ELASTIC-PLASTIC-FRACTURE ANALYSIS OF CONCRETE STRUCTURES

SHYI-SHING HSIEH, Purdue University

Abstract

To extend the analytical capability of a general purpose computer code to include the nonlinear and fractural behaviors of concrete structures, it requires improved fractural criteria, more accurate constitutive formulations, and the appropriate numerical solution techniques. The present research effort is an attempt to formulate an Elastic-Plastic-Fracture model, and to develop solution methods for finite element analysis to study progressive failures of plain concrete structures under short term triaxial loading conditions. For the material modeling, a four-parameter fractural (or yielding) criterion is proposed, which has the advantage of simplicity in material characterization and structural analysis. It also embraces some of the existing concrete models. An isotropic elastic model and an anisotropic elastic model are proposed respectively, for the initial concrete response and the post-fracture behavior. A plastic model displaying mixed-hardening behavior is proposed to describe the material response between the initial yielding and the fractural failure. Incremental stress-strain relationships for the plastic region are derived based on an associated flow rule and the Ziegler's kinematic-hardening criterion. Three different types of concrete fracture modes are considered. A simple crushing coefficient is defined based on the concept of a dual criterion to identify the crushing type of fracture, the cracking type of fracture, and the mixed type. Simple concrete tests required for the determination of material constants for the plastic-fracture model are identified. An important feature of the study is that all the matrix formulations of the constitutive relationships have been derived and their implementation for numerical analysis is illustrated by three sample problems using nonlinear finite element methods. To obtain nonlinear finite element solutions, some numerical schemes have been introduced and validated. These include a step-iteration procedure to handle the nonlinear structural history, an initial stress method to correct the bias of stress path due to linear idealization, a scaling procedure to evaluate the yield of fracture load, and a stress redistribution procedure to reestablish the stress equilibrium during the progress of fractural process. The solution techniques and the material model are coded in two computer programs. The program EFCP is developed for the study of crack propagation procedures, and the program ELT2D6 is developed in subroutine form to integrate with a general structural nonlinear finite element program (NFAP). Three illustrative nonlinear concrete problems are solved. They are a thin-walled concrete cylinder under hydrostatic pressure, a pull-out Lok test, and a splitting tension Brazilian test. Good agreements are obtained for the structural response, the maximum loading capacity and the fractural mode, as numerical solutions are compared to the reported experimental and analytical results.

Degree

Ph.D.

Subject Area

Civil engineering

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