Since the finite element method was first applied to the analysis of reinforced concrete structures, the theory and application of nonlinear finite element have made great progress. There are two types of nonlinear analysis problems in finite element analysis. One is the material nonlinear problem, which means that the stress-strain relationship of the material is nonlinear. In the problem of material nonlinearity, if the same structure under the same load is used, if different material stress-strain relationship curves are used, the response of the displacement of the structure will also be different. The other is the geometric nonlinear problem, which is caused by the large displacement of the solid, including the problem of large deflection of the structure and the problem of structural stability. In the geometric nonlinear problem, the main research is the motion relationship and balance relationship of the structure. Research on nonlinear problems mainly focuses on the establishment and improvement of mathematical models. In the nonlinear stress-strain relationship mathematical model, concrete and steel bars are generally treated separately, and then the continuity of the structure is considered to obtain the joint effect of the two.
(1) Non-linear elastic model uses piecewise linear elastic material with variable modulus to simulate the nonlinear deformation performance of concrete. This model is a model based on elasticity, that is, stress and strain are not proportional, and the elastic modulus is a function of stress. After unloading, the deformation can be completely restored. In this way, the stress state is completely determined by the strain state, regardless of the loading history. Using this model to simulate the characteristics of monotonic loading is more effective, but its disadvantage is that it can not accurately describe the characteristics of concrete under high stress when it is close to failure.
(2) The elastoplastic model can reflect the unrecoverable deformation or plastic deformation that occurs when the deformed material is unloaded, and its theory is the plastic theory. Plasticity theory includes deformation theory and incremental theory. The so-called incremental theory means that the constitutive relationship describing the plastic state of the material adopts incremental form, and the calculation is relatively cumbersome. However, in recent years, due to the rapid development of computer technology, the application of incremental theory has become more and more widely used. Among several elastoplastic models of reinforced concrete, strain-strengthened models are often used.
(3) The internal time model is expressed in the form of viscoplastic theory, using incremental nonlinearity. It is applicable to the unsteady ratio of the load in the three loading directions, which is the so-called non-proportional loading situation. The internal time model can simulate many complex properties of concrete materials. Its disadvantage is that it requires too many input material constants and the computer runs for a long time.
(4) Concrete fracture mechanics are divided into concrete elastic fracture mechanics and nonlinear fracture mechanics. The former includes two methods. One method is the stress intensity factor method. This method considers that the crack is stable when the stress intensity factor Ki at the joint end is less than the material fracture resistance toughness Kic of the material against crack propagation; the other method is Energy method, this method believes that when the structure cracks propagate per unit area, the rate of decrease of the energy of the entire structural system Gi is less than the energy Gic required per unit crack surface, then the crack is stable.
(5) Damage mechanics believes that there are micro-defects in engineering materials. Therefore, a damage variable is introduced as a physical quantity to characterize the internal defects of the material. The damage variable refers to the irreversible reduction of the internal bonding part of the material. Based on the damage variables, the effective stress and other parameters are used to establish the constitutive relationship of the concrete material. Damage mechanics not only considers the initial crack before the material is stressed, but also reflects the crack propagation and strain softening caused by the accumulation of damage during the stress process. The elastoplastic damage mechanics developed in recent years have adopted an elastoplastic model in the concrete strengthening stage and a damage mechanics model in the softening stage, which has opened up a new idea for dealing with the problem of concrete strain softening.
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