Search

Auxetic structures, known for their negative Poisson's ratio, exhibit effective elastic properties heavily influenced by their underlying geometry and base material properties. While periodic homogenization of auxetic unit cells can be used to investigate these properties, it is computationally expensive and limits design space exploration and inverse analysis. In this paper, the fast Fourier transform (FFT)-based homogenization approach is adopted to efficiently generate data for developing surrogate models, bypassing concerns about periodic mesh generation and boundary conditions typically associated with the finite element method (FEM). Surrogate models are developed for the real-time prediction of the effective elastic properties of auxetic unit cells with orthogonal voids of different shapes. The generated surrogate models accept geometric parameters and base material properties as inputs to predict the effective elastic constants in real-time. This rapid evaluation enables a practical inverse analysis framework for obtaining the optimal design parameters that yield the desired effective response. The performance of the generated surrogate models is rigorously examined through a train/test split methodology, a parametric study, and an inverse problem. Finally, a graphical user interface (GUI) is developed, offering real-time prediction of the effective tangent stiffness and performing inverse analysis to determine optimal geometric parameters.

We establish a computational methodology to incorporate interfaces with lower crack energy than the surrounding phases when computing the effective crack energy of brittle composite materials. Recent homogenization results for free discontinuity problems are directly applicable to the time-discretized Francfort-Marigo model of brittle fracture in the anti-plane shear case, and computational tools were introduced to evaluate the effective crack energy on complex microstructures using FFT-based solvers and a discretization scheme based on a combinatorially consistent grid. However, this approach only accounts for the crack resistance per volume and is insensitive to the crack resistance of the interface which is expected to play a significant role by considerations from materials science. In this work we introduce a remedy exploiting laminate composite voxels. The latter were originally introduced to enhance the accuracy of solutions for elasticity problems on regular voxel grids. We propose an accurate approximation of the effective crack energy of a laminate with weak interface where an explicit solution is available. We incorporate this insight into an efficient algorithmic framework. Finally, we demonstrate the capabilities of our approach on complex microstructures with weak interfaces between different constituents. [ABSTRACT FROM AUTHOR]

In this paper, a multiscale optimization approach for composite material design is presented. The objective is to find different material designs for a short fiber reinforced polymer (SFRP) with a desired effective (in general anisotropic) viscoelastic behavior. The paper extends the work of Staub et al. (2012) and proposes a combination of material homogenization, surrogate modeling, parameter optimization and robustness analysis. A variety of microstructure design parameters including the fiber volume fraction, the fiber orientation distribution, the linear elastic fiber properties, and the temperature dependent material behavior are considered. For the solution of the structural optimization problem, a surrogate-based optimization framework is developed. The individual steps of that framework consist of using design of experiments (DoE) for the sampling of the constraint material design space, numerical homogenization for the creation of a material property database, a surrogate modeling approach for the interpolation of the single effective viscoelastic parameters and the use of differential evolution (DE) for optimization. In the numerical homogenization step, creep simulations on virtually created representative volume elements (RVEs) are performed and a fast Fourier transform (FFT)-based homogenization is used to obtain the effective viscoelastic material parameters. For every identified optimal design, the robustness is evaluated. The considered Kriging surrogate models of Kriging type have a high prediction accuracy. Numerical examples demonstrate the efficiency of the proposed approach in determining SFRPs with target viscoelastic behavior. An experimental validation shows a good agreement of the homogenization method with corresponding measurements. During the manufacturing of composite parts, the results of such optimizations allow a consideration of the local microstructure in order to achieve the desired macroscopic viscoelastic behavior. [ABSTRACT FROM AUTHOR]

