A Continuum Theory of Creep and Creep Damage

Murakami, Sumio; Ohno, Nobutada

doi:10.1007/978-3-642-81598-0_28

Cited by 290 publications

(165 citation statements)

References 9 publications

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“…the grid size, a few metres). When considering an anisotropic approach, damage must be represented as a second-order tensor (Murakami and Ohno, 1981;Pralong and Funk, 2005). However, following Pralong and Funk (2005), here we consider isotropic damage as a first approximation.…”

Section: Continuum Damage Mechanics Modelmentioning

confidence: 99%

Combining damage and fracture mechanics to model calving

et al. 2014

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Abstract.Calving of icebergs is a major negative component of polar ice-sheet mass balance. Here we present a new calving model relying on both continuum damage mechanics and linear elastic fracture mechanics. This combination accounts for both the slow sub-critical surface crevassing and the rapid propagation of crevasses when calving occurs. First, damage to the ice occurs over long timescales and enhances the viscous flow of ice. Then brittle fractures propagate downward, at very short timescales, when the ice body is considered as an elastic medium. The model was calibrated on Helheim Glacier, Southeast Greenland, a well-monitored glacier with fast-flowing outlet. This made it possible to identify sets of model parameters to enable a consistent response of the model and to produce a dynamic equilibrium in agreement with the observed stable position of the Helheim ice front between 1930 and today.

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Section: Continuum Damage Mechanics Modelmentioning

confidence: 99%

Combining damage and fracture mechanics to model calving

et al. 2014

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“…The spatial scale of interest in mechanical modeling is typically the macroscale response of a material or structure, which may be orders of magnitude larger than the fractures that exist at the microscale. Even though fractures are by nature local phenomena, and their spatial extent may be small relative to the macroscale response of interest, their effect on deformation or strain can be measured at the macroscale (Murakami and Ohno, 1981). Ignoring these features simply because they cannot be resolved by a model is not prudent.…”

Section: Damage Theorymentioning

confidence: 99%

“…For scalar (isotropic) damage, damage is interpreted as representing the weakest cross section of the element since this section governs the ultimate load bearing capacity of the element as a whole. For fully viscous (long timescale) deformation, this type of simple area reduction due to fractures likely dominates the material response over the shape or orientation of the cracks (Murakami and Ohno, 1981), which favors a scalar representation of damage. However, damage can also be represented as a tensor to account for varying damage on different orthogonal planes, which can account for any anisotropy induced by the orientation of fractures in a material.…”

Section: Linear Mapping Between Physical and Effective Spacesmentioning

confidence: 99%

“…However, this vanishing influence of fractures does not necessarily imply that the fractures are fully healing and disappearing. When a fracture first forms, it contributes to damage in two ways; first, by reducing the available load bearing surface area, and second, by causing a stress concentration at the tip of the fracture (Murakami and Ohno, 1981). Both mechanisms would contribute to increasing the mean stress over the remaining load bearing cross section.…”

Section: Damage Patternsmentioning

confidence: 99%

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Creep deformation and buttressing capacity of damaged ice shelves: theory and application to Larsen C ice shelf

et al. 2013

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Abstract. Around the perimeter of Antarctica, much of the ice sheet discharges to the ocean through floating ice shelves. The buttressing provided by ice shelves is critical for modulating the flux of ice into the ocean, and the presently observed thinning of ice shelves is believed to be reducing their buttressing capacity and contributing to the acceleration and thinning of the grounded ice sheet. However, relatively little attention has been paid to the role that fractures play in the ability of ice shelves to sustain and transmit buttressing stresses. Here, we present a new framework for quantifying the role that fractures play in the creep deformation and buttressing capacity of ice shelves. We apply principles of continuum damage mechanics to derive a new analytical relation for the creep of an ice shelf that accounts for the softening influence of fractures on longitudinal deformation using a state damage variable. We use this new analytical relation, combined with a temperature calculation for the ice, to partition an inverse method solution for ice shelf rigidity into independent solutions for softening damage and stabilizing backstress. Using this new approach, field and remote sensing data can be utilized to monitor the structural integrity of ice shelves, their ability to buttress the flow of ice at the grounding line, and thus their indirect contribution to ice sheet mass balance and global sea level. We apply this technique to the Larsen C ice shelf using remote sensing and Operation IceBridge data, finding damage in areas with known crevasses and rifts. Backstress is highest near the grounding line and upstream of ice rises, in agreement with patterns observed on other ice shelves. The ice in contact with the Bawden ice rise is weakened by fractures, and additional damage or thinning in this area could diminish the backstress transmitted upstream. We model the consequences for the ice shelf if it loses contact with this small ice rise, finding that flow speeds would increase by 25 % or more over an area the size of the former Larsen B ice shelf. Such a perturbation could potentially destabilize the northern part of Larsen C along pre-existing lines of weakness, highlighting the importance of the feedback between buttressing and fracturing in an ice shelf.

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“…The resulting effective stress is expressed in terms of the damage tensor [7]. For definitions of a second order damage tensor see also [3,8,9,10,11].…”

Section: Phenomenological Definitions Of Damage Parameters Numerous mentioning

confidence: 99%

Scalar, vectorial, and tensorial damage parameters from the mesoscopic background

Papenfuß¹,

Ván²

2008

Proc. Estonian Acad. Sci.

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ABSTRACT. In the mesoscopic theory a distribution of different crack sizes and crack orientations is introduced. A scalar damage parameter, a second order damage tensor and a vectorial damage parameter are defined in terms of this distribution function. As an example of a constitutive quantity the free energy density is given as a function of the damage tensor. This equation is reduced in the uniaxial case to a function of the damage vector and in case of a special geometry to a function of the scalar damage parameter.

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A Continuum Theory of Creep and Creep Damage

Cited by 290 publications

References 9 publications

Combining damage and fracture mechanics to model calving

Combining damage and fracture mechanics to model calving

Creep deformation and buttressing capacity of damaged ice shelves: theory and application to Larsen C ice shelf

Scalar, vectorial, and tensorial damage parameters from the mesoscopic background

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