Concrete is the most versatile material used for construction. Concrete structures generally consist of numerous micro-cracks and the accumulation and propagation of these cracks might lead to the growth of major cracks. A better understanding of the stress-deformation behavior of concrete structures is inevitable to maintain the structural integrity and to avoid catastrophic failures.
Damage modeling constitutes a branch of material modeling grounded in the principles of continuum damage mechanics theory. It incorporates the progressive degradation of material stiffness into constitutive relationship. The initial applications of such models were mainly for metals and subsequently expanded to brittle materials like concrete. The simplest type of damage model introduces a scalar damage variable to describe the material stiffness degradation. But failure in concrete is associated with the mutual interactions of micro-cracks and micro-voids which are arbitrarily oriented. When the material experiences multi-axial loading conditions, conventional isotropic damage models fall short in capturing the relative variation in stiffness degradation between axial and transverse directions. Therefore damage-induced anisotropy is introduced using higher order tensors as damage variables. For simplicity, a second order tensor is used to describe the anisotropic damage evolution. An exponential damage evolution law is utilized with distinct model paramters for capturing the behavior of concrete in tensile and compressive loading conditions.
Failure in concrete is associated with the nucleation and propagation of micro-cracks, due to which the load-carrying capacity of the material decreases after the peak stress. This phenomenon is called strain softening. Finite element implementation of the damage models is known for its mesh sensitivities due to the strain localization effects. It is observed that the dissipated energy decreases upon mesh refinement. Such a dependence is inadmissible as this is an ill-posed boundary value problem and results in loss of ellipticity of governing differential equations. To overcome the mesh dependencies associated with the localization of damage, a gradient-enhancement approach is used in the model. Such regularization techniques use internal length scale as a localization limiter to enrich the standard continuum into nonlocal continuum.
Further research is focused on developing a regularized anisotropic damage model. This involves formulating a nonlocal model capable of producing a comparable material response considering the anisotropic evolution of damage in global coordinate system. Other important aspects that need to be considered are the dissimilarity in the behavior of concrete under tension and compression and crack closure effects under alternate tension-compression loading.
The project is part of the DFG programme GRK 2075 - Modelling the constitutional evolution of building materials and structures with respect to aging.