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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 03 Nov 2024 23:45:00 GMT2024-11-03T23:45:00ZDeep homogenization networks for elastic heterogeneous materials with two- and three-dimensional periodicity
http://hdl.handle.net/10985/24281
Deep homogenization networks for elastic heterogeneous materials with two- and three-dimensional periodicity
WU, Jiajun; JIANG, Jindong; CHEN, Qiang; CHATZIGEORGIOU, George; MERAGHNI, Fodil
We present a deep learning framework that leverages computational homogenization expertise to predict the local stress field and homogenized moduli of heterogeneous materials with two- and three-dimensional periodicity, which is named physics-informed Deep Homogenization Networks (DHN). To this end, the displacement field of a repeating unit cell is expressed as two-scale expansion in terms of averaging and fluctuating contributions dependent on the global and local coordinates, respectively, under arbitrary multi-axial loading conditions. The latter is regarded as a mesh-free periodic domain estimated using fully connected neural network layers by minimizing residuals of Navier's displacement equations of anisotropic microstructured materials for specified macroscopic strains with the help of automatic differentiation. Enabled by the novel use of a periodic layer, the boundary conditions are encoded directly in the DHN architecture which ensures exact satisfaction of the periodicity conditions of displacements and tractions without introducing additional penalty terms. To verify the proposed model, the local field variables and homogenized moduli were examined for various composites against the finite-element technique. We also demonstrate the feasibility of the proposed framework for simulating unit cells with locally irregular fibers via transfer learning and find a significant enhancement in the accuracy of stress field recovery during neural network retraining.
Fri, 01 Dec 2023 00:00:00 GMThttp://hdl.handle.net/10985/242812023-12-01T00:00:00ZWU, JiajunJIANG, JindongCHEN, QiangCHATZIGEORGIOU, GeorgeMERAGHNI, FodilWe present a deep learning framework that leverages computational homogenization expertise to predict the local stress field and homogenized moduli of heterogeneous materials with two- and three-dimensional periodicity, which is named physics-informed Deep Homogenization Networks (DHN). To this end, the displacement field of a repeating unit cell is expressed as two-scale expansion in terms of averaging and fluctuating contributions dependent on the global and local coordinates, respectively, under arbitrary multi-axial loading conditions. The latter is regarded as a mesh-free periodic domain estimated using fully connected neural network layers by minimizing residuals of Navier's displacement equations of anisotropic microstructured materials for specified macroscopic strains with the help of automatic differentiation. Enabled by the novel use of a periodic layer, the boundary conditions are encoded directly in the DHN architecture which ensures exact satisfaction of the periodicity conditions of displacements and tractions without introducing additional penalty terms. To verify the proposed model, the local field variables and homogenized moduli were examined for various composites against the finite-element technique. We also demonstrate the feasibility of the proposed framework for simulating unit cells with locally irregular fibers via transfer learning and find a significant enhancement in the accuracy of stress field recovery during neural network retraining.Adaptive deep homogenization theory for periodic heterogeneous materials
http://hdl.handle.net/10985/25184
Adaptive deep homogenization theory for periodic heterogeneous materials
WU, Jiajun; CHEN, Qiang; JIANG, Jindong; CHATZIGEORGIOU, George; MERAGHNI, Fodil
We present an adaptive physics-informed deep homogenization neural network (DHN) approach to formulate a full-field micromechanics model for elastic and thermoelastic periodic arrays with different microstructures. The unit cell solution is approximated by fully connected multilayers via minimizing a loss function formulated in terms of the sum of residuals from the stress equilibrium and heat conduction partial differential equations (PDEs), together with interfacial traction-free or adiabatic boundary conditions. In comparison, periodicity boundary conditions are directly satisfied by introducing a network layer with sinusoidal functions. Fully trainable weights are applied on all collocation points, which are simultaneously trained alongside the network
weights. Hence, the network automatically assigns higher weights to the collocation points in the vicinity of the interface (particularly challenging regions of the unit cell solution) in the loss function. This compels the neural networks to enhance their performance at these specific points. The accuracy of adaptive DHN is verified against the finite element and the elasticity solution respectively for elliptical and circular cylindrical pores/fibers. The advantage of the adaptive DHN over the original DHN technique is justified by considering locally irregular porous architecture where pore–pore interaction makes training the network particularly slow and hard to
optimize.
