Many-scale finite strain computational homogenization via concentric interpolation. (English) Zbl 07863238
Summary: A method for efficient computational homogenization of hyperelastic materials under finite strains is proposed. Multiple spatial scales are homogenized in a recursive procedure: starting on the smallest scale, few high fidelity FE computations are performed. The resulting fields of deformation gradient fluctuations are processed by a snapshot POD resulting in a reduced basis (RB) model. By means of the computationally efficient RB model, a large set of samples of the homogenized material response is created. This data set serves as the support for the Concentric Interpolation (CI) scheme, interpolating the effective stress and stiffness. Then, the same procedure is invoked on the next larger scale with this CI surrogating the homogenized material law. A three-scale homogenization process is completed within few hours on a standard workstation. The resulting model is evaluated within minutes on a laptop computer in order to generate fourth-scale results. Open source code is provided.
{© 2020 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.}
{© 2020 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.}
MSC:
| 74Qxx | Homogenization, determination of effective properties in solid mechanics |
| 74Exx | Material properties given special treatment |
| 74Sxx | Numerical and other methods in solid mechanics |
Keywords:
computational homogenization; concentric interpolation; Hencky strain; hyperelasticity; multiscale; reduced basisSoftware:
GitHubReferences:
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