In this contribution, an online adaptive reduced order model is presented for small-strain elasto-plasticity. Using the GALERKIN method, the problem is projected to a lower subspace giving a reduced problem based on the displacement field snapshots. The adaptivity lies in the update of the projection operator, which is carried out in different parts of the simulation if certain criteria related to the convergence behavior are not fulfilled. With a relative POD analysis called Proper Snapshot Selection (PSS), the new basis is chosen and the simulation is proceeded.

In this paper, an adaptive reduced order method for small strain elasto‐plasticity is discussed. This method works purely online, meaning no preliminary offline calculations have to be conducted. Using a GALERKIN projection, the high‐fidelity problem is reduced to a lower vector space. For this, the basis is extracted from an initial POD after the first few load steps of the simulation. Later on, POD is used again to check the relevance of new snapshots gained from the load stepping. Corrections of the basis ensure the best performance of the current basis.

In this contribution, an adaptive method for Model Order Reduction (MOR) is presented for simulating physically non-linear material behavior of micro-heterogeneous structures. The method is purely online and includes a Galerkin projection, which is performed using a projection operator initially gained by a Proper Orthogonal Decomposition (POD). By this projection, the number of degrees of freedom to solve for is decreased drastically and can be projected back to the vector space of the high fidelity problem after the solution process. The composition of the projection operator follows an adaptive algorithm, which evaluates an update of the operator if convergence is not ensured during the Newton Raphson scheme. Later on, during the simulation, the number of degrees of freedom to solve is controlled using a POD-based control criterion for sorting out non-relevant basis vectors from previous updates. This results in an efficient method and leads to a satisfying speedup of the simulation process. The performance and efficiency of the presented adaptive MOR scheme is investigated in numerical simulations of a hexagon-shaped unit cell.

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