John E. Bolander

Fracture analyses using spring networks with random geometry

Abstract Rigid-body-spring networks are used to model brittle fracture in homogeneous, isotropic materials. Discretization is based on Voronoi diagrams with random geometry. Methods are given for ensuring elastic uniformity and maximizing the degree of isotropy with respect to potential crack direction. A method for rendering ordinary beam-spring networks elastically uniform is also given. Model abilities to predict crack patterns are demonstrated through analyses of mixed mode fracture in cement mortar panels and shear failure in reinforced concrete beams. The latter example utilizes an effective method for introducing continuous reinforcement into random geometry beam-spring networks.

Structural Concrete Analysis Using Rigid‐Body‐Spring Networks

This paper presents a new computational approach for supporting the design of structural concrete. The primary aim of this research is to facilitate construction, interpretation, and revision of the analysis model through: 1) highly automated mesh generation, 2) discrete modeling of the material components and cracking, 3) dependence on basic material parameters, and 4) graphic rendering of the response quantities, most notably crack locations and widths. Concrete material is represented by a rigid-body-spring network whose geometry is defined by a Voronoi diagram on randomly distributed points. Random geometry of the network reduces mesh bias on potential cracking directions. Concrete cracking is modeled using an energetic fracture mechanics approach that is objective with respect to network component density and random geometry. Reinforcing material may assume any piecewise linear trajectory and is positioned irrespective of the spring network defining the concrete material. Viability of the approach is demonstrated through elastic stress analyses and ultimate failure analyses of T-shape bridge piers subjected to eccentric loading.

Discrete modeling of short-fiber reinforcement in cementitious composites

Abstract This article presents a computationally efficient method for analyzing the performance of short-fiber reinforcement in cementitious composites. Each fiber is modeled as a discrete entity. Realistic, nonuniform fiber distributions can be specified as program input. Discrete element systems are used to represent the matrix material. Fiber response is constrained to the kinematics of the discrete elements; the number of system degrees of freedom is therefore independent of the number of fibers. Pre-cracking contributions of the fibers are modeled using an elastic shear lag theory. Post-cracking contributions depend on pullout relations based on the micromechanics of the fiber-matrix interface. In either case, there is a direct link between fiber-local actions and composite response. Numerical results for both aligned and randomly oriented fiber composites are compared with theoretical predictions based on simple mixture rules.

Explicit representation of physical processes in concrete fracture

The utility of concrete as a cost-effective, durable structural material depends largely on its fracture properties. Improved understandings of the physical bases and scaling of concrete fracture are needed to meet the growing expectations and constraints on concrete usage in high-performance applications, and to develop alternative cementitious materials for reduced environmental load. This paper reviews relevant knowledge of fracture processes in concrete, with a particular focus on ways new 3D measurements may be coupled with discrete modelling approaches. The microstructure of concrete is briefly reviewed in the context of the physical processes that dictate fracture properties. We advocate a modelling approach where, to the extent possible, a direct correspondence is made between measured material structure and the structures explicitly represented by numerical models. This correspondence is made by utilizing x-ray microtomography, a high-resolution 3D imaging technique, and lattice models that mimic physical structure and processes. 3D image analysis provides us with quantitative measurements of internal damage progression. 3D lattice simulations offer the potential for extracting additional knowledge from these high-fidelity measurements.

An adaptive procedure for fracture simulation in extensive lattice networks

Abstract The potential for simulating fracture processes using lattice networks remains largely unrealized due to the computational expense associated with such approaches. The range of specimen sizes and mesh densities which can be practically explored is quite limited. This paper shows that, for localized fracture processes, both computing time and storage requirements can be greatly reduced by modeling only the fracture process zone and its immediate vicinity with a lattice network. The material surrounding the lattice work is represented using boundary elements and is assumed to be linear elastic. The model layout is updated as the fracture process evolves; updates are guided by a conventional fuzzy control scheme. Effectiveness of this adaptive procedure is shown through examples involving concrete fracture.

