Deformation and Failure of Amorphous Solidlike Materials

Since the 1970's, theories of deformation and failure of amorphous, solidlike materials have started with models in which stress-driven, molecular rearrangements occur at localized flow defects via "shear transformations". This picture is the basis for the modern theory of "shear transformation zones" (STZ's), which is the focus of this review. We begin by describing the structure of the theory in general terms and by showing several applications, specifically: interpretation of stress-strain measurements for a bulk metallic glass, analysis of numerical simulations of shear banding, and the use of the STZ equations of motion in free-boundary calculations. In the second half of this article, we focus for simplicity on what we call an "athermal" model of amorphous plasticity, and use that model to illustrate how the STZ theory emerges within a systematic formulation of nonequilibrium thermodynamics.Comment: 28 pages, 4 figures, submitted to Annual Reviews of Condensed Matter Physic

Collaborative learning utilizing a domain-based shared data repository to enhance learning outcomes

A number of learning paradigms have postulated that knowledge formation is a dynamic process where learners actively construct a representation of concepts integrating information from multiple sources. Current teaching strategies utilize a compartmentalized approach where individual courses contain a small subset of the knowledge required for a discipline. The intent of this research is to provide a framework to integrate the components of a discipline into a cohesive whole and accelerate the integration of concepts enhancing the learning process. The components utilized to accomplish these goals include two new knowledge integration models; a Knowledge Weighting Model (KWM) and the Aggregate-Integrate-Master (AIM) model. Semantic Web design principles utilizing a Resource Description Framework (RDF) schema and Web Ontology Language (OWL) will be used to define concepts and relationships for this knowledge domain that can then be extended for other domains. Lastly, a Design Research paradigm will be utilized to analyze the IT artifact, the Constructivist Unifying Baccalaureate Epistemology (CUBE) knowledge repository that was designed to validate this research. The prototype testing population utilized sixty students spanning five classes, in the fall 2007, following IRB approved protocols. Data was gathered using a Constructivist Multimedia Learning Survey (CMLES), focus groups and semi-structured interviews. This preliminary data supported the hypotheses that students using the Integrated Knowledge Repository will first; have a more positive perception of the learning process than those who use conventional single course teaching paradigms and second; students utilizing the IKR will develop a more complex understanding of the interconnected nature of the materials linking a discipline than those who take conventional single topic courses. Learning is an active process in which learners construct new ideas or concepts based upon their current/past knowledge. The goal is to develop a knowledge structure that is capable of facilitating the integration of conceptual development in a field of study

Dissipative Visco-plastic Deformation in Dynamic Fracture: Tip Blunting and Velocity Selection

Dynamic fracture in a wide class of materials reveals "fracture energy" $\Gamma$ much larger than the expected nominal surface energy due to the formation of two fresh surfaces. Moreover, the fracture energy depends on the crack velocity, $\Gamma=\Gamma(v)$. We show that a simple dynamical theory of visco-plasticity coupled to asymptotic pure linear-elasticity provides a possible explanation to the above phenomena. The theory predicts tip blunting characterized by a dynamically determined crack tip radius of curvature. In addition, we demonstrate velocity selection for cracks in fixed-grip strip geometry accompanied by the identification of $\Gamma$ and its velocity dependence.Comment: 4 pages, 1 figures; presentation improved, refs. changed, figure omitte

Roughening of Fracture Surfaces: the Role of Plastic Deformations

Post mortem analysis of fracture surfaces of ductile and brittle materials on the $\mu$m-mm and the nm scales respectively, reveal self affine graphs with an anomalous scaling exponent $\zeta\approx 0.8$. Attempts to use elasticity theory to explain this result failed, yielding exponent $\zeta\approx 0.5$ up to logarithms. We show that when the cracks propagate via plastic void formations in front of the tip, followed by void coalescence, the voids positions are positively correlated to yield exponents higher than 0.5.Comment: 4 pages, 6 figure

