A non-intrusive stochastic phase field method for crack propagation in functionally graded materials

Dsouza, Shaima Magdaline; Hirshikesh,; Mathew, Tittu Varghese; Singh, I.V.; Natarajan, Sundararajan

doi:10.1007/s00707-021-02956-z

Cited by 23 publications

(1 citation statement)

References 59 publications

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“…Of course, more number of replications will include more possible events (provides more informative data) that result in a more accurate expected value and variance. For the quasi-brittle materials, the Monte Carlo finite element method (MC-FEM) was used to model the dependence of the computed crack probabilities on the type of perturbation in [55,56,57], and the polynomial chaos expansion in functionally graded materials with random material properties is used to model the phase-field fracture, see [58]. In computational mechanics, stochastic discretization techniques have been employed for variational theory for nonlinear problems with stochastic coefficients [59,60,61], inelastic media under uncertainty [62], elastic-plastic material with uncertain parameters [63], fatigue crack propagation due to the inherent uncertainties according to the material properties [64], nonlinear fracture mechanics of concrete [65], and stochastic fracture response and crack growth analysis of laminated composites [66].…”

Section: Introductionmentioning

confidence: 99%

Probabilistic failure mechanisms via Monte Carlo simulations of complex microstructures

Noii,

Khodadadian,

Aldakheel

2022

Preprint

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A probabilistic approach to phase-field brittle and ductile fracture with random material and geometric properties is proposed within this work. In the macroscopic failure mechanics, materials properties and exactness of spatial quantities (of different phases in the geometrical domain) are assumed to be homogeneous and deterministic. This is unlike the lower-scale with strong fluctuation in the material and geometrical properties. Such a response is approximated through some uncertainty in the model problem. The presented contribution is devoted to providing a mathematical framework for modeling uncertainty through stochastic analysis of a microstructure undergoing brittle/ductile failure. Hereby, the proposed model employs various representative volume elements with random distribution of stiff-inclusions and voids within the composite structure. We develop an allocating strategy to allocate the heterogeneities and generate the corresponding meshes in two-and three-dimensional cases. Then the Monte Carlo finite element technique is employed for solving the stochastic PDE-based model and approximate the expectation and the variance of the solution field of brittle/ductile failure by evaluating a large number of samples. For the prediction of failure mechanisms, we rely on the phase-field approach which is a widely adopted framework for modeling and computing the fracture phenomena in solids. Incremental perturbed minimization principles for a class of gradient-type dissipative materials are used to derive the perturbed governing equations. This analysis enables us to study the highly heterogeneous microstructure and monitor the uncertainty in failure mechanics. Several numerical examples are given to examine the efficiency of the proposed method.

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