An optimal framework for assessing uncertain parameters in large-scale composites using nonlinear MS-GFEM.
Topic(s) : Material and Structural Behavior - Simulation & Testing
Co-authors :
Jean BÉNÉZECH (UNITED KINGDOM), Linus SEELINGER (GERMANY), Anne REINARZ , Richard BUTLER (UNITED KINGDOM), Robert SCHEICHLAbstract :
We have introduced a novel multi-scale spectral generalised finite element method (MS-GFEM) [1] designed to efficiently model the multi-scale behaviour exhibited by large composite structures. Our methodology involves constructing a coarse approximation of large heterogeneous problems through the solution of local generalised eigenproblems within an A-harmonic subspace, resulting in excellent approximation properties. Notably, our method enables precise control over the approximation error by establishing a threshold on eigenvalues that determines which eigenvectors are included in local spaces, thereby maximising model order reduction.
Our primary objective is to predict the onset of damage in realistically scaled slender composite parts. These structures may exhibit buckling prior to damage onsets, necessitating the consideration of geometrically nonlinear behaviour to capture large displacements. Simultaneously, decohesion at the interfaces between plies plays a significant role. Our recent development involves integrating MS-GFEM into a Newton-Raphson scheme, incorporating geometric nonlinearity through the co-rotational formulation [2], and a cohesive zone model [3] to describe inter-ply behaviour.
The domain decomposition method and subdomain independence enable the parallelisation of Newton iterations. A coarse space update is generated at load increments, facilitating the computation of residual forces and total displacement updates at the coarse level. Employing a two-scale approach [4], where local Newton steps proceed in parallel, reduces the total number of global iterations and accelerates local subdomain solves. In contrast to [4], our method provides a better subdomain interaction at the coarse level due to the partition of unity method in the overlaps.
This framework enables the solution of nonlinear problems with several million degrees of freedom in just a few hours, providing sufficient computational resources. Furthermore, by implementing UM-Bridge [5] support, our method seamlessly integrates with state-of-the-art uncertainty quantification codes and additionally parallelises on the stochastic side. We will demonstrate the framework's capabilities on the CerTest demonstrator case: a half-meter C-spar subjected to compression, considering uncertainties in model geometry, material defects, and material properties.
The research was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) through the Programme Grant: “Certification of Design: Reshaping the Testing Pyramid” EP/S017038/1 (https://gow.epsrc.ukri.org/NGBOViewGrant.aspx?GrantRef=EP/S017038/1). The method is developed and integrated in the Distributed and Unified Numerics Environment (DUNE) https://www.dune-project.org/. This work has made use of the Hamilton HPC Service of Durham University.
Our primary objective is to predict the onset of damage in realistically scaled slender composite parts. These structures may exhibit buckling prior to damage onsets, necessitating the consideration of geometrically nonlinear behaviour to capture large displacements. Simultaneously, decohesion at the interfaces between plies plays a significant role. Our recent development involves integrating MS-GFEM into a Newton-Raphson scheme, incorporating geometric nonlinearity through the co-rotational formulation [2], and a cohesive zone model [3] to describe inter-ply behaviour.
The domain decomposition method and subdomain independence enable the parallelisation of Newton iterations. A coarse space update is generated at load increments, facilitating the computation of residual forces and total displacement updates at the coarse level. Employing a two-scale approach [4], where local Newton steps proceed in parallel, reduces the total number of global iterations and accelerates local subdomain solves. In contrast to [4], our method provides a better subdomain interaction at the coarse level due to the partition of unity method in the overlaps.
This framework enables the solution of nonlinear problems with several million degrees of freedom in just a few hours, providing sufficient computational resources. Furthermore, by implementing UM-Bridge [5] support, our method seamlessly integrates with state-of-the-art uncertainty quantification codes and additionally parallelises on the stochastic side. We will demonstrate the framework's capabilities on the CerTest demonstrator case: a half-meter C-spar subjected to compression, considering uncertainties in model geometry, material defects, and material properties.
The research was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) through the Programme Grant: “Certification of Design: Reshaping the Testing Pyramid” EP/S017038/1 (https://gow.epsrc.ukri.org/NGBOViewGrant.aspx?GrantRef=EP/S017038/1). The method is developed and integrated in the Distributed and Unified Numerics Environment (DUNE) https://www.dune-project.org/. This work has made use of the Hamilton HPC Service of Durham University.