Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularl...Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.展开更多
This paper addresses the application of the continuum mechanics-based multiplicative decomposition for thermohyperelastic materials by Lu and Pister to Reissner’s structural mechanics-based,geometrically exact theory...This paper addresses the application of the continuum mechanics-based multiplicative decomposition for thermohyperelastic materials by Lu and Pister to Reissner’s structural mechanics-based,geometrically exact theory for finite strain plane deformations of beams,which represents a geometrically consistent non-linear extension of the linear shear-deformable Timoshenko beam theory.First,the Lu-Pister multiplicative decomposition of the displacement gradient tensor is reviewed in a three-dimensional setting,and the importance of its main consequence is emphasized,i.e.,the fact that isothermal experiments conducted over a range of constant reference temperatures are sufficient to identify constitutive material parameters in the stress-strain relations.We address various isothermal stress-strain relations for isotropic hyperelastic materials and their extensions to thermoelasticity.In particular,a model belonging to what is referred to as Simo-Pister class of material laws is used as an example to demonstrate the proposed procedure to extend isothermal stress-strain relations for isotropic hyperelastic materials to thermoelasticity.A certain drawback of Reissner’s structural-mechanics based theory in its original form is that constitutive relations are to be stipulated at the one-dimensional level,between stress resultants and generalized strains,so that the standardized small-scale material testing at the stress-strain level is not at disposal.In order to overcome this,we use a stress-strain based extension of the Reissner theory proposed by Gerstmayr and Irschik for the isothermal case,which we utilize here in the framework of the considered thermoelastic extension of the Simo-Pister stressstrain law.Consistent with the latter extension,we derive non-linear thermo-hyperelastic constitutive relations between stress-resultants and general strains.Special emphasis is given to linearizations and their consequences.A numerical example demonstrates the efficacy of the structural-mechanics approach in large-deformation problems.展开更多
文摘Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.
基金The authors acknowledge the support by the Linz Center of Mechatronics(LCM)in the framework of the Austrian COMET-K2 program。
文摘This paper addresses the application of the continuum mechanics-based multiplicative decomposition for thermohyperelastic materials by Lu and Pister to Reissner’s structural mechanics-based,geometrically exact theory for finite strain plane deformations of beams,which represents a geometrically consistent non-linear extension of the linear shear-deformable Timoshenko beam theory.First,the Lu-Pister multiplicative decomposition of the displacement gradient tensor is reviewed in a three-dimensional setting,and the importance of its main consequence is emphasized,i.e.,the fact that isothermal experiments conducted over a range of constant reference temperatures are sufficient to identify constitutive material parameters in the stress-strain relations.We address various isothermal stress-strain relations for isotropic hyperelastic materials and their extensions to thermoelasticity.In particular,a model belonging to what is referred to as Simo-Pister class of material laws is used as an example to demonstrate the proposed procedure to extend isothermal stress-strain relations for isotropic hyperelastic materials to thermoelasticity.A certain drawback of Reissner’s structural-mechanics based theory in its original form is that constitutive relations are to be stipulated at the one-dimensional level,between stress resultants and generalized strains,so that the standardized small-scale material testing at the stress-strain level is not at disposal.In order to overcome this,we use a stress-strain based extension of the Reissner theory proposed by Gerstmayr and Irschik for the isothermal case,which we utilize here in the framework of the considered thermoelastic extension of the Simo-Pister stressstrain law.Consistent with the latter extension,we derive non-linear thermo-hyperelastic constitutive relations between stress-resultants and general strains.Special emphasis is given to linearizations and their consequences.A numerical example demonstrates the efficacy of the structural-mechanics approach in large-deformation problems.
