Nonlinear homogenization using the nonuniform transformation field analysis

Fritzen, Felix; Böhlke, Thomas

doi:10.1002/pamm.201110250

Cited by 7 publications

(3 citation statements)

References 15 publications

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“…The fibrous material was oriented such that the mean fiber axis was perpendicular to the planar surface of the specimen, while the coordinate system of the near isotropic porous material was aligned with the global system. The authors would like to point out that by using local material orientations, arbitrary distributions of the orientation of the microstructure can be assigned to each integration point on the macroscopic scale (see for an example with local‐material orientations using the NTFA). Although the specimen geometry suggests the use of planar boundary conditions, the underlying 3D microstructure induces a nonlinear, rate‐dependent, and anisotropic overall response.…”

Section: Two‐scale Finite Element Simulation Resultsmentioning

confidence: 99%

The finite element square reduced (FE^2R) method with GPU acceleration: towards three‐dimensional two‐scale simulations

Fritzen

Hodapp

2016

Numerical Meth Engineering

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SUMMARYThe FE 2 method is a renown computational multiscale simulation technique for solid materials with finescale microstructure. It allows for the accurate prediction of the mechanical behavior of structures made of heterogeneous materials with nonlinear material behavior. However, the FE 2 method leads to excessive CPU time and storage requirements, even for academic two-dimensional problems. In order to allow for realistic three-dimensional two-scale simulations, a significant reduction of the CPU and memory usage is required. For this purpose, the authors have recently proposed a reduced basis homogenization scheme based on a mixed incremental variational principle. The approach exploits the potential structure of generalized standard materials. Thereby, important speed-ups and memory savings can be achieved. Using high-performance GPUs, the reduced-basis method can be further accelerated. In the present contribution, our previous works are combined and extended to form the FE 2 -reduced method: the FE 2R . The FE 2R can be used to simulate three-dimensional structural problems with consideration of the nonlinearity and microstructure of the underlying material at acceptable computational cost. Thereby, it allows for a new level of complexity in nonlinear multiscale simulations. Numerical examples illustrate the capabilities of the chosen approach.

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Section: Two‐scale Finite Element Simulation Resultsmentioning

confidence: 99%

The finite element square reduced (FE^2R) method with GPU acceleration: towards three‐dimensional two‐scale simulations

Fritzen

Hodapp

2016

Numerical Meth Engineering

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“…The shape, size, and spatial distribution of the Phase-II region in the DRTMC microstructure exhibit a certain degree of randomness. In order to provide an improved representation of the DRTMC microstructure, a realistic modeling method was developed in our work, based on the algorithm of shrinking the Voronoi cells (Thiessen polygons) [ 14 ], which was developed by scholars [ 15 , 16 ]. By means of Fortran programming, the network-like microstructure model containing Phase-I and Phase-II can be generated automatically, and finally transferred to form a 2D RVE finite element model for mechanical simulation.…”

Section: Modeling Of Network-like Microstructurementioning

confidence: 99%

Microstructural Modeling and Strengthening Mechanism of TiB/Ti-6Al-4V Discontinuously-Reinforced Titanium Matrix Composite

Zhao

Pan

et al. 2019

Materials

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A novel modeling method was proposed to provide an improved representation of the actual microstructure of TiB/Ti-6Al-4V discontinuously-reinforced titanium matrix composite (DRTMC). Based on the Thiessen polygon structure, the representative volume element (RVE) containing the complex microstructures of the DRTMC was first generated. Thereafter, by using multiple user-defined subroutines in the commercial finite element software ABAQUS, the application of asymmetric mesh periodic boundary conditions on the RVE was realized, and the equivalent elastic modulus of the DRTMC was determined according to the homogenization method. Through error analyses on the experimental and calculated results regarding the equivalent elastic parameters of the DRTMC, the rationality of generating the DRTMC finite element model by using the present method was validated. Finally, simulations based on four types of network-like models revealed that the present simplifications to the particle shape of the reinforcement phase had less of an influence on the overall composite strength. Moreover, the present study demonstrates that the DRTMC enhancement is mainly attributed to the matrix strengthening, rather than the load-transferring mechanism. The strengthening influences of the distribution forms of the reinforcement phases, including their distribution density and orientation, were studied further. It was found that both the higher distribution density and limited distribution orientation of the particles would increase the probability of overlapping and merging between particles, and; therefore, higher strength could be yielded when the volume fraction of the reinforcement phase reached a certain threshold. Owing to the versatility of the developed methods and programs, this work can provide a useful reference for the characterization of the mechanical properties of other composites types.

