Topic
Continuum mechanics
About: Continuum mechanics is a research topic. Over the lifetime, 5042 publications have been published within this topic receiving 181027 citations.
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TL;DR: In this paper, a viscoplastic flow of granular solids within rigid walls is modeled using continuum mechanics, in which the discontinuity function is taken as in previous works by Gray and Stiles, while the flow rule is modeled by the von-Mises criterion.
39 citations
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TL;DR: In this paper, the formation of accommodation microcracks from the deformation ledges is considered in detail, and it is shown that the type of the accommodation micro-cracks depends on the type and stiffness of the deformed ledge and can be spontaneously nucleated.
Abstract: Polycrystalline deformation leads to the creation of deformation ledges at grain boundaries undergoing heterogeneous shear. The large strain fields of the deformation ledges can be relieved either by nucleation of further slip or by initiation of microcracks to accommodate the interface strains set up by the deformation of adjacent grains. The formation of accommodation microcracks from the deformation ledges is considered in detail. It is shown that the type of the accommodation microcrack—tensile or shear, transgranular or intergranular—depends on the type of the deformation ledge, and can be spontaneously nucleated. Stability, equilibrium, and the shape of the microcrack are determined from a discrete dislocation approach. Computer techniques are used in this study and the results are compared with those of the continuum mechanics approach. The effect of the application of an external stress is considered in detail and it is shown that a given stable microcrack has a critical stress at which it becomes...
39 citations
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TL;DR: In this paper, the authors developed a new continuum mechanics modeling framework for the sea ice cover, called Maxwell-elasto-brittle, which can reproduce the main characteristics of sea ice mechanics, including anisotropy, spatial localization and intermittency.
Abstract: Mechanics plays a key role in the evolution of the sea ice cover through its control on drift, on momentum and thermal energy exchanges between the polar oceans and the atmosphere along cracks and faults, and on ice thickness distribution through opening and ridging processes. At the local scale, a significant variability of the mechanical strength is associated with the microstructural heterogeneity of saline ice, however characterized by a small correlation length, below the ice thickness scale. Conversely, the sea ice mechanical fields (velocity, strain and stress) are characterized by long-ranged (more than 1000 km) and long-lasting (approx. few months) correlations. The associated space and time scaling laws are the signature of the brittle character of sea ice mechanics, with deformation resulting from a multi-scale accumulation of episodic fracturing and faulting events. To translate the short-range-correlated disorder on strength into long-range-correlated mechanical fields, several key ingredients are identified: long-ranged elastic interactions, slow driving conditions, a slow viscous-like relaxation of elastic stresses and a restoring/healing mechanism. These ingredients constrained the development of a new continuum mechanics modelling framework for the sea ice cover, called Maxwell–elasto-brittle. Idealized simulations without advection demonstrate that this rheological framework reproduces the main characteristics of sea ice mechanics, including anisotropy, spatial localization and intermittency, as well as the associated scaling laws. This article is part of the themed issue ‘Microdynamics of ice’.
39 citations
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TL;DR: In this article, the authors proposed an approach based on energy to determine material parameters, which results in a simple linear regression problem for highly nonlinear material equations, where the inverse problem leads to a unique solution.
Abstract: Many polymer-type materials show a rate-dependent and nonlinear rheological behavior. Such a response may be modeled by using a series of spring-dashpot systems. However, in order to cover different time scales the number of systems may become unreasonably large. A more appropriate treatment based on continuum mechanics will be presented herein. This approach uses representation theorems for deriving material equations and allows for a systematic increase in modeling complexity. Moreover, we propose an approach based on energy to determine thematerial parameters.This method results in a simple linear regression problemeven for highly nonlinearmaterial equations. Therefore, the inverse problem leads to a unique solution. The significance of the proposed method is that the stored and dissipated energies necessary for the procedure are measurable quantities. We apply the proposed method to a “semi-solid” material and measure its material parameters by using a simple-shear rheometer.
39 citations