What are the common methods used for numerical analysis of asphalt pavement's fatigue?5 answersCommon methods for numerical analysis of asphalt pavement's fatigue include fatigue life models, stiffness-modulus-based methods, energy-based methods, and viscoelastic continuum damage (VECD) methods. These methods are crucial for assessing the fatigue performance of asphalt mixtures and predicting fatigue damage in pavement structures. Additionally, a heterogeneous multiscale approach has been proposed for numerically computing and assessing the mechanical properties of bituminous materials, including fatigue damage evaluation. This approach utilizes finite element simulations to characterize the effect of temperature and loading conditions on asphalt layers, providing a comprehensive understanding of fatigue behavior under various environmental and loading scenarios. By integrating these methods, researchers can enhance the accuracy and reliability of fatigue analysis in asphalt pavements.
How to obtain the properties for geological faults (considering damage zone and damage core) in numerical simulations?5 answersTo obtain properties for geological faults, including the damage zone and core, in numerical simulations, various methods have been proposed. One approach involves estimating deformation intensity in damage zones, calculating representative values within cell domains, and determining equivalent permeability in cells with oblique deformation bands. Another method includes implementing fault cores as transmissibility multipliers and modifying grid permeability in cells adjacent to faults to account for damage zones. Additionally, a new conceptual model considers fault cores and damage zones as lower-dimensional structures embedded in the rock matrix, enhancing the accuracy of simulation outcomes. Analog modeling studies have shown that fault damage zones evolve non-linearly with displacement, transitioning towards a threshold thickness influenced by fault segment linkage and lithology.
What are the current approaches to model rate dependent fracture response of polymers via the phase field method?5 answersCurrent approaches to model rate dependent fracture response of polymers via the phase field method involve the use of explicit phase field material point methods (ex-PFMPM). These methods discretize the rate-dependent phase field governing equation using a set of particles and update the phase field using explicit forward-difference time integration. The stability of ex-PFMPM is studied, and a critical time step formula is obtained based on system eigenvalues, which considers particle position and neighboring cell interaction. Another approach involves the development of a phase-field fracture model that considers the orientation-dependent fracture of fiber-reinforced polymer matrix composites (PMC). This model captures the damage mechanisms such as matrix cracking and fiber pullout/breakage and can predict the direction-dependent damage propagation and load-deformation response at fracture. Additionally, a model that combines shear yielding, crazing, and void formation is proposed, which considers both ductile and brittle failure simultaneously. These approaches provide physically motivated and computationally tractable frameworks for modeling the fracture response of polymers.
How calculate the crack density?5 answersCrack density can be calculated using different parameters and methods. One approach is to use the crack energy density (CED) parameter, which is defined throughout the life of a crack and can describe various crack behaviors. The CED can be determined independently of the coordinate system and plane on which the integral path is set. It can also be expressed as mode I and mode II contributions, which can be represented by domain integrals without any restrictions on the constitutive equation. Another method is to evaluate the crack energy density from load-displacement curves. The growth rate of a crack can be determined by the increment of crack energy density per one cycle and the gradient of the distribution of crack energy density. These approaches provide valuable insights into understanding crack density and its implications in various fields such as forensic science, medical diagnosis, and creep crack analysis.
How to calculate the crack density in rock?5 answersThe crack density in rock can be calculated using various methods. One approach is to use elastic wave velocities to determine the crack density. The Biot-Gassmann model, which includes elastic moduli and Poisson's ratio, can be used to predict the crack density of rocks. Another method involves measuring the S wave speed, P wave speed, and specific resistance of the rock-bed using elastic wave tomography and specific resistance tomography, and then calculating the crack density based on predetermined relations. Additionally, the crack density can be described using a theoretical model based on the thermodynamic balance law, and the evolution equation of crack density can be derived. Analytic expressions can also be derived for crack density tensor components using effective medium theory and anisotropic poroelastic theory. Finally, crack densities can be compared with in situ shear stress variation to study the relationship between stress state and rock material properties.
Who was the first to use matlab to simulate pn junctions??5 answersThe first person to use MATLAB to simulate pn junctions is not mentioned in the provided abstracts.