Parametric study of random fields of the mechanical properties of the material in a peridynamic model (original) (raw)

Introducing stress random fields of polycrystalline aggregates into the local approach to fracture

Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures, 2014

The coupling of the local approach to fracture and the polycrystalline aggregates simulations is investigated in this paper. A series of Representative Volume Elements (RVEs) drawing randomly the crystallographic orientations and the grain geometries are firstly simulated. Then the resulting realizations of the principal stress random field are used in order to identify the properties of a Gaussian random field using the periodogram approach. The anisotropy of the stress random field is observed and the correlation lengths are identified. Then the synthetic realizations of the identified principal stress random field are simulated using the spectral simulation method. The weakest link theory is lastly applied with this identified principal stress field and simulations of carbides distributions.

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

2021

Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, The Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities with their relative advantages and challenges are summarized.

Statistical models of fracture

Advances in Physics, 2006

Disorder and long-range interactions are two of the key components that make material failure an interesting playfield for the application of statistical mechanics. The cornerstone in this respect has been lattice models of the fracture in which a network of elastic beams, bonds or electrical fuses with random failure thresholds are subject to an increasing external load. These models describe on a qualitative level the failure processes of real, brittle or quasi-brittle materials. This has been particularly important in solving the classical engineering problems of material strength: the size dependence of maximum stress and its sample to sample statistical fluctuations. At the same time, lattice models pose many new fundamental questions in statistical physics, such as the relation between fracture and phase transitions. Experimental results point out to the existence of an intriguing crackling noise in the acoustic emission and of self-affine fractals in the crack surface morphology. Recent advances in computer power have enabled considerable progress in the understanding of such models. Among these partly still controversial issues, are the scaling and size effects in material strength and accumulated damage, the statistics of avalanches or bursts of microfailures, and the morphology of the crack surface. Here we present an overview of the results obtained with lattice models for fracture, highlighting the relations with statistical physics theories and more conventional fracture mechanics approaches.

Cohesive Crack Propagation in a Random Elastic Medium

ABSTRACT. The issue of generating non-Gaussian, multivariate and correlated random fields, while preserving the internal auto-correlation structure of each single-parameter field, is discussed with reference to the problem of cohesive crack propagation. Three different fields are introduced to model the spatial variability of the Young modulus, the tensile strength of the material, and the fracture energy, respectively. Within a finite-element context, the crack-propagation phenomenon is analyzed by coupling a Monte Carlo simulation scheme with an iterative solution algorithm based on a truly-mixed variational formulation which is derived from the Hellinger–Reissner principle. The selected approach presents the advantage of exploiting the finite-element technology without the need to introduce additional modes to model the displacement discontinuity along the crack boundaries. Furthermore, the accuracy of the stress estimate pursued by the truly-mixed approach is highly desirable, the direction of crack propagation being determined on the basis of the principal stress criterion. The numerical example of a plain concrete beam with initial crack under a three-point bending test is considered. The statistics of the response is analyzed in terms of peak load and load–mid deflection curves, in order to investigate the effects of the uncertainties on both the carrying capacity and the post-peak behaviour. A sensitivity analysis is preliminarily performed and its results emphasize the negative effects of not accounting for the auto-correlation structure of each random field. A probabilistic method is then applied to enforce the auto-correlation without significantly altering the target marginal distributions. The novelty of the proposed approach with respect to other methods found in the literature consists of not requiring the a priori knowledge of the global correlation structure of the multivariate random field. KEYWORDS: Multivariate non-Gaussian random fields; Auto-correlation; Cohesive crack propagation; Truly-mixed finite element method; Monte Carlo simulations

Random field models of heterogeneous materials

International Journal of Solids and Structures, 1998

One of the main challenges in solid mechanics lies in the passage from a heterogeneous microstructure to an approximating continuum model. In many cases (e.g. stochastic finite elements, statistical fracture mechanics), the interest lies in resolution of stress and other dependent fields over scales not infinitely larger than the typical microscale. This may be accomplished with the help of a meso-scale window which becomes the classical representative volume element (RVE) in the infinite limit. It turns out that the material properties at such a mesoscale cannot be uniquely approximated by a random field of stiffness/compliance with locally isotropic realizations, but rather two random continuum fields with locally anisotropic realizations, corresponding, respectively, to essential and natural boundary conditions on the meso-scale, need to be introduced to bound the material response from above and from below. We study the first-and second-order characteristics of these two meso-scale random fields for anti-plane elastic response of random matrix-inclusion composites over a wide range of contrasts and aspect ratios. Special attention is given to the convergence of effective responses obtained from the essential and natural boundary conditions, which sheds light on the minimum size of an RVE. Additionally, the spatial correlation structure of the crack density tensor with the meso-scale moduli is studied.

Crack propagation in a material with random toughness

International Journal of Fracture, 2004

An efficient Monte Carlo procedure is presented for characterizing the propagation of a crack in a material whose fracture toughness is a random field. The simulations rely on accurate approximate solutions of the integral equations that govern the dislocation densities, stress intensity factors, and energy release rates of curvilinear cracks. For a plate containing an edge crack that propagates towards a subsurface crack representing a traction-free boundary, results for the distributions of crack trajectories, critical applied far-field stresses, and nominal fracture toughness are presented for various parameters that quantify the randomness of the material's critical energy release rate. A demonstrative probabilistic model for crack trajectories is built and size effects are discussed.

Crack propagation in random materials: computational analysis

Computational Materials Science, 2003

Combining random features with continuum-damage mechanics and fracture mechanics, it is possible to study the effect of the brittle materialÕs strength randomness for a case of crack propagation. The mode-I fracture analysis based on discretisation of the cross-section of specimens containing a sharp notch into rectangular elements (cells) provides detailed information on the failure process. The effect of the initial damage (due to porosity) on the processes of damage accumulation and failure is analysed. A computational procedure for simulation of crack-damage interaction and crack propagation in porous alumina specimens at tension is suggested on the basis of a continuum-damage model, concept of local stress intensity factors and modification of a lattice scheme. The inhomogeneity of material properties is modelled in terms of initial damage distribution in the specimenÕs cross-section.

Stochastic models of two-dimensional fracture

Physical review. B, Condensed matter, 1992

Two statistical models of (strictly two-dimensional) layer destruction are presented. The first is built as a strict percolation model with an added "conservation law" (conservation of mass) as physical constraint. The second allows for damped or limited fracture. Two successive fracture crack thresholds are considered. Percolation (i.e. , fracture) probability and cluster distributions are studied by use of numerical simulations. Different fractal dimension, critical exponents for cluster distribution, and universality laws characterize both models.