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The Data-Driven Harmonic Analysis of Damage (DDHAD) has been proposed recently to construct arbitrarily anisotropic damage models in quasi-brittle heterogeneous materials from calculations on Representative Volume Elements. During preliminary off-line calculations, numerical crack propagations are simulated and the effective damaged elasticity tensor is computed by numerical homogenization. A macroscopic damage model with internal variables is defined using harmonic analysis of the elasticity tensor. The method, called DDHAD, is in this work improved by two key novelties. First, a numerical framework is proposed to evaluate efficiently the model during on-line calculations by computing all the integral terms during off-line calculations and expressing the damage model in a compact matrix form. Second, a reduced model is introduced to further reduce the number of internal variables which is in general large in 3D. It is shown in an application to the damage of 3D printed lattice that even for a complex 3D induced anisotropy, the number of internal variables can drop to a very small number (3 or 4) with the aid of the proposed strategy. [ABSTRACT FROM AUTHOR]

Summary: This paper presents a topology optimization framework for optimizing the fracture resistance of two‐phase composites considering interfacial damage interacting with crack propagation through a redistribution of the inclusions phase. A phase field method for fracture capable of describing interactions between bulk brittle fracture and interfacial damage is adopted within a diffuse approximation of discontinuities. This formulation avoids the burden of remeshing problem during crack propagation and is well adapted to topology optimization purpose. Efficient design sensitivity analysis is performed by using the adjoint method, and the optimization problem is solved by an extended bidirectional evolutionary structural optimization method. The sensitivity formulation accounts for the whole fracturing process involving crack nucleation, propagation, and interaction, either from the interfaces and then through the solid phases, or the opposite. The spatial distribution of material phases are optimally designed using the extended bidirectional evolutionary structural optimization method to improve the fractural resistance. We demonstrate through several examples that the fracture resistance of the composite can be significantly increased at constant volume fraction of inclusions by the topology optimization process. [ABSTRACT FROM AUTHOR]

In this paper, we propose a numerical framework for optimizing the fracture resistance of quasi-brittle composites through a modification of the topology of the inclusion phase. The phase field method to fracturing is adopted within a regularized description of discontinuities, allowing to take into account cracking in regular meshes, which is highly advantageous for topology optimization purpose. Extended bi-directional evolutionary structural optimization (BESO) method is employed and formulated to find the optimal distribution of inclusion phase, given a target volume fraction of inclusion and seeking a maximal fracture resistance. A computationally efficient adjoint sensitivity formulation is derived to account for the whole fracturing process, involving crack initiation, propagation and complete failure of the specimen. The effectiveness of developed framework is illustrated through a series of 2D and 3D benchmark tests. [ABSTRACT FROM AUTHOR]

A new multi-phase-field method is developed for modeling the fracture of polycrystals at the microstructural level. Inter and transgranular cracking, as well as anisotropic effects of both elasticity and preferential cleavage directions within each randomly oriented crystal are taken into account. For this purpose, the proposed phase field formulation includes: (a) a smeared description of grain boundaries as cohesive zones avoiding defining an additional phase for grains; (b) an anisotropic phase field model; (c) a multi-phase field formulation where each preferential cleavage direction is associated with a damage (phase field) variable. The obtained framework allows modeling interactions and competition between grains and grain boundary cracks, as well as their effects on the effective response of the material. The proposed model is illustrated through several numerical examples involving a full description of complex crack initiation and propagation within 2D and 3D models of polycrystals. [ABSTRACT FROM AUTHOR]

A phase field model for anisotropic, elastoplastic fracture model in layered structures obtained by 3D printing processes is proposed. An extension of anisotropic phase field to elastoplasticity model is developed. The model is able to describe a transition from quasi-brittle to elastoplastic fracture behaviors depending on the angle of layers in the microstructure with respect to the external loading. Such feature is of special interest to describe the anisotropic fracture behavior in layered 3D printed materials. The present model introduces two phase field variables, one bulk fracture damage and one micro interfacial damage variables, describing two different micro damage mechanisms. Finally, we have proposed an original methodology to identify the macroscopic strain density as a function of the micro interfacial damage variable using numerical homogenization on Representative Volume Elements. Numerical investigations show that the present model is convergent with respect to mesh refinement, and allows to describe complex crack initiation and propagation in layered elastoplastic structures. An experimental comparison is provided to validate the use of such model for 3D printed polymer materials. [ABSTRACT FROM AUTHOR]

Experimental results for the cracking of heterogeneous clay samples during desiccation are reported, and an associated numerical model is developed for comparison. The clay samples contain embedded rigid inclusions to induce heterogeneous strain fields during drying. The crack paths and local strain fields are monitored during the desiccation process using digital image correlation. A numerical phase field model for crack initiation and propagation is introduced and compared with the experimental results. A qualitative agreement is found for the obtained crack paths, whereas discrepancies remain for the local strain fields. A discussion regarding the comparison between the experimental results and model is provided. • Original experimental results of desiccation cracks in heterogeneous clay samples including macro inclusions. • Cracks evolution in heterogeneous samples is measured using optical experimental techniques. • Strain fields are evaluated experimentally using digital image correlation. • A phase field crack model is developed to reproduce the experiments. • A comparison and critical discussion on the agreement between experiments and numerical simulations is provided. [ABSTRACT FROM AUTHOR]

In this work, we extend a phase field formulation for dynamic ductile fracture to consider interfacial debonding in elastoplastic composites. The interfacial weak zone is created through a regularization of the sharp interfaces, and the singular strain part along the interfaces is approximated by using a Taylor expansion. Then, a strain density depending on the displacement jump related to matrix/inclusions decohesion is added to the total energy to take into account interfacial debonding. The coupling problems (displacement, plasticity and damage problems) are derived within the variational framework and a staggered iterative algorithmic procedure is described to solve the coupling problems. Numerical examples demonstrate that this method can handle the initiation, propagation, and interaction between bulk dynamic fracture and interface cracks, as well as the anisotropic behavior in the complex microstructure of elastic–plastic composite materials. It also indicates that this model is convergent in terms of mesh refinement. • A numerical framework for dynamic crack propagation in elastoplastic composites interacting with interfacial debonding is proposed. • An associated phase field framework is developed, and the convergence with respect to the mesh is verified. • The framework is applicable to 3D elastoplastic composite microstructures obtained from X-ray computed tomography (XRCT) technique. [ABSTRACT FROM AUTHOR]

In this study, we explore the use of SIMP topology optimization and the phase field approach to fracture to maximize fracture resistance in functionally graded materials (FGMs) in the presence of a second phase. We derive a mathematical formulation using a consistent derivation of the second law of thermodynamics to maximize the external work under the constraints of volume fraction. We also demonstrate that, for every distribution of the density function, the topology optimization problem Γ − Converges. We highlight the significant difference between the fracture resistance in FGMs and homogeneous materials. We investigate the crack propagation path along with the optimum topology for the FGM under different grading profiles, elastic mismatch ratio, strength mismatch ratio, and inclusion mismatch ratio. We present several numerical examples to demonstrate the predictive capability of the presented model. A comparison between the initial design guess and the final optimized design is also provided for each example, to further assess the model capability. • Minimization of compliance and maximization of the fracture resistance in FGMs. • Proof of Γ -Convergence for every distribution of optimisation density function. • Effect of elastic mismatch, strength mismatch, and inclusion mismatch with comparison to homogenous materials on optimum topology. • Comparison between initial design guess and optimum design. • Convergence properties of the design. [ABSTRACT FROM AUTHOR]