混凝土或其他脆性材料的塑性破坏

Damaged plasticity model for concrete and other quasi-brittle materials

Products:

Abaqus/Standard Abaqus/Explicit

This section describes the concrete damaged plasticity model provided in Abaqus for the analysis of concrete and other quasi-brittle materials. The material library in Abaqus also includes other constitutive models for concrete based on the smeared crack approach.These are the smeared crack model in

Abaqus/Standard,described in “Aninelastic constitutive model for concrete,”Section 4.5.1, and the brittle cracking model in Abaqus/Explicit, described in “A cracking modelfor concrete and other brittle materials,” Section 4.5.3.

stiffness recovery effects during cyclic loading; and

rate sensitivity, especially an increase in the peak strength with strain rate.

The plastic-damage model in Abaqus is based on the models proposed by Lubliner et al.

(1989)and by Lee and Fenves

(1998).The model is described in the remainder of this section.An overview of the main ingredients of the model is given first,followed by a more detailed discussion of the different aspects of the constitutive model.

Overview

where is the total strain rate,is the elastic part of the strain rate, and is the plastic part of the strain rate.

Stress-strain relations

The stress-strain relations are governed by scalar damaged elasticity:

where is the initial (undamaged)elastic stiffness of the material;is the degraded elastic stiffness; and d is the scalar stiffness degradation variable, which can take values in the range from zero (undamaged material) to one (fully damaged material). Damage associated with the failure mechanisms of the concrete (cracking and crushing) therefore results in a reduction in the elastic stiffness. Within the context of the scalar-damage theory, the stiffness degradation is isotropic and characterized by a single degradation variable,d.Following the usual notions of continuum damage mechanics, the effective stress is defined as

The Cauchy stress is related to the effective stress through the scalar degradation relation:

For any given cross-section of the material,the factor represents the ratio of the effective load-carrying area (i.e., the overall area minus the damaged area) to the overall section area. In the absence of damage,,the effective stress is equivalent to the Cauchy stress, .When damage occurs, however, the effective stress is more representative than the Cauchy stress because it is the effective stress area that is resisting the external loads. It is, therefore, convenient to formulate the plasticity problem in terms of the effective stress.As discussed later,the evolution of the degradation variable is governed by a set of hardening variables, , and the effective stress; that is, .Hardening variables

as described later in this section.

Microcracking and crushing in the concrete are represented by increasing values of the hardening variables.These variables control the evolution of the yield surface and the degradation of the elastic stiffness.They are also intimately related to the dissipated fracture energy required to generate micro-cracks.