Lumped damage mechanics

Lumped damage mechanics or LDM is a branch of structural mechanics that is concerned with the analysis of frame structures. It is based on continuum damage mechanics and fracture mechanics. It combines the ideas of these theories with the concept of plastic hinge[1] LDM can be defined as the fracture mechanics of complex structural systems. In the models of LDM, cracking or local buckling as well as plasticity are lumped at the inelastic hinges. As in continuum damage mechanics, LDM uses state variables to represent the effects of damage on the remaining stiffness and strength of the frame structure. In reinforced concrete structures, the damage state variable quantifies the crack density in the plastic hinge zone;[1] in unreinforced concrete components and steel beams, it is a dimensionless measure of the crack surface;[2] in tubular steel elements, the damage variable measures the degree of local buckling[3] The LDM evolution laws can be derived from continuum damage mechanics[3][4] or fracture mechanics.[1][2] In the latter case, concepts such as the energy release rate or the stress intensity factor of a plastic hinge are introduced. LDM allows for the numerical simulation of the collapse of complex structures with a fraction of the computational cost and human effort of its continuum mechanics counterparts. LDM is also a regularization procedure that eliminates the mesh-dependence phenomenon that is observed in structural analysis with local damage models.[5] In addition, LDM method has been implemented in the finite element analysis of crack propagation of steel beam-to-column connections subjected to ultra-low cycle fatigue.[6][7]

References
  1. Marante, M.E., Flórez-López, J., “Three-Dimensional Analysis Of Reinforced Concrete Frames Based On Lumped Damage Mechanics” International Journal of Solids and Structures Vol 40, No 19, 5109-5123, 2003.
  2. Amorim, D.L.N.D.F., Proença, S.P.B.,Flórez-López, J. “Simplified modeling of cracking in concrete: Application in tunnel linings” Engineering Structures, 70, pp. 23-25 (2014)
  3. Marante, M.E., Picón, R., Guerrero, N. And Flórez-López, J. “Local buckling in tridimensional frames: experimentation and simplified analysis” 9(2012) 691 – 712 Latin-American Journal of Solids and Structures.
  4. Santoro M, Kunnath S. Damage-based RC beam element for nonlinear structural analysis. Eng. Struct. 2013; 49:733–742.
  5. Toi, Y., Hasegawa, K.H.,. "Element-size independent, elasto-plastic damage analysis of framed structures using the adaptively shifted integration technique" Comput. Struct. 2011; 89, 2162-2168
  6. Bai, Yongtao; Kurata, Masahiro; Flórez-López, Julio; Nakashima, Masayoshi (October 2016). "Macromodeling of Crack Damage in Steel Beams Subjected to Nonstationary Low Cycle Fatigue". Journal of Structural Engineering. 142 (10): 04016076. doi:10.1061/(asce)st.1943-541x.0001536. ISSN 0733-9445.
  7. Bai, Yongtao; Guan, Shaoyu; Flórez-López, Julio (December 2017). "Development of a damage model for assessing fracture failure of steel beam-to-column connections subjected to extremely low-cycle fatigue". Engineering Failure Analysis. 82: 823–834. doi:10.1016/j.engfailanal.2017.07.032. ISSN 1350-6307.
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