Chandrasekhar Annavarapu

Indian Institute of Technology Madras | IIT Madras · Department of Civil Engineering

We develop a numerical strategy based on a weighted Nitsche’s approach to model a general class of interface problems with higher-order simplex elements. We focus attention on problems in which the jump in the field quantities across an interface is given. The presented method generalizes the weighted Nitsche’s approach of Annavarapu et al. (Comput...

We demonstrate the ability of a stabilized finite element method, inspired by the weighted Nitsche approach, to alleviate spurious traction oscillations at interlaminar interfaces during composite delamination. The method allows for the use of any value for the cohesive stiffness and obviates the need for ad hoc approaches to estimate the minimum p...

We demonstrate the ability of a stabilized finite element method, inspired by the weighted Nitsche approach, to alleviate spurious traction oscillations at interlaminar interfaces in multi-ply multi-directional composite laminates. In contrast with the standard (penalty-like) method, the stabilized method allows the use of arbitrarily large values...

We present a stabilized finite element method that generalizes Nitsche's method for enforcing stiff anisotropic cohesive laws with different normal and tangential stiffness. For smaller values of cohesive stiffness, the stabilized method resembles the standard method, wherein the traction on the crack surface is enforced as a Neumann boundary condi...

In this work, we present the application of a fully-coupled hydro-mechanical method to investigate the effect of fracture heterogeneity on fluid flow through fractures at the laboratory scale. Experimental and numerical studies of fracture closure behavior in the presence of heterogeneous mechanical and hydraulic properties are presented. We compar...

Delamination of composite materials is commonly modeled using intrinsic cohesive zone models (CZMs), which are generally incorporated into the standard finite element (FE) method through a zero-thickness interface (cohesive) element; however, intrinsic CZMs exhibit numerical instabili-ties when the cohesive stiffness parameters is assumed to be lar...

In traditional hydraulic fracturing stimulation, the effective conductivity of low permeability rock is increased by generating/activating fractures through injection of pressurized fluid. One possible extension of traditional hydraulic fracturing is to increase the loading rate that the driving fluid applies on the formation. Methods that use dyna...

We develop a local, implicit crack tracking approach to propagate embedded failure surfaces in three-dimensions. We build on the global crack-tracking strategy of Oliver et al. (Int J. Numer. Anal. Meth. Geomech., 2004; 28:609–632) that tracks all potential failure surfaces in a problem at once by solving a Laplace equation with anisotropic conduct...

This paper describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir....

Heterogeneous aperture distributions are an intrinsic characteristic of natural fractures. The presence of highly heterogeneous aperture distributions can lead to flow channeling, thus influencing the macroscopic behavior of the fluid flow. High-fidelity numerical simulation tools are needed for realistic simulation of fracture flow when such featu...

The extended finite element method (X-FEM) has proven to be an accurate, robust method for solving embedded interface problems. With a few exceptions, the X-FEM has mostly been used in conjunction with piecewise-linear shape functions and an associated piecewise-linear geometrical representation of interfaces. In the current work, the use of spline...

We propose a weighted Nitsche framework for small-sliding frictional contact problems on three-dimensional interfaces. The proposed method inherits the advantages of both augmented Lagrange multiplier and penalty methods while also addressing their shortcomings. Algorithmic details of the traction update and consistent linearization in the presence...

We propose a stabilized approach based on Nitsche's method for enforcing contact constraints over crack surfaces. The proposed method addresses the shortcomings of conventional penalty and augmented Lagrange multiplier approaches by combining their attractive features. Similar to an augmented Lagrange multiplier approach, the proposed method has a...

We investigate a finite element method for frictional sliding along embedded interfaces within a weighted Nitsche framework. For such problems, the proposed Nitsche stabilized approach combines the attractive features of two traditionally used approaches: viz. penalty methods and augmented Lagrange multiplier methods. In contrast to an augmented La...

We extend the weighted Nitsche’s method proposed in the first part of this study to include multiple intersecting embedded interfaces. These intersections arise either inside a computational domain – where two internal interfaces intersect; or on the boundary of the computational domain – where an internal interface intersects with the external bou...

We investigate various strategies to enforce the kinematics at an embedded interface for transient problems within the extended finite element method. In particular, we focus on explicit time integration of the semi‐discrete equations of motion and extend both dual and primal variational frameworks for constraint enforcement to a transient regime....

In this work, we propose a novel weighting for the interfacial consistency terms arising in a Nitsche variational form. We demonstrate through numerical analysis and extensive numerical evidence that the choice of the weighting parameter has a great bearing on the stability of the method. Consequently, we propose a weighting that results in an esti...

We develop both stable and stabilized methods for imposing Dirichlet constraints on embedded, three-dimensional surfaces in finite elements. The stable method makes use of the vital vertex algorithm to develop a stable space for the Lagrange multipliers together with a novel discontinuous set of basis functions for the multiplier field. The stabili...