Solid Mechanics (Emphasis on Damage and Fracture Mechanics)

This thesis contains several distinct studies aimed at better understanding fracturing in compressional fault-cored folds. At outcrops of growth strata in the Oliana anticline in the Spanish Pyrenees, the relationship of two joint sets may reflect changing mechanical properties (i.e. via diagenesis) during the folding process. Using a Schmidt hammer, I assess the rigidity contrast between the individual units and suggest that late-stage, throughgoing joints formed in strata with conditions similar to those of the present day and that early, bed-contained joints formed when the rigidity contrast between beds was significantly greater than the present day contrast. Modeling algorithms that are used for fracture prediction assume plane strain to construct, model and restore fault-cored folds. Using mechanical models that allow heterogeneous transport in three dimensions, I explore the distribution and magnitude of out-of-plane transport in plunging fault-cored anticlines and provide guidelines of where plane strain should and should not be applied. I show that out-of-plane transport is significant in the simplest non-cylindrical folds, and suggest that complex non-cylindrical structures should not be modeled using plane strain. I mapped five bed-orthogonal fracture sets associated with folding and faulting events at Sant Corneli anticline, a non-cylindrical, fault related anticline in the Spanish Pyrenees. Fold axis perpendicular, calcite healed joint sets associated with similarly oriented normal faulting both pre-date, and are cross cut by calcite healed, N-NW striking joints. Later bed strike oblique joint sets are distinguished by the presence of iron oxide mineralization that probably occurred during Paleocene-Oligocene time. This study directly links fold-related fracturing to fold evolution because fracture sets can be dated relative to the structural evolution of the anticline. I use three-dimensional restorations of Sant Corneli anticline in the Spanish Pyrenees to test the fracture prediction capability of a fully three-dimensional finite element geomechanical restoration algorithm. Reconstruction of the three-dimensional architecture of the syn-tectonic strata provides a template for incrementally unfolding the anticline. Strains predicted by the restorations are compared to the fracture sets that formed over the corresponding time intervals, which are consistent with the observed fracture patterns at Sant Corneli anticline.

We develop a fully implicit stress-return algorithm for a wide range of nonlocal inelastic models (of integral type) with coupling among integration points. Two examples of nonlocal models are presented, which combine plasticity with either damage or breakage. Using these models, we emphasize the need for a versatile integration scheme for nonlocal incremental constitutive equations. Furthermore, these models are used to demonstrate the importance of adequately selecting the way constitutive equations for softening materials are regularized. The stress update process requires the construction of a nonlocal constitutive matrix: we highlight and take advantage of its sparsity. Numerical solutions to relevant structural and geomechanical boundary value problems are used to demonstrate the performance of the proposed approach.

The rectangular specimens with an edge crack were subjected to symmetric three-point bending and asymmetric four-point bending to determine the mode I and mode II fracture toughness of the walnut particle and coconut fiber-reinforced biocomposite. Epoxy resin was used as matrix material and 10 wt% of coconut fiber and 20 wt% of walnut shell particle were used as reinforcing materials. The mode I and mode II fracture toughness and mechanical tests were conducted on a servo hydraulic universal testing machine and the results were analyzed and discussed. POLYM. COMPOS.,

We present a damage model for softening materials with evolving nonlocal interactions. The thermodynamic implications and the material stability issue are addressed. The proposed nonlocal averaging scheme provides the obtained constitutive models with an evolving nonlocal interaction which is activated only when damage occurs. In the analysis of structures made of quasi-brittle materials, this feature helps not only to overcome some issues with the incorrect initiation of damage but also to better control the evolving size of the active fracture process zone. This is an essential feature that is usually not considered in depth in many existing nonlocal approaches to the continuum modelling of quasi-brittle fracture. Numerical examples are given to demonstrate features of the proposed modelling approach.

Frictional sliding along an interface between two identical isotropic elastic plates under impact shear loading is investigated experimentally and numerically. The plates are held together by a compressive stress and one plate is subject to edge impact near the interface. The experiments exhibit both a crack-like and a pulse-like mode of sliding. Plane stress finite element calculations modeling the experimental configuration are carried out, with the interface characterized by a rate and state dependent frictional law. A variety of sliding modes are obtained in the calculations depending on the impact velocity, the initial compressive stress and the values of interface variables. For low values of the initial compressive stress and impact velocity, sliding occurs in a crack-like mode. For higher values of the initial compressive stress and/or impact velocity, sliding takes place in a pulse-like mode. One pulselike mode involves well-separated pulses with the pulse amplitude increasing with propagation distance. Another pulse-like mode involves a pulse train of essentially constant amplitude. The propagation speed of the leading pulse (or of the tip of the crack-like sliding region) is near the longitudinal wave speed and never less than ffiffi ffi 2 p times the shear wave speed. Supersonic ARTICLE IN PRESS www.elsevier.com/locate/jmps 0022-5096/$ -see front matter r (A. Needleman).

Most constitutive models for quasi-brittle materials ignore the fact that the measurable fracture energy represents more than one dissipative mechanism, including those from the creation of new surface areas and frictions between surfaces. Specifically, these models “see” the measurable fracture energy as one that comes only from the creation of new surface area. However, experimental deduction by Bažant indicates that the frictional dissipation is not at all negligible, even in mode I failure, where it contributes an energy loss of around 50–75% to the total dissipation budget. Here we study the consequences of this simplification by adopting simple local and nonlocal damage models, which include a new powerful parameter that represents the measurable partition of the dissipation. It is found that the oversight of frictional dissipation can lead to a critical over-prediction of both the magnitude and the spreading of damage.

Little work has been done on the localization of microcracks in bone using acoustic emission. Microcrack localization is useful to study the fracture process in bone and to prevent fractures in patients. Locating microcracks that occur before fracture allows one to predict where fracture will occur if continued stress is applied to the bone. Two source location algorithms were developed to locate microcracks on rectangular bovine bone samples. The first algorithm uses a constant velocity approach which has some difficulty dealing with the anisotropic nature of bone. However, the second algorithm uses an iterative technique to estimate the correct velocity for the acoustic emission source location being located. In tests with simulated microcracks, the constant velocity algorithm achieves a median error of 1.78 mm (IQR 1.51 mm) and the variable velocity algorithm improves this to a median error of 0.70 mm (IQR 0.79 mm). An experiment in which the bone samples were loaded in a three point bend test until they fractured showed a good correlation between the computed location of detected microcracks and where the final fracture occurred. Microcracks can be located on bovine bone samples using acoustic emission with good accuracy and precision.

Microstructure and tensile deformation behavior of interstitial-free (IF) steel subjected to near-cryogenic (−150°C to −100°C) rolling followed by annealing have been investigated. Twining has been found to be the dominant mode of deformation during rolling. Both the rolled and annealed sample exhibited limited work hardening due to high matrix resistance. In the rolled sample cleavage, nuclei acted as potential fracture initiation site. Annealing has resulted in effective blunting of cleavage nuclei giving rise to large total elongation due to prolonged damage growth process.