A homogeneous constitutive model for masonry

Masonry has been a broadly used material since the beginning of human life. Despite its popularity, the analysis of masonry structures is a complex task due to the heterogeneity and the non‐linear material behaviour. The need for reliable analysis procedures capable of predicting damage evolution and failure in historical structures in order to design efficient repair and maintenance has motivated the work of many structural analysts in this field. Here the finite element method has emerged as one of the most powerful procedures for linear and non‐linear analysis of masonry structures. The main problem pending is the development of accurate and efficient constitutive models capable of predicting the behaviour of masonry in the non‐linear range and this has been the motivation of this work. The constitutive model presented is based on the homogenized anisotropic elastoplasticity previously developed by the authors. The effect of anisotropy is introduced by means of fictitious isotropic stress and strain spaces. The material properties in the fictitious isotropic spaces are mapped into the actual anisotropic space by means of a consistent fourth‐order tensor. The advantage of the model is that the classical theory of plasticity can be used to model the non‐linear behaviour in the isotropic spaces. Details of the model for masonry structures and its implementation in a general non‐linear finite element code are given. Examples of application to the analysis of some masonry structures are presented, showing the efficiency of the model

Void Formation and Roughening in Slow Fracture

Slow crack propagation in ductile, and in certain brittle materials, appears to take place via the nucleation of voids ahead of the crack tip due to plastic yields, followed by the coalescence of these voids. Post mortem analysis of the resulting fracture surfaces of ductile and brittle materials on the $\mu$m-mm and the nm scales respectively, reveals self-affine cracks with anomalous scaling exponent $\zeta\approx 0.8$ in 3-dimensions and $\zeta\approx 0.65$ in 2-dimensions. In this paper we present an analytic theory based on the method of iterated conformal maps aimed at modelling the void formation and the fracture growth, culminating in estimates of the roughening exponents in 2-dimensions. In the simplest realization of the model we allow one void ahead of the crack, and address the robustness of the roughening exponent. Next we develop the theory further, to include two voids ahead of the crack. This development necessitates generalizing the method of iterated conformal maps to include doubly connected regions (maps from the annulus rather than the unit circle). While mathematically and numerically feasible, we find that the employment of the stress field as computed from elasticity theory becomes questionable when more than one void is explicitly inserted into the material. Thus further progress in this line of research calls for improved treatment of the plastic dynamics.Comment: 15 pages, 20 figure

Nonequilibrium Thermodynamics of Amorphous Materials I: Internal Degrees of Freedom and Volume Deformation

This is the first of three papers devoted to the nonequilibrium thermodynamics of amorphous materials. Our focus here is on the role of internal degrees of freedom in determining the dynamics of such systems. For illustrative purposes, we study a solid whose internal degrees of freedom are vacancies that govern irreversible volume changes. Using this model, we compare a thermodynamic theory based on the Clausius-Duhem inequality to a statistical analysis based directly on the law of increase of entropy. The statistical theory is used first to derive the the Clausius-Duhem inequality. We then use the theory to go beyond those results and obtain detailed equations of motion, including a rate factor that is enhanced by deformation-induced noisy fluctuations. The statistical analysis points to the need for understanding how both energy and entropy are shared by the vacancies and their environments.Comment: 7 pages. First of a three-part serie

Free-Boundary Dynamics in Elasto-plastic Amorphous Solids: The Circular Hole Problem

We develop an athermal shear-transformation-zone (STZ) theory of plastic deformation in spatially inhomogeneous, amorphous solids. Our ultimate goal is to describe the dynamics of the boundaries of voids or cracks in such systems when they are subjected to remote, time-dependent tractions. The theory is illustrated here for the case of a circular hole in an infinite two-dimensional plate, a highly symmetric situation that allows us to solve much of the problem analytically. In spite of its special symmetry, this example contains many general features of systems in which stress is concentrated near free boundaries and deforms them irreversibly. We depart from conventional treatments of such problems in two ways. First, the STZ analysis allows us to keep track of spatially heterogeneous, internal state variables such as the effective disorder temperature, which determines plastic response to subsequent loading. Second, we subject the system to stress pulses of finite duration, and therefore are able to observe elasto-plastic response during both loading and unloading. We compute the final deformations and residual stresses produced by these stress pulses. Looking toward more general applications of these results, we examine the possibility of constructing a boundary-layer theory that might be useful in less symmetric situations.Comment: 30 pages (preprint format), 9 figure