is observed in the matrix heat flux distributions, noticeable discrepancies persist in the fiber phase due to varying ability to capture the singular heat flux fields. Furthermore, uniform collocation points converge faster than random points during solution refinement. Finally, transfer learning is employed to accelerate training for new configurations, allowing the network to achieve comparable accuracy after only 2000 training epochs, which is substantially fewer than the 9,000 epochs required when training from scratch.