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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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Journal ArticleDOI
TL;DR: Li et al. as discussed by the authors proposed a first-principle model of nanoindentation and ideal strength to reveal the genesis of materials deformation and fracture, which is based on the Outstanding Young Investigator Award presentation given by Ju Li on April 19, 2006.
Abstract: The following article is based on the Outstanding Young Investigator Award presentation given by Ju Li on April 19, 2006, at the Materials Research Society Spring Meeting in San Francisco. Li received the award “for his innovative work on the atomistic and first-principles modeling of nanoindentation and ideal strength in revealing the genesis of materials deformation and fracture.”Defect nucleation plays a critical role in the mechanical behavior of materials, especially if the system size is reduced to the submicron scale. At the most fundamental level, defect nucleation is controlled by bond breaking and reformation events, driven typically by mechanical strain and electronegativity differences. For these processes, atomistic and first-principles calculations are uniquely suited to provide an unprecedented level of mechanistic detail. Several connecting threads incorporating notions in continuum mechanics and explicit knowledge of the interatomic energy landscape can be identified, such as homogeneous versus heterogeneous nucleation, cleavage versus shear-faulting tendencies, chemomechanical coupling, and the fact that defects are singularities at the continuum level but regularized at the atomic scale. Examples are chosen from nano-indentation, crack-tip processes, and grain-boundary processes. In addition to the capacity of simulations to identify candidate mechanisms, the computed athermal strength, activation energy, and activation volume can be compared quantitatively with experiments to define the fundamental properties of defects in solids.

133 citations

01 Apr 1983
TL;DR: In this paper, an analytical model of crack closure is used to study the crack growth and closure behavior of small cracks in plates and at notches, and the calculated crack opening stresses for small and large cracks, together with elastic and elastic plastic fracture mechanics analyses, are used to correlate crack growth rate data.
Abstract: An analytical model of crack closure is used to study the crack growth and closure behavior of small cracks in plates and at notches. The calculated crack opening stresses for small and large cracks, together with elastic and elastic plastic fracture mechanics analyses, are used to correlate crack growth rate data. At equivalent elastic stress intensity factor levels, calculations predict that small cracks in plates and at notches should grow faster than large cracks because the applied stress needed to open a small crack is less than that needed to open a large crack. These predictions agree with observed trends in test data. The calculations from the model also imply that many of the stress intensity factor thresholds that are developed in tests with large cracks and with load reduction schemes do not apply to the growth of small cracks. The current calculations are based upon continuum mechanics principles and, thus, some crack size and grain structure exist where the underlying fracture mechanics assumptions become invalid because of material inhomogeneity (grains, inclusions, etc.). Admittedly, much more effort is needed to develop the mechanics of a noncontinuum. Nevertheless, these results indicate the importance of crack closure in predicting the growth of small cracks from large crack data.

132 citations

Book ChapterDOI
01 Jan 2003
TL;DR: The peridynamic model is an alternate theory of continuum mechanics that is specifically oriented toward modeling problems, in which cracks or other discontinuities emerge spontaneously as a body deforms under load.
Abstract: Publisher Summary The peridynamic model is an alternate theory of continuum mechanics that is specifically oriented toward modeling problems, in which cracks or other discontinuities emerge spontaneously as a body deforms under load. In this study, a code that implements this theory is applied to the Kalthoff-Winkler dynamic single-fracture experiment in a tough steel specimen. Many problems of fundamental importance in mechanics involve the spontaneous emergence of discontinuities, such as cracks, in the interior of a body. The classical theory of continuum mechanics is in some ways suited to modeling this type of problem because the theory uses partial differential equations as a mathematical description. Although much work has been devoted to special techniques aimed at working around this problem—particularly in the theory of fracture mechanics—these techniques are not fully satisfactory either in principle or in practice as general descriptions of fracture. This difficulty is inherited by numerical methods that implement the classical theory, including almost all finite-element and finite-difference codes in common usage.

132 citations

Journal ArticleDOI
TL;DR: In this paper, the forming behavior of non-crimp fabric (NCF) was simulated using finite element analysis incorporating a non-orthogonal constitutive model, which consists of two parts: the tensile contribution from fibre reinforcement and the shear stiffness.
Abstract: The forming behaviour of non-crimp fabric (NCF) was simulated using finite element (FE) analysis incorporating a non-orthogonal constitutive model. NCFs feature asymmetric shear behaviour caused by the stitching used to hold the tows together. This asymmetric shear property causes an asymmetric draping pattern of NCF, even when formed over a symmetrical hemispherical forming tool. Current work focuses on the feasibility of a continuum mechanics model to simulate the asymmetric forming behaviour of NCF. The constitutive equation consists of two parts: the tensile contribution from fibre reinforcement and the shear stiffness. For the fibre directional properties, a non-orthogonal equation originally developed for woven fabric was adopted. The shear stiffness was modelled through a constitutive equation incorporating picture-frame shear data. Both a picture-frame shear test and forming of NCF over a hemisphere tool were simulated by commercial finite element software with the current constitutive model implemented within a user material subroutine. The virtual picture-frame test confirmed the validity of the constitutive equation in simulating planar deformation behaviour of NCF. Furthermore, the numerical analysis of hemispherical forming suggests that increasing blank-holder force decreases the asymmetry of the draped pattern.

131 citations

Journal ArticleDOI
TL;DR: In this article, a constitutive approach of finite viscoelasticity was developed to represent the Payne effect in the context of continuum mechanics. But this model is not suitable for the case of carbon black-filled elastomers.

130 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202363
2022136
2021150
2020176
2019181
2018185