Hydro-mechanical model for wetting/drying and fracture development in geomaterials

This paper presents a modeling approach for studying hydro-mechanical coupled processes, including fracture development, within geological formations. This is accomplished through the novel linking of two codes: TOUGH2, which is a widely used simulator of subsurface multiphase flow based on the finite volume method; and an implementation of the Rigid-Body-Spring Network (RBSN) method, which provides a discrete (lattice) representation of material elasticity and fracture development. The modeling approach is facilitated by a Voronoi-based discretization technique, capable of representing discrete fracture networks. The TOUGH-RBSN simulator is intended to predict fracture evolution, as well as mass transport through permeable media, under dynamically changing hydrologic and mechanical conditions. Numerical results are compared with those of two independent studies involving hydro-mechanical coupling: (1) numerical modeling of swelling stress development in bentonite; and (2) experimental study of desiccation cracking in a mining waste. The comparisons show good agreement with respect to moisture content, stress development with changes in pore pressure, and time to crack initiation. The observed relationship between material thickness and crack patterns (e.g., mean spacing of cracks) is captured by the proposed modeling approach.

Modeling crack development in reinforced concrete structures under service loading

Abstract Reinforced and partially prestressed concrete structures are generally designed to allow cracking under service loading. Accurate modeling of crack formation and propagation at lower load levels is therefore important, especially in severe environments where structural durability is a concern. Here, a spring-network approach is used to study cracking in scaled models of reinforced concrete bridge piers, which are subjected to eccentric loading. An energetic fracture mechanics approach is used to model tension softening of developing cracks. Numerical results for cracking loads, crack opening profiles, and global load–displacement response agree well with experimentally measured values. In contrast, a brittle fracture model significantly underestimates the load level of crack formation, provides unrealistic crack opening profiles at low load levels, and indicates a mechanism for structural failure different from that witnessed in the test program.

Rigid-Body-Spring Network Modeling of Prestressed Concrete Members

In this research, random lattice models were used to simulate structural concrete members under short-term monotonic loadings. The approach is based on the use of rigid-body-spring networks, which are constructed from Voronoi tessellations of the concrete domain. Reinforcing material can be positioned within the model irrespective of the rigid-body-spring network defining the concrete material. Construction of the concrete network, reinforcement discretization, and the assignment of associated bond linkages are highly automated. Model accuracy and efficacy are demonstrated through examples involving self-weight balancing in prestressed beams, elastic stress analyses local to the prestressing anchorages, and failure analyses of partially prestressed concrete beams. The model reproduces the main features of the test program results in an objective manner, independent of mesh size and random geometry.

Simulation of fracture in cement-based composites

Abstract A nonlocal smeared-cracking finite element model is used to simulate tensile fracture in mortar notched-beam specimens. The nonlocal model resolves the distributions of damage and energy consumption within the fracture process zone, as well as accounts for variance in fracture energy along the ligament length. Results correlate well to experimental and analytical results given by other researchers for fracture over the central portion of the ligament. However, standard nonlocal averaging causes excess energy consumption in regions subjected to high strain gradients. To promote natural fracture development and realistic energy consumption near the pre-notch tip, the nonlocal averaging process is modified in this vicinity.

Fracture in concrete specimens of differing scale

A planar lattice network of beam elements is used to study the mechanisms of fracture in cement‐based materials. Beam properties are controlled by a nonlinear elastic fracture law which roughly accounts for three‐dimensionality of the material and fracture process. Special attention is given to modeling toughening mechanisms associated with aggregate‐matrix interface failure. The distributions of damage and fracture energy consumption are resolved at the material mesoscale and are shown to depend on strain gradient. An adaptive remeshing procedure is used to reduce computational cost and enable analyses of specimens of significantly differing scale, while keeping the lattice density constant. Larger process zones, higher specific fracture energies, and lower specific peak loads are obtained with increasing specimen size, in agreement with published test results. These computations provide information useful in developing refined macromodels for engineering analyses.