Our objective is to model static multi-cracking processes in concrete. The explicit dynamic relaxation (DR) method, which gives the solutions of non-linear static problems on the basis of the steady-state conditions of a critically damped explicit transient solution, is chosen to deal with the high geometric and material non-linearities stemming from such a complex fracture problem. One of the common difficulties of the DR method is its slow convergence rate when non-monotonic spectral response is involved. A modified concept that is distinct from the standard DR method is introduced to tackle this problem. The methodology is validated against the stable three point bending test on notched concrete beams of different sizes. The simulations accurately predict the experimental load-displacement curves. The size effect is caught naturally as a result of the calculation. Micro-cracking and non-uniform crack propagation across the fracture surface also come out directly from the 3D simulations.

The examinations carried out have confirmed a relationship existing between the character of fracture surfaces and the composition and structure of (basalt and gravel) concretes. For both concretes investigated, a very good correlation was obtained between the profile line development factor, $R_L$, and the fracture surface development factor, $R_S$. With the increase in the $R_L$ parameter, the fracture surface development factor $R_S$ also increased. Agreement between the proposed relationship of $R_S=f(R_L)$ and the proposal given by Coster and Chermant (1983) was obtained. Stereological examinations carried out along with fractographic examinations made it possible to obtain a statistical model for the determination of $R_L$ (or $R_S$) based on the volume of air voids in concrete, $V_{air}$, the specific surface of air pores, $S_V_{air}$ the specific surface of coarse aggregate, $S_{Vagg.}$, and the volume of mortar, $V_m$. An effect of coarse aggregate type on the obtained values of the profile line development factor, $R_L$, as well as on the relationship $R_S=f(R_L)$ was observed. The increment in the fracture surface development factor $R_S$ with increasing $R_L$ parameter was larger in basalt concretes than in gravel concretes, which was a consequence of the level of complexity of fractures formed, resulting chiefly from the shape of coarse aggregate grains.

This paper presents investigation of a three-dimensional (3-D) nonlinear finite element model analysis to examine the behavior of reinforced concrete beams strengthened with Carbon Fiber Reinforced Polymer (CFRP) composites to enhance the flexural capacity and ductility of the beams. Three-dimensional nonlinear finite element models were developed between the internal reinforcement and concrete using a smeared relationship. In addition, bond models between the concrete surface and CFRP composite were developed using a smeared bond for general analyses and a contact bond for sensitivity analyses. The results of the FEA were compared with the experimental data on full-scale members. The results of two finite-element bonding models showed good agreement with those of the experimental tests.

An analytical model which can simulate the post-cracking nonlinear behavior of reinforced concrete (RC) members such as bars and panels subject to uniaxial and biaxial stresses is presented. The proposed model includes the description of biaxial failure criteria and the average stress-strain relation of reinforcing steel. Based on strain distribution functions of steel and concrete after cracking, a criterion to consider the tension-stiffening effect is proposed using the concept of average stresses and strains. The validity of the introduced model is established by comparing the analytical predictions for reinforced concrete uniaxial tension members with results from experimental studies. In advance, correlation studies between analytical results and experimental data are also extended to RC panels subject to biaxial tensile stresses to verify the efficiency of the proposed model and to identify the significance of various effects on the response of biaxially loaded reinforced concrete panels.

The paper presents results of FE-calculations on shear localizations in quasi-brittle materials during both an uniaxial plane strain compression and uniaxial plane strain extension. An elasto-plastic model with a linear Drucker-Prager type criterion using isotropic hardening and softening and non-associated flow rule was used. A non-local extension was applied in a softening regime to capture realistically shear localization and to obtain a well-posed boundary value problem. A characteristic length was incorporated via a weighting function. Attention was focused on the effect of mesh size, mesh alignment, non-local parameter and imperfections on the thickness and inclination of shear localization. Different methods to calculate plastic strain rates were carefully discussed.