黏弹-双曲线Drucker-Prager塑性模型应力更新隐式算法
发布时间：2019-03-09 12:28
【摘要】：黏弹-塑性模型是由黏弹性模型与塑性元件串联而成,可视为黏弹-黏塑性模型中黏塑性黏度参数趋于0的一种极限情况,为黏弹性材料的结构破坏分析提供了一个途径。把黏弹-塑性模型的应变增量分解为黏弹和塑性增量两部分,考虑黏弹性应变历史,把黏弹性积分型本构关系在一个时步内线性化,定义与时间增量相关的剪切模量和体积模量,导出应力递推公式,把黏弹-塑性本构积分转化为与弹塑性相似的形式。针对由黏弹性和双曲线Drucker-Prager塑性、各向同性硬化的黏弹-塑性模型,通过黏弹性预估和塑性校正"二步"算法实现对应力的更新,给出完全隐式算法和最终的计算公式。算例比较分析表明,由于迭代过程中仅需要简单的函数计算,该算法具有很好的收敛性。一般经过2次迭代运算后,屈服函数值已达到10-10的量级,应力点便返回到屈服面上。
[Abstract]:Visco-elasto-plastic model is made up of viscoelastic model and plastic element in series. It can be regarded as a limit case of Visco-plastic viscosity parameter approaching to zero in Visco-plastic model, which provides a way for structural failure analysis of Visco-elastic materials. The strain increment of Visco-elastic-plastic model is decomposed into two parts: viscoelastic and plastic increment. Considering the history of viscoelastic strain, the viscoelastic integral constitutive relation is linearized in one time step. The shear modulus and volume modulus related to time increment are defined, and the recurrence formula of stress is derived. The viscoelastic-plastic constitutive integral is transformed into a form similar to that of elasto-plastic. For the viscoelastic-plastic model with isotropic hardening from viscoelastic and hyperbolic Drucker-Prager plasticity, the "two-step" algorithm of Visco-elastic prediction and plastic correction is used to update the stress, and the fully implicit algorithm and the final calculation formula are given. The comparison and analysis of numerical examples show that the algorithm has good convergence because only simple function calculation is needed in the iterative process. Generally, after two iterations, the value of the yield function has reached the order of 10 脳 10, and the stress point will return to the yield surface.
【作者单位】： 郑州大学土木工程学院;
【基金】：国家自然科学基金项目(No.51578511)~~
【分类号】：O34
本文编号：2437451
[Abstract]:Visco-elasto-plastic model is made up of viscoelastic model and plastic element in series. It can be regarded as a limit case of Visco-plastic viscosity parameter approaching to zero in Visco-plastic model, which provides a way for structural failure analysis of Visco-elastic materials. The strain increment of Visco-elastic-plastic model is decomposed into two parts: viscoelastic and plastic increment. Considering the history of viscoelastic strain, the viscoelastic integral constitutive relation is linearized in one time step. The shear modulus and volume modulus related to time increment are defined, and the recurrence formula of stress is derived. The viscoelastic-plastic constitutive integral is transformed into a form similar to that of elasto-plastic. For the viscoelastic-plastic model with isotropic hardening from viscoelastic and hyperbolic Drucker-Prager plasticity, the "two-step" algorithm of Visco-elastic prediction and plastic correction is used to update the stress, and the fully implicit algorithm and the final calculation formula are given. The comparison and analysis of numerical examples show that the algorithm has good convergence because only simple function calculation is needed in the iterative process. Generally, after two iterations, the value of the yield function has reached the order of 10 脳 10, and the stress point will return to the yield surface.
【作者单位】： 郑州大学土木工程学院;
【基金】：国家自然科学基金项目(No.51578511)~~
【分类号】：O34
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1 李建宇;张洪武;;解Drucker-Prager塑性问题的二阶锥互补法[J];计算力学学报;2014年03期
，本文编号：2437451
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