Abstract
Like softening in elastic-plastic solids and fluid-saturated porous media, damage in brittle solids is likely to induce instabilities. The corresponding equations of motion loose their hyperbolicity and the computations depend pathologically on the finite element mesh. Non-local operators are introduced to bring an internal length into the governing equations. For elastic-damaging solids, the associated computational aspects are addressed in a unified framework, which views the non-local operators as constraints and introduces them into the energy through a Lagrange multiplier: the resulting matrix systems, although larger, are symmetric.
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Benvenuti, E., Loret, B. (2001). Internal Length-Scales in Damaged Solids: a Lagrange Multiplier Approach. In: Griffiths, V.D., Gioda, G. (eds) Advanced Numerical Applications and Plasticity in Geomechanics. International Centre for Mechanical Sciences, vol 426. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2578-6_1
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DOI: https://doi.org/10.1007/978-3-7091-2578-6_1
Publisher Name: Springer, Vienna
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