Mon, 01 Jul 2024 00:00:00 GMThttp://hdl.handle.net/10985/251842024-07-01T00:00:00ZWU, JiajunCHEN, QiangJIANG, JindongCHATZIGEORGIOU, GeorgeMERAGHNI, FodilWe present an adaptive physics-informed deep homogenization neural network (DHN) approach to formulate a full-field micromechanics model for elastic and thermoelastic periodic arrays with different microstructures. The unit cell solution is approximated by fully connected multilayers via minimizing a loss function formulated in terms of the sum of residuals from the stress equilibrium and heat conduction partial differential equations (PDEs), together with interfacial traction-free or adiabatic boundary conditions. In comparison, periodicity boundary conditions are directly satisfied by introducing a network layer with sinusoidal functions. Fully trainable weights are applied on all collocation points, which are simultaneously trained alongside the network
weights. Hence, the network automatically assigns higher weights to the collocation points in the vicinity of the interface (particularly challenging regions of the unit cell solution) in the loss function. This compels the neural networks to enhance their performance at these specific points. The accuracy of adaptive DHN is verified against the finite element and the elasticity solution respectively for elliptical and circular cylindrical pores/fibers. The advantage of the adaptive DHN over the original DHN technique is justified by considering locally irregular porous architecture where pore–pore interaction makes training the network particularly slow and hard to
optimize.Physically informed deep homogenization neural network for unidirectional multiphase/multi-inclusion thermoconductive composites
http://hdl.handle.net/10985/23502
Physically informed deep homogenization neural network for unidirectional multiphase/multi-inclusion thermoconductive composites
JIANG, Jindong; WU, Jiajun; CHEN, Qiang; CHATZIGEORGIOU, George; MERAGHNI, Fodil
Elements of the periodic homogenization framework and deep neural network were seamlessly connected for the first time to construct a new micromechanics theory for thermoconductive composites called physically informed Deep Homogenization Network (DHN). This method utilizes a two-scale expansion of the temperature field of spatially uniform composites in terms of macroscopic and fluctuating contributions. The latter is estimated using deep neural network layers. The DHN is trained on a set of collocation points to obtain the fluctuating temperature field over the unit cell domain by minimizing a cost function given in terms of residuals of strong form steady-state heat conduction governing differential equations. Novel use of a periodic layer with several independent periodic functions with adjustable training parameters ensures that periodic boundary conditions of temperature and temperature gradients at the unit cell edges are exactly satisfied. Automatic differentiation is utilized to correctly compute the fluctuating temperature gradients. Homogenized properties and local temperature and gradient distributions of unit cells reinforced by unidirectional fiber or weakened by a hole are compared with finite-element reference results, demonstrating remarkable correlation but without discontinuities associated with temperature gradient distributions in the finite-element simulations. We also illustrate that the DHN enhanced with transfer learning provides a substantially more efficient and accurate simulation of multiple random fiber distributions relative to training the network from scratch.
Mon, 01 May 2023 00:00:00 GMThttp://hdl.handle.net/10985/235022023-05-01T00:00:00ZJIANG, JindongWU, JiajunCHEN, QiangCHATZIGEORGIOU, GeorgeMERAGHNI, FodilElements of the periodic homogenization framework and deep neural network were seamlessly connected for the first time to construct a new micromechanics theory for thermoconductive composites called physically informed Deep Homogenization Network (DHN). This method utilizes a two-scale expansion of the temperature field of spatially uniform composites in terms of macroscopic and fluctuating contributions. The latter is estimated using deep neural network layers. The DHN is trained on a set of collocation points to obtain the fluctuating temperature field over the unit cell domain by minimizing a cost function given in terms of residuals of strong form steady-state heat conduction governing differential equations. Novel use of a periodic layer with several independent periodic functions with adjustable training parameters ensures that periodic boundary conditions of temperature and temperature gradients at the unit cell edges are exactly satisfied. Automatic differentiation is utilized to correctly compute the fluctuating temperature gradients. Homogenized properties and local temperature and gradient distributions of unit cells reinforced by unidirectional fiber or weakened by a hole are compared with finite-element reference results, demonstrating remarkable correlation but without discontinuities associated with temperature gradient distributions in the finite-element simulations. We also illustrate that the DHN enhanced with transfer learning provides a substantially more efficient and accurate simulation of multiple random fiber distributions relative to training the network from scratch.