Proper Orthogonal Decomposition – Based Material Parameter Identification



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University of Cape Town

With regard to efficiency in the design and manufacturing of structural elements it was found that understanding constitutive material laws is essential to civil engineers. When modelling engineering materials engineers face the task of making various assumptions including the choice of a material law applicable to their need. Furthermore, it should be noted that these assumptions affect the accuracy of constitutive material constants which not only influence the purpose for which said material could be used but in addition the economic value of the said material. The use of Finite Element software could be employed and was found to be an important tool in reproducing environmentally accurate constitutive behaviour. This kind of software discretises a material specimen into finite elements in order to monitor different forms of constitutive behaviour. Moreover, the accuracy of this virtual environment is directly proportional to the amount of discretised elements a material is comprised of. This research project aims to provide sufficient preliminary literature to cement the fact that computational methods should be used as reference in computing non-linear constitutive material parameters. This hypothesis is primarily based on the fact that numerous literature, which could be found in section 2, all come to the same conclusion. That is, as the complexity of a constitutive material law increases so does the time it takes to compute a solution from said law. This literature aims to identify methods that could be employed to minimize the simulation time of computing material constants from non-linear constitutive laws. The distinctiveness of using the Proper Orthogonal Decomposition-based (POD) software ORION is that it reduces the complexity of a large dataset. It does so by using linear algebraic operations, namely Eigen vectors and their associated Eigenvalues, to project said dataset to a lower order solution space. In this lower order solution space ORION employs an interpolation technique in order to compute effective constitutive material constants. With regard to computational time, it should be noted that ORION could reduce simulation time greatly. Furthermore, this work provides an outline of the hyperelastic and elastoplastic constitutive material laws and their respective constitutive models. The aforementioned material laws have been implemented within the framework of SESKA, Mesh free in-house software developed by Doctor Sebastian Skatulla, to analyse simple geometric layouts. Moreover, the author provides numerical examples in order to analyse these materials using in-house POD-based and SESKA software packages respectively. Finally, this document provides the relevant preliminary conclusions with regard to the use of POD-based software and its effect on the simulation time of a non-linear constitutive material law. In contrast with coupling the Levenberg-Marquardt algorithm directly with the SESKA software package, the work in this research project is unique as it uses POD-based software as an intermediate software package in order to decrease computational simulation time.