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“…Hence, the numerical estimation of ε n (λ) can be performed by the usual implementation of the constitutive equations of generalized standard materials [40][41][42].…”

Section: Numerical Implementation Of the Crementioning

confidence: 99%

Estimation of the validity domain of hyper-reduction approximations in generalized standard elastoviscoplasticity

Ryckelynck

Gallimard

Jules

2015

Adv. Model. and Simul. in Eng. Sci.

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Background:We propose an a posteriori estimator of the error of hyper-reduced predictions for elastoviscoplastic problems. For a given fixed mesh, this error estimator aims to forecast the validity domain in the parameter space, of hyper-reduction approximations. This error estimator evaluates if the simulation outputs generated by the hyper-reduced model represent a convenient approximation of the outputs that the finite element simulation would have predicted. We do not account for the approximation error related to the finite element approximation upon which the hyper-reduction approximation is introduced. Methods: We restrict our attention to generalized standard materials. Upon use of incremental variational principles, we propose an error in constitutive relation. This error is split into three terms including a tailored norm of the hyper-reduction approximation error. This error norm is defined by using the convexity of an incremental potential introduced to state the constitutive equations. The second term of the a posteriori error is related to the stress recovery technique that generates stresses fulfilling the finite element equilibrium equations. The last term is a coupling term between the hyperreduction approximation error at each time step and the errors committed before this time step. Unfortunately, this last term prevents error certification. In this paper, we restrict our attention to outputs extracted by a Lipschitz function of the displacements. Results: In the proposed numerical examples, we show very good preliminary results in predicting the validity domain of hyper-reduction approximations. The average computational time of the predictions obtained by hyper reduction, is accelerated by a factor of 6 compared to that of finite element simulations. This speed-up incorporates the computational time devoted to the error estimation. Conclusions: The numerical implementation of the proposed error estimator is straightforward. It does not require the computation of the incremental potential. In the numerical results, the estimated validity domain of hyper-reduced approximations is inside the reference validity domain. This paper is a first attempt for a posteriori error estimation of hyper-reduction approximations.

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Nonlinear homogenization using the nonuniform transformation field analysis

Cited by 7 publications

References 15 publications

The finite element square reduced (FE^2R) method with GPU acceleration: towards three‐dimensional two‐scale simulations

The finite element square reduced (FE^2R) method with GPU acceleration: towards three‐dimensional two‐scale simulations

Microstructural Modeling and Strengthening Mechanism of TiB/Ti-6Al-4V Discontinuously-Reinforced Titanium Matrix Composite

Estimation of the validity domain of hyper-reduction approximations in generalized standard elastoviscoplasticity

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Nonlinear homogenization using the nonuniform transformation field analysis

Cited by 7 publications

References 15 publications

The finite element square reduced (FE2R) method with GPU acceleration: towards three‐dimensional two‐scale simulations

The finite element square reduced (FE2R) method with GPU acceleration: towards three‐dimensional two‐scale simulations

Microstructural Modeling and Strengthening Mechanism of TiB/Ti-6Al-4V Discontinuously-Reinforced Titanium Matrix Composite

Estimation of the validity domain of hyper-reduction approximations in generalized standard elastoviscoplasticity

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The finite element square reduced (FE^2R) method with GPU acceleration: towards three‐dimensional two‐scale simulations

The finite element square reduced (FE^2R) method with GPU acceleration: towards three‐dimensional two‐scale simulations