Modeling of Stress-Strain Relationship for Fibrous Concrete Under Cyclic Loads

Abstract

A mathematical model to predict the stress-strain behavior of fibrous concrete composites under random cyclic compressive loadings is developed. The envelope unloading strain is used as an index of load history, while the plastic strain and reloading strain are predicted as functions of the envelope unloading strain for both full and partial unloading and reloading. The model is independent of the expression used for the envelope curve. Comparison with cyclic data shows good agreement. The model can be used for completely random loadings, in both the pre-peak and post-peak ranges. It is suitable for both plain and fibrous concrete composites. The model has been built using MATLAB language computer program facilitating the advanced mathematical difficulties of solving and differentiating complex expressions. In this paper, the monotonic stress-strain curves of Al-Sulayfani model [1] for fibrous concrete had been adopted. ‫ﺍﻹﺠﻬﺎﺩ‬ ‫ﻤﻨﺤﻨﻰ‬ ‫ﻨﻤﺫﺠﺔ‬-‫ﻟﻠﺨﺭﺴ‬ ‫ﺍﻻﻨﻔﻌﺎل‬ ‫ﺍﻟﺩﻭﺭﻱ‬ ‫ﺍﻟﺤﻤل‬ ‫ﺘﺤﺕ‬ ‫ﺍﻟﻠﻴﻔﻴﺔ‬ ‫ﺎﻨﺔ‬ ‫ﺍﻟﺨﻼﺼﺔ‬ ‫ﺎد‬ ‫اﻹﺟﮭ‬ ‫ﻲ‬ ‫ﻣﻨﺤﻨ‬ ‫ﻠﻮك‬ ‫ﺑﺴ‬ ‫ﺘﻜﮭﻦ‬ ‫ﯾ‬ ‫ﻲ‬ ‫رﯾﺎﺿ‬ ‫ﻮذج‬ ‫ﻧﻤ‬ ‫ﻮﯾﺮ‬ ‫ﺗﻄ‬ ‫ﻢ‬ ‫ﺗ‬-‫ﺎل‬ ‫أﺣﻤ‬ ‫ﺖ‬ ‫ﺗﺤ‬ ‫ﻠﺤﺔ‬ ‫اﻟﻤﺴ‬ ‫ﺔ‬ ‫اﻟﻠﯿﻔﯿ‬ ‫ﺎﻧﺔ‬ ‫ﻟﻠﺨﺮﺳ‬ ‫ﺎل‬ ‫اﻻﻧﻔﻌ‬ ً ‫ﻮاﺋﯿﺎ‬ ‫ﻋﺸ‬ ‫ﻠﻄﺔ‬ ‫اﻟﻤﺴ‬ ‫ﺔ‬ ‫اﻟﺪورﯾ‬ ‫ﻐﺎط‬ ‫اﻻﻧﻀ‬. ‫ﻞ‬ ‫اﻟﺤﻤ‬ ‫ﺪه‬ ‫ﻋﻨ‬ ‫ﻊ‬ ‫ﯾﺮﻓ‬ ‫ﺬي‬ ‫اﻟ‬ ‫ﺎل‬ ‫اﻻﻧﻔﻌ‬ ‫ﺪ‬ ‫اﻋﺘﻤ‬ ‫ﺪ‬ ‫وﻗ‬ Unloading Strain ‫ف‬ ‫ﻼ‬ ‫اﻟﻐ‬ ‫ﻲ‬ ‫ﻣﻨﺤﻨ‬ ‫ﻰ‬ ‫ﻋﻠ‬ ‫ﻊ‬ ‫اﻟﻮاﻗ‬ Envelope Curve ‫ﺔ‬ ‫اﻟﻠﺪوﻧ‬ ‫ﺎل‬ ‫اﻧﻔﻌ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﻞ‬ ‫ﻛ‬ ‫ﺎب‬ ‫ﺣﺴ‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﮫ‬ ‫ﻋﻠﯿ‬ ‫ﺪ‬ ‫ﯾﻌﺘﻤ‬ ‫ﺎ‬ ‫ﻣﺮﺟﻌ‬ Plastic Strain ‫اﻟﺤﻤﻞ‬ ‫إﻋﺎدة‬ ‫واﻧﻔﻌﺎل‬ Reloading Strain