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Modified Multi-surface Kinematic Hardening Plasticity 18 K = K 0*D) The multi-surface kinematic hardening plasticity model (Mroz 1967) is modified for the fiber of the CZM-based macro-model to model cyclic loadings, softening and fracture n – line segments of constant tangent modulii: E 1, E 2, E 3,.., E n f 0, f 1, f 2 ,…, f n are hyper-surfaces with constant hardening modulii. All surfaces can translate in space without changing form and orientation - Loading/unloading �� cyclic
Modified Multi-surface Kinematic Hardening Plasticity 19 Cantilever example Applied load Top displacement (Danevit, Opensees) vs. (macro-model) Elastic -plastic Applied load elastic
Page 1 and 2: A CZM-based Macro-model for Progres
Page 3 and 4: 3 Key elements of structural analys
Page 5 and 6: 5 Existing approaches for collapse
Page 7 and 8: 7 Existing approaches for collapse
Page 9 and 10: 9 Scope of research This research s
Page 11 and 12: 11 Cohesive law CZM schematics Intr
Page 13 and 14: 13 CZM: PPR cohesive model Based on
Page 15 and 16: CZM for ductile materials �� Va
Page 17: N 17 A CZM-based macro-model 1 3 3
Page 21: 21 Progressive collapse � Aim to

presentation - Northeastern University

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