Internal Length-Scales in Damaged Solids: a Lagrange Multiplier Approach

  • Elena Benvenuti
  • Benjamin Loret
Part of the International Centre for Mechanical Sciences book series (CISM, volume 426)


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.


Equivalent Strain Concrete Slab Internal Length Compressive Damage Control Volume Versus 
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Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Elena Benvenuti
    • 1
  • Benjamin Loret
    • 2
  1. 1.Dipartimento di IngegneriaUniversità degli Studi di FerraraFerraraItalia
  2. 2.Laboratoire Sols, Solides, StructuresGrenoble CedexFrance

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