The link between experimental characterization and the constitutive behavior of an anisotropic linear viscoelastic unidirectional carbon fiber-reinforced thermoplastic composite is explored using micromechanics modeling. Dynamic torsion tests were conducted at 1 Hz over a wide temperature range, from the glassy to the rubbery states of the polymeric matrix, on both the pure matrix and the composite, for various cutting angles relative to the fibers. A two-step modeling procedure in the frequency domain is presented to predict and validate the effective behavior of the composite. The first step involves FFT-based homogenization, which maps the microstructure and constituent behaviors to effective transversely isotropic viscoelastic properties. The second step consists of finite element simulations using the effective behavior calculated from homogenization as input to replicate the experiments. A comparison between experimental results and model predictions across the entire temperature range is performed. The modeling predictions show good accuracy at low temperatures, where the matrix is in the glassy state. At high temperatures, where the matrix is in the rubbery state, the predicted behavior becomes too soft. As the phase contrast increases and the ratio of matrix bulk modulus to shear modulus rises significantly, the impact of fiber arrangement on the effective properties becomes more pronounced. [Display omitted] • FFT-based homogenization of viscoelastic properties of carbon fiber reinforced polymers in the frequency domain. • Transversely isotropic linear viscoelasticity characterization and modeling. • Impact of spatial arrangement of fibers on effective viscoelastic properties in glassy and rubbery states. • Comparison between DMA experiments and predictions in glassy and rubbery states. • Dynamic Mechanical Analysis experiments and Finite element simulations in the frequency domain. [ABSTRACT FROM AUTHOR]

We propose a universal method for the evaluation of generalized standard materials that greatly simplifies the material law implementation process. By means of automatic differentiation and a numerical integration scheme, AutoMat reduces the implementation effort to two potential functions. By moving AutoMat to the GPU, we close the performance gap to conventional evaluation routines and demonstrate in detail that the expression level reverse mode of automatic differentiation as well as its extension to second order derivatives can be applied inside CUDA kernels. We underline the effectiveness and the applicability of AutoMat by integrating it into the FFT-based homogenization scheme of Moulinec and Suquet and discuss the benefits of using AutoMat with respect to runtime and solution accuracy for an elasto-viscoplastic example. [ABSTRACT FROM AUTHOR]

The work deals with a macroscopically isotropic energetic material based on triamino-trinitrobenzene (TATB) crystals bonded with a small volume fraction of a thermoplastic polymer. This material is shown experimentally to display an irreversible thermal expansion behavior characterized by dilatancy and variations of its thermal expansion coefficient when heated or cooled outside a narrow reversibility temperature range. The analysis of cooling results suggests the existence of residual stresses in the initial state, attributed to the manufacturing process. Microstructure-level FFT computations including the very strong anisotropic thermoelastic TATB crystal response and temperature-dependent binder plasticity, show that strong internal stresses develop in the disoriented crystals under thermal load, either heating or cooling. Upon cooling, binder plastic yielding in hindered, thus promoting essentially brittle microcracking, while it is favored upon heating. Despite its low volume fraction, the role of the binder is essential, its plastic yielding causing stress redistribution and residual stresses upon cooling back to ambient.

An FFT-based algorithm is developed to simulate the propagation of elastic waves in heterogeneous d -dimensional rectangular shape domains. The method allows one to prescribe the displacement as a function of time in a subregion of the domain, emulating the application of Dirichlet boundary conditions on an outer face. Time discretization is performed using an unconditionally stable beta-Newmark approach. The implicit problem for obtaining the displacement at each time step is solved by transforming the equilibrium equations into Fourier space and solving the corresponding linear system with a preconditioned Krylov solver. The resulting method is validated against analytical solutions and compared with implicit and explicit finite element simulations and with an explicit FFT approach. The accuracy of the method is similar to or better than that of finite elements, and the numerical performance is clearly superior, allowing the use of much larger models. To illustrate the capabilities of the method, some numerical examples are presented, including the propagation of planar, circular, and spherical waves and the simulation of the propagation of a pulse in a polycrystalline medium. [ABSTRACT FROM AUTHOR]

A novel numerical method is developed for three-dimensional modeling of damage and cracking in heterogeneous rock-like materials. Two key issues are addressed. For the first issue, influences of materials heterogeneities such as pores and inclusions on damage evolution and cracking processes are investigated by a homogenization approach with Fast Fourier Transform technique. For the second issue, the nucleation and propagation of cracks from diffuse damage evolution are formulated in Fourier space and described by a phase-field method. To do this, an efficient numerical procedure is developed for the stress–strain relationships and crack phase field propagation. A new elastic degradation function is proposed in order to describe a large range of cracking processes. A range of heterogeneous materials with different microstructure are generated and performed numerically to study effects of pores and inclusions on the damage evolution and cracking process in heterogeneous materials. • A new FFT-based phase field method is developed for modeling damage and cracking in heterogeneous materials. • The proposed method is able to consider complex micro-structures. • This proposed method is able to describe a large range of cracking modes. • Effects of pores and inclusions on cracking evolution patterns are fully investigated through a series of examples. [ABSTRACT FROM AUTHOR]