Karl Kalina

Chair of Comp. And Exp. Solid Mechanics, TU Dresden, Germany

Chair of Comp. And Exp. Solid Mechanics, TU Dresden, Germany

The formulation and parametrization of constitutive equations is still a challenging task for materials which reveal complex behavior such as highly nonlinear elasticity, anisotropy or dissipative properties. Due to this, numerous novel approaches - generally referred to as data-based or data-driven methods - have arised recently [1]. These methods circumvent the classical constitutive modeling by directly using data in finite element computations, constructing constitutive manifolds or using artificial neural networks (ANNs).

In this contribution, an automated ANN-based strategy for the efficient description of isotropic hyperelastic solids is presented. Starting from a large data set comprising deformation and corresponding stresses, a simple, physically based reduction of the problem’s dimensionality is performed in a data processing step. More specifically, three deformation type invariants serve as the input instead of the deformation tensor itself which is similar to Liang and Chandrashekhara [2]. In the same way, three corresponding stress coefficients which are derived from the stress-strain tuples replace the stress tensor in the output layer. Using the reduced data set, a constitutive ANN is trained by using standard machine learning methods. Furthermore, in order to fulfill the thermodynamic laws, the previously trained network is modified by constructing a pseudo potential within an integration step and a subsequent derivation.

The proposed method is exemplarily shown for the description of a highly nonlinear Ogden type material in several demonstrative examples. Thereby, the necessary data sets are collected from virtual experiments of a discs with holes. Influences of different loading types and specimen geometries on the resulting data sets are investigated in a systematic study. The developed approach is applied on thevirtually generated data set. Thereby, an excellent approximation quality could be achieved for training,test and validation data with only one hidden layer comprising a comparatively low number of neurons.Finally, the application of the trained constitutive ANN for the simulation of more complex samples verifies the capability of the method.

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Karl Kalina

Chair of Comp. And Exp. Solid Mechanics, TU Dresden, Germany

Chair of Comp. And Exp. Solid Mechanics, TU Dresden, Germany

In this contribution, an automated ANN-based strategy for the efficient description of isotropic hyperelastic solids is presented. Starting from a large data set comprising deformation and corresponding stresses, a simple, physically based reduction of the problem’s dimensionality is performed in a data processing step. More specifically, three deformation type invariants serve as the input instead of the deformation tensor itself which is similar to Liang and Chandrashekhara [2]. In the same way, three corresponding stress coefficients which are derived from the stress-strain tuples replace the stress tensor in the output layer. Using the reduced data set, a constitutive ANN is trained by using standard machine learning methods. Furthermore, in order to fulfill the thermodynamic laws, the previously trained network is modified by constructing a pseudo potential within an integration step and a subsequent derivation.

The proposed method is exemplarily shown for the description of a highly nonlinear Ogden type material in several demonstrative examples. Thereby, the necessary data sets are collected from virtual experiments of a discs with holes. Influences of different loading types and specimen geometries on the resulting data sets are investigated in a systematic study. The developed approach is applied on thevirtually generated data set. Thereby, an excellent approximation quality could be achieved for training,test and validation data with only one hidden layer comprising a comparatively low number of neurons.Finally, the application of the trained constitutive ANN for the simulation of more complex samples verifies the capability of the method.

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