From local failure toward global collapse of elastic–plastic structures in fluctuating fields

Application of shakedown theory to study the load-bearing capacity of truss structures subjected to varying loads is presented. Inadaptation may cause local fractures not leading to the global collapse (the loss of load-bearing capacity) of a structure. A full analysis requires a step-by-step application of the reduced kinematic formulae constructed recently by the author to check the occurrence of a local fracture by alternating plasticity and a possible spreading of the fracture zone until the critical state of global incremental (or instantaneous) collapse is reached. This basic phenomenon, in somehow more sophisticated appearance, might be observed in many more general structures and in inhomogeneous materials working in changing fields, as in some fiber bundle models presented. The solution procedure could also help to improve the design of a structure for particular working conditions.