Simulation of Reinforced Concrete Structure under Impact Loading using Meshfree Cohesive Failure Approach

Reliable numerical simulation of failure is important for the design and planning of new solids and structures, as well as for the safety assessment of existing ones. In the past two decades, gradient and non-local models for regularizing loss of ellipticity due to material failure using non-standard finite element method and more recently the meshfree method have been the topic of considerable research. Alternatively, discontinuous partition of unity enrichments and meshfree visibility concepts were proposed and used in finite element method (also called extended finite element method XFEM) and meshfree method to model cracks. Due to the fact that the description of crack plane in XFEM using level set method still presents several difficulties in the three-dimensional simulation of solids, the meshfree method using visibility concept is tested for the solid failure analysis of reinforced concrete structure under impact loading. The current method incorporates the discontinuous field into the generalized meshfree approximation [1] by the introduction of visibility approach [2]. To determine the onset of fracture and subsequently the crack propagation, a stress-based initial-rigid cohesive cracking model was developed for the brittle and semi-brittle materials. After the insertion of new crack, the state variables are interpolated and transferred to the new stress point using second-order meshfree approximation [3]. To integrate the discrete equations involving the crack plane, the strain smoothing algorithm developed in SCNI method [4] was adopted in this development. A typical reinforced concrete structure under impact loading failure involving multi-cracks is modeled using the developed method and results are presented. Generalized Meshfree Approximation The generalized meshfree (GMF) approximation method can be used to construct a convex, nonconvex, or combined convex and non-convex approximation for meshfree computation. The GMF approximation has one unique feature. That is it naturally bears the weak Kronecker-delta property at boundaries regardless of its convexity or non-convexity. This property makes the imposition of essential boundary conditions in meshfree methods easier. The first-order GMF approximation in one dimension is described as follows: Simulation(1) 12 th International LS-DYNA ® Users Conference 2 1 (x; ) ( , ) (x, ) (x; ) ( , ) i a i i i i n a j j j j X X X X               for fixed x , (1)