We present a new phase field paradigm to predict hydrogen-assisted fatigue. The model combines a phase field description of fracture and fatigue, stress-assisted hydrogen diffusion, and a toughness degradation formulation with cyclic and hydrogen contributions. The predictive capacity of the proposed phase field formulation is verified via CT experiments over all the scenarios considered, spanning multiple load ratios, hydrogen gas pressures and loading frequencies. Results exhibit excellent agreements without any calibration with hydrogen-assisted fatigue data, taking as input only mechanical and hydrogen transport material properties, the material’s fatigue characteristics (from a single test in air), and the sensitivity of fracture toughness to hydrogen content. Then, the model is used to examine the suitable test loading frequencies to obtain conservative Paris curve data, giving new insight into the frequency-dependent fatigue crack growth rate in the hydrogen-containing environment. Finally, we extend the formulation to simulate the fatigue failure of real large-scale hydrogen pressure vessels, showcasing the potential of the Virtual Testing paradigm in infrastructure exposed to hydrogen environments and cyclic loading.

Generalized continuum models for representing nonlinear material behavior including material failure in the finite strain regime are commonly formulated based on scalar elastic and dissipation potential functions. The evolution of stresses and internal variables, i.e., the material state, is governed by partial derivatives of the potential functions with respect to deformation and stress measures. Furthermore, for application of such models in implicit numerical analyses, the tangent operators, consistent with the numerical integration algorithm, are required. The present contribution introduces a semi-analytical split approach for the robust and efficient implementation of generalized continuum models in software for implicit numerical analysis, e.g. Finite Element codes. For this novel semi-analytical approach, automatic differentiation with hyper-dual numbers is utilized for computing partial derivatives of constitutive equations, i.e., scalar potential functions, which are then combined with hand-coded analytical derivatives for operations which are independent of the employed material model, e.g., push/pull operations. In a first step, this approach is introduced on a simple finite strain J2-plasticity model for a better understanding of the underlying concepts. Subsequently, a comprehensive 2D and 3D finite element study employing a finite strain gradient-enhanced micropolar damage-plasticity model is presented. Thereby, we demonstrate the superior properties of the novel semi-analytical split approach compared to numerical differentiation methods with regards to accuracy and robustness. Furthermore, the additional computational cost for automatic differentiation using the proposed split approach becomes negligible for large problems.

Cohesive fracture develops at the macro level of some composites through micro-cracks coalescence and their interaction with micro-heterogeneity. A macroscopic damage model for such a material requires the prescription of an accurate homogenized constitutive behaviour, including elastic, strength and toughness characteristics. Numerical homogenization offers a way to predict these properties utilizing the microscale response. However, it involves two critical challenges: the ill-posedness of the microscale boundary value problem described through local constitutive models and the lack of separation of length scales, which invalidates the conventional scale transition rules. Circumventing these challenges, we propose a numerical scheme based on phase-field fracture (PFF) modelling and failure zone (FZ) homogenization to predict the macroscale constitutive response. The upscaling rule proposed ensures convergence of homogenized post-peak responses to unique functions with increasing size of microscopic volume element (MVE), justifying its representativeness. In earlier works, the actively damaging regions defined the evolving FZ in a Cauchy or micro-morphic continuum. However, in the PFF modelling, rapid strain localization leads to excessive shrinking of the active area within the damaged band. The homogenized jump predicted based on the strain of this active zone turns out to be erroneous. Hence, we implement a modified approach wherein the FZ remains unchanged throughout the loading and is marked based on the phase field at the stage of complete fracture. The zone of the non-zero phase field representing the through crack in the MVE is the modified FZ. One may interpret this FZ as a diffused interface between two adjacent parts of the MVE. We estimate the localization width and macroscopic direction of cracking from the identified FZ and gradient of PF contours. The average strain within FZ is used to compute the homogenized displacement jump across the diffused interface. Numerical experiments demonstrate the accurate prediction of homogenized traction versus separation.

In this work, we compare two approaches for preconditioning the iterative solution of a coupled multi-field problem derived from a generalized continuum model.
The model is aimed at simulating failure in quasi-brittle materials such as concrete and rocks and it couples microrotation and nonlocal damage fields with the displacement field.
Solving large and sparse linear systems can be a challenge, especially when dealing with complex systems like multi-field problems.
The success of iterative methods depends on the spectral properties of the system matrix, so careful construction of the preconditioner is crucial.
A usual approach for the multi-field case involves using a block preconditioner based on factorization, which requires problem-specific approximations of the Schur complement and sub-block inverses.
A popular choice for these inverse approximations is the Algebraic Multigrid Method (AMG), which has proven effective in many cases.
Another strategy is to use AMG on the entire system as a monolithic preconditioner, which treats the block structure inside the preconditioner during hierarchy construction.
Our investigations intend to demonstrate, for the proposed problem, the usefulness of treating the whole block system inside the AMG hierarchy and hence preserve the coupling aspects of the problem.

The mechanical properties of fiber-reinforced cementitious composites FRCC are strongly influenced not only by the matrix and fiber characteristics but also by the fiber-matrix interfaces. In this study, the correlation between microstructural characteristics and mechanical properties of FRCC, i.e., polyvinyl alcohol (PVA) fibers embedded in cement paste matrix, was analyzed through a synergistic approach of combining experiment and simulation.

The microstructural characteristics of FRCC including the fiber-matrix interface were investigated using 3D X-ray micro-CT images. The 3D FRCC microstructures were segmented into 5 phases (pores, fibers, outer products, inner products, and unhydrated phases). PVA fibers have the similar density compared with the cement paste matrix so that the grayscale values from micro-CT images are not distinct. Therefore, segmentation methods for FRCC including an artificial intelligence based approach were proposed in this study.

Using the microstructures obtained from the micro-CT, mechanical responses under direct tension were evaluated by phase-field fracture model simulations. The input modeling parameters for the multiple phases of the cement paste matrix were determined from the nanoindentation test results. Input parameters between fiber and matrix interfaces were parameterized based on the grayscale values of micro-CT images to investigate their effect on the mechanical behaviors of FRCC. The simulation confirmed that the analysis framework provides insights into the effect of microstructural features of FRCC on its mechanical behavior.