Lumped damage mechanics or LDM is a branch of

structural mechanics Structural mechanics or mechanics of structures is the computation of deformations, deflections, and internal forces or stresses (''stress equivalents'') within structures, either for design or for performance evaluation of existing structures. ...

that is concerned with the analysis of frame structures. It is based on continuum

damage mechanics Damage mechanics is concerned with the representation, or modeling, of damage of materials that is suitable for making engineering predictions about the initiation, propagation, and fracture of materials without resorting to a microscopic descriptio ...

and

fracture mechanics Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics t ...

. It combines the ideas of these theories with the concept of

plastic hinge In the structural engineering beam theory, plastic hinge is the deformation of a section of a Beam (structure), beam where plastic bending occurs. In earthquake engineering plastic hinge is also a type of energy Damping ratio, damping device allo ...

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. LDM can be defined as the fracture mechanics of complex

structural system The term structural system or structural frame in structural engineering refers to the load-resisting sub-system of a building or object. The structural system transfers loads through interconnected elements or members. Commonly used structu ...

s. 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 A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of a ...

to represent the effects of damage on the remaining stiffness and strength of the frame structure. In

reinforced concrete Reinforced concrete, also called ferroconcrete or ferro-concrete, is a composite material in which concrete's relatively low tensile strength and ductility are compensated for by the inclusion of reinforcement having higher tensile strength or ...

structures, the damage state variable quantifies the crack density in the plastic hinge zone; in unreinforced concrete components and steel beams, it is a dimensionless measure of the crack surface;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) in tubular steel elements, the damage variable measures the degree of local bucklingMarante, 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. The LDM evolution laws can be derived from continuum damage mechanicsSantoro M, Kunnath S. Damage-based RC beam element for nonlinear structural analysis. Eng. Struct. 2013; 49:733–742. or fracture mechanics. In the latter case, concepts such as the

energy release rate In fracture mechanics, the energy release rate, G, is the rate at which energy is Energy transformation, transformed as a material undergoes fracture. Mathematically, the energy release rate is expressed as the decrease in total potential energy pe ...

or the

stress intensity factor In fracture mechanics, the stress intensity factor () is used to predict the Stress (mechanics), stress state ("stress intensity") near the tip of a Fracture, crack or Notch (engineering), notch caused by a remote load or residual stresses. It i ...

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.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 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.

References

{{reflist * * * * Continuum mechanics Materials degradation