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1. Modeling of rock inhomogeneity and anisotropy by explicit and implicit representation of microcracks

   Abedi, R. ; Clarke, P.L. ( January 2018 , Proceeding 52th U.S. Rock Mechanics/Geomechanics Symposium)

   Fracture patterns experienced under a dynamic uniaxial compressive load are highly sensitive to rock microstructural defects due to its brittleness and the absence of macroscopic stress concentration points. We propose two different approaches for modeling rock microstructural defects and inhomogeneity. In the explicit realization approach, microcracks with certain statistics are incorporated in the computational domain. In the implicit realization approach, fracture strength values are sampled using a Weibull probability distribution. We use the Mohr-Coulomb failure criterion to define an effective stress in the context of an interfacial damage model. This model predicts crack propagation at angles ±ɸch = ±(45 − ɸ/2) relative to the direction of compressive load, where ɸ is the friction angle. By using appropriate models for fracture strength anisotropy, we demonstrate the interaction of rock weakest plane and ɸch. Numerical results demonstrate the greater effect of strength anisotropy on fracture pattern when an explicit approach is employed. In addition, the density of fractures increases as the angle of the weakest planes approaches ±ɸch. The fracture simulations are performed by an h-adaptive asynchronous spacetime discontinuous Galerkin (aSDG) method that can accommodate crack propagation in any directions.
2. Comparison of Interfacial and Continuum Models for Dynamic Fragmentation Analysis

   https://doi.org/10.1115/IMECE2018-88294  

   Bahmani, Bahador ; Clarke, Philip ; Abedi, Reza ( November 2018 , Proceedings of ASME 2018 International Mechanical Engineering Congress and Exposition)

   The microstructural design has an essential effect on the fracture response of brittle materials. We present a stochastic bulk damage formulation to model dynamic brittle fracture. This model is compared with a similar interfacial model for homogeneous and heterogeneous materials. The damage models are rate-dependent, and the corresponding damage evolution includes delay effects. The delay effect provides mesh objectivity with much less computational efforts. A stochastic field is defined for material cohesion and fracture strength to involve microstructure effects in the proposed formulations. The statistical fields are constructed through the Karhunen-Loeve (KL) method. An advanced asynchronous Spacetime Discontinuous Galerkin (aSDG) method is used to discretize the final system of coupled equations. Application of the presented formulation is shown through dynamic fracture simulation of rock under a uniaxial compressive load. The final results show that a stochastic bulk damage model produces more realistic results in comparison with a homogenizes model.
3. A homogenization model for the rheology and local field statistics of suspensions of particles in yield stress fluids

   https://doi.org/10.1122/8.0000337  

   Kammer, Christoph ; Blackwell, Brendan ; Arratia, Paulo E. ; Ponte Castañeda, Pedro ( May 2022 , Journal of Rheology)

   We investigate the rheological behavior of athermal particle suspensions using experiments and theory. A generalized version of the homogenization estimates of Ponte Castañeda and Willis [J. Mech. Phys. Solids, 43(12), 1919–1951 (1995)] is presented for the effective viscosity of athermal suspensions accounting for additional microstructural features (e.g., polydispersity) via an empirical parameter, [Formula: see text]. For the case of identically sized spheres dispersed with statistical isotropy in a Newtonian fluid, the parameter [Formula: see text] is estimated from the results of Batchelor and Green [J. Fluid Mech. 56(2), 375–400 (1972)] for the Huggins coefficient. Predictions for the macroscopic viscosity are found to be in good agreement with measurements for monodisperse polymethyl methacrylate (PMMA) spheres in glycerol, as well as for the empirical Krieger–Dougherty equation for the shear viscosity. The proposed estimates have the added benefit that they can also be used to get information on the statistics of the stress and strain-rate fields in the fluid and particle phases. In addition, results for the effective shear viscosity are used in combination with the linear comparison method of Ponte Castañeda [J. Mech. Phys. Solids 39(1), 45–71 (1991)] to generate the corresponding estimates for the effective macroscopic behavior and field statistics ofmore »particle suspensions in (viscoplastic) yield stress fluids. Good agreement is also found between the theoretical estimates and experimental results for the effective yield and flow stress of suspensions with monodisperse PMMA spheres in Carbopol. Finally, it is argued that the results for the phase averages and fluctuations of the stress and strain-rate fields can be used to provide a physical interpretation for the parameter [Formula: see text] in terms of the polydispersity of the suspension and its implications for the percolation threshold.

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4. Li, B. and Hoo Fatt, M.S., “Use of a Cohesive Zone Model to Predict Dynamic Tearing of Rubber,” Tire Science and Technology, Vol. 43, No. 4, pp. 297-334, 2015.

   Li, B. and ( July 2015 , Tire science & technology)

   ABSTRACT: Tire failures, such as tread separation and sidewall zipper fracture, occur when internal flaws (cracks) nucleate and grow to a critical size as result of fatigue or cyclic loading. Sudden and catastrophic rupture takes place at this critical crack size because the strain energy release rate exceeds the tear energy of the rubber in the tire. The above-mentioned tire failures can lead to loss of vehicle stability and control, and it is important to develop predictive models and computational tools that address this problem. The objective of this article was to develop a cohesive zone model for rubber to numerically predict crack growth in a rubber component under dynamic tearing. The cohesive zone model for rubber was embedded into the material constitutive equation via a user-defined material subroutine (VUMAT) of ABAQUS. It consisted of three parts: (1) hyperviscoelastic behavior before damage, (2) damage initiation based on the critical strain energy density, and (3) hyperviscoelastic behavior after damage initiation. Crack growth in the tensile strip and pure shear specimens was simulated in ABAQUS Explicit, and good agreement was reported between finite element analysis predictions and test results
5. Modeling of rock inhomogeneity and anisotropy by explicit and implicit representation of microcracks

   Abedi, Reza ; Clarke, Philip L. ( January 2018 , Proceedings of ARMA 2018)

   Fracture in rock as a heterogeneous brittle material, having significant inherent randomness, requires including probabilistic considerations at different scales. Crack growth in rocks is generally associated with complex features such as crack path oscillations, microcrack and crack branching events. Two methods will be presented to address rock inhomogeneity and anisotropy. First, microcracks are explicitly realized in a domain based on specific statistics of crack length and location. Second, a statistical model is used to implicitly represent an inhomogeneous field for fracture strength. Both approaches can be used for rocks in which the natural fractures are oriented in a specific angle, i.e. an aspect for modeling bedding planes in sedimentary rocks.