Abstract The present work aims at the identification of effective constitutive behavior $$\Sigma 5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Σ</mml:mi><mml:mn>5</mml:mn></mml:mrow></mml:math> aluminum grain boundaries (GB) for proportional loading by using machine learning (ML) techniques. input ML approach is high accuracy data gathered in challenging molecular dynamics (MD) simulations atomic scale varying temperatures and conditions. traction-separation...

A multi-fidelity surrogate model for highly nonlinear multiscale problems is proposed. It based on the introduction of two different models and an adaptive on-the-fly switching. The concurrent surrogates are built incrementally starting from a moderate set evaluations full order model. Therefore, reduced (ROM) generated. Using hybrid ROM-preconditioned FE solver additional effective stress-strain data simulated while number samples kept to level by using dedicated physics-guided sampling...

Abstract Mechanical metamaterials such as open‐ and closed‐cell lattice structures, foams, composites, so forth can often be parametrized in terms of their microstructural properties, for example, relative densities, aspect ratios, material, shape, or topological parameters. To model the effective constitutive behavior facilitate efficient multiscale simulation, design, optimization parametric finite deformation regime, a machine learning‐based is presented this work. The approach...

Abstract In this paper aspects of the nonuniform transformation field analysis (NTFA) introduced by Michel and Suquet ( Int. J. Solids Struct . 2003; 40 :6937–6955) are investigated for materials with three‐dimensional microtopology. A novel implementation NTFA into finite element method (FEM) is described in detail, whereas was originally used combination fast Fourier (FFT). particular, discrete equivalents averaging operators required preprocessing steps an algorithm implicit time...

Summary The FE 2 method is a renown computational multiscale simulation technique for solid materials with fine‐scale microstructure. It allows the accurate prediction of mechanical behavior structures made heterogeneous nonlinear material behavior. However, leads to excessive CPU time and storage requirements, even academic two‐dimensional problems. In order allow realistic three‐dimensional two‐scale simulations, significant reduction memory usage required. For this purpose, authors have...

Summary This paper extends current concepts of topology optimization to the design structures made nonlinear microheterogeneous materials. The objective is maximize macroscopic structural stiffness for a prescribed material volume usage while accounting nonlinearity and microstructure material. resulting problem considers two scales: scale at which performed microscopic heterogeneities nonlinearities are observed. by means bi‐directional evolutionary method. solution boundary value requires...

Abstract Computational homogenization is the gold standard for concurrent multi-scale simulations (e.g., FE2) in scale-bridging applications. Often are based on experimental and synthetic material microstructures represented by high-resolution 3D image data. The computational complexity of operating such voxel data distinct. inability voxelized geometries to capture smooth interfaces accurately, along with necessity reduction, has motivated a special local coarse-graining technique called...

A novel algorithmic discussion of the methodological and numerical differences competing parametric model reduction techniques for nonlinear problems is presented. First, Galerkin reduced basis (RB) formulation presented, which fails at providing significant gains with respect to computational efficiency problems. Renowned methods computing time order models are Hyper-Reduction (Discrete) Empirical Interpolation Method (EIM, DEIM). An description a comparison both provided. The accuracy...

The computational homogenization of hyperelastic solids in the geometrically nonlinear context has yet to be treated with sufficient efficiency order allow for real-world applications true multiscale settings. This problem is addressed by a problem-specific surrogate model founded on reduced basis approximation deformation gradient microscale. setup phase based upon snapshot POD fluctuations, contrast widespread displacement-based approach. In reduce offline costs, space relevant macroscopic...