Modeling of progressive damage in concrete using multidimensional virtual internal bond method

Damage simulation via tensile and shear failure modes in quasi-brittle material like concrete is computationally challenging. Multidimensional virtual internal bond (MVIB) method is one of the promising method developed to capture shear failure in materials like concrete. It assumes continuum as an assemblage of material points joined by normal and shear bonds possessing harmonic potential and bond density evolution function, which degrades with deformation to yield at macroscopic level, stress-strain law with inbuilt feature of failure via Cauchy-Born rule. The degradation of bond-density in MVIB method originally based solely on compressive failure is extended to include tensile failure synonymous with tension and compression asymmetry in concrete. The modified MVIB model is applied to a variety of problems, and the effect of inclusion of both tensile and compressive failure is thoroughly assessed. Through the example of two notches in a square plate subjected to biaxial loading, a systematic study of damage evolution vis-a-vis biaxial loading ratio is presented. Capture of crack closure and formation of crack retarding protective shield are unique outcomes of the present work.