混凝土弹塑性损伤本构模型研究 Ⅰ:基本公式

ELASTOPLASTIC DAMAGE CONSTITUTIVE MODEL FOR CONCRETE BASED ON DAMAGE ENERGY RELEASE RATES, PART I:BASIC FORMULATIONS

从分析混凝土材料的基本损伤机制出发,本文采用受拉损伤变量和受剪损伤变量反映微观损伤对混凝土材料宏观力学性能劣化的影响,建议了一类基于能量的弹塑性损伤本构模型。该模型基于有效应力张量分解定义材料的弹性Helmholtz自由能,并根据有效应力空间塑性力学确定了塑性变形的演化法则和塑性Helmholtz自由能。由此给出了材料的总Helmholtz自由能和弹塑性损伤能释放率,建立了符合热动力学基本原理的损伤准则,并根据正交法则得到了损伤变量的演化法则。对Kupfer双轴试验的数值模拟结果初步说明了模型的有效性。文中涉及到的数值算法及进一步的试验验证将在本文第Ⅱ部分给出。

In this paper, starting from an analysis of basic damage mechanisms leading to the failure of concrete materials, a tensile damage variable and a shear damage variable are adopted to describe the influence of micro-defects on the degrading of macromechanical properties. Based on the decomposition of the effective stress tensor, the elastic Helmhotlz free energy is defined, from which the elastoplastic damage constitutive relation with internal variables is derived, and based on the effective stress space plasticity, the evolution law for the plastic strains and the plastic Helmhotlz free energy are determined. The total elastoplastic Helmhotlz free energy and the damage energy release rates are employed to establish the damage criteria in accordance with the thermodynamics principle, and the evolution laws for damage variables are established in accordance with the normal rule. Finally, the model is applied to simulate the tests of Kupfer et al. The agreement between the predictive results and the test data shows the correctness and validity of the present model. The numerical algorithm and further verifications of the model are provided in Part Ⅱ of this paper series.