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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]

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]