Taking the strain tensor, the scalar damage variable, and the damage gradient as the state variables of the Helmholtz free energy, the general expressions of the firstorder gradient damage constitutive equations are d...Taking the strain tensor, the scalar damage variable, and the damage gradient as the state variables of the Helmholtz free energy, the general expressions of the firstorder gradient damage constitutive equations are derived directly from the basic law of irreversible thermodynamics with the constitutive functional expansion method at the natural state. When the damage variable is equal to zero, the expressions can be simplified to the linear elastic constitutive equations. When the damage gradient vanishes, the expressions can be simplified to the classical damage constitutive equations based on the strain equivalence hypothesis. A one-dimensional problem is presented to indicate that the damage field changes from the non-periodic solutions to the spatial periodic-like solutions with stress increment. The peak value region develops a localization band. The onset mechanism of strain localization is proposed. Damage localization emerges after damage occurs for a short time. The width of the localization band is proportional to the internal characteristic length.展开更多
利用Abaqus提供的用户材料本构接口,将Gurson模型用UMAT(user defined material subroutine)和VUMAT(vectorized user defined material subroutine)分别实现。其中UMAT适用于Abaqus中的Standard计算模块,忽略惯性效应,而VUMAT适用于Aba...利用Abaqus提供的用户材料本构接口,将Gurson模型用UMAT(user defined material subroutine)和VUMAT(vectorized user defined material subroutine)分别实现。其中UMAT适用于Abaqus中的Standard计算模块,忽略惯性效应,而VUMAT适用于Abaqus中的Explicit计算模块,包含惯性效应。通过对二者的计算结果进行对比分析,考察惯性效应对孔洞长大的作用与影响。结果表明:(1)惯性效应对加载速率非常敏感,随着加载速率的提高,惯性效应先是抑制,继而促进孔洞的长大。(2)存在一个临界应变率,在临界应变率时,惯性效应不抑制也不促进孔洞的长大,对LY12CZ铝合金,临界应变率大约在1 740 s-1。(3)从惯性效应的角度,不但可以解释高应变率下断裂应变随应变率的增加而增大的现象,而且也能解释超高应变率条件下铝合金表现出的脆性特征。展开更多
Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionles...Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionless form is isomorphic with the Mises criterion for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations are established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates considering damage effect are obtained, and solved with the finite difference and iteration methods. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of orthotropic plates are discussed in detail.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 50978036)the Natural Science Foundation of Hunan Province of China (No. 09JJ6080)the Applied Basic Research Programs of Ministry of Transportation of China (No. 2009-319-825-100)
文摘Taking the strain tensor, the scalar damage variable, and the damage gradient as the state variables of the Helmholtz free energy, the general expressions of the firstorder gradient damage constitutive equations are derived directly from the basic law of irreversible thermodynamics with the constitutive functional expansion method at the natural state. When the damage variable is equal to zero, the expressions can be simplified to the linear elastic constitutive equations. When the damage gradient vanishes, the expressions can be simplified to the classical damage constitutive equations based on the strain equivalence hypothesis. A one-dimensional problem is presented to indicate that the damage field changes from the non-periodic solutions to the spatial periodic-like solutions with stress increment. The peak value region develops a localization band. The onset mechanism of strain localization is proposed. Damage localization emerges after damage occurs for a short time. The width of the localization band is proportional to the internal characteristic length.
文摘利用Abaqus提供的用户材料本构接口,将Gurson模型用UMAT(user defined material subroutine)和VUMAT(vectorized user defined material subroutine)分别实现。其中UMAT适用于Abaqus中的Standard计算模块,忽略惯性效应,而VUMAT适用于Abaqus中的Explicit计算模块,包含惯性效应。通过对二者的计算结果进行对比分析,考察惯性效应对孔洞长大的作用与影响。结果表明:(1)惯性效应对加载速率非常敏感,随着加载速率的提高,惯性效应先是抑制,继而促进孔洞的长大。(2)存在一个临界应变率,在临界应变率时,惯性效应不抑制也不促进孔洞的长大,对LY12CZ铝合金,临界应变率大约在1 740 s-1。(3)从惯性效应的角度,不但可以解释高应变率下断裂应变随应变率的增加而增大的现象,而且也能解释超高应变率条件下铝合金表现出的脆性特征。
基金Project supported by the National Natural Science Foundation of China (No.10572049)
文摘Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionless form is isomorphic with the Mises criterion for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations are established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates considering damage effect are obtained, and solved with the finite difference and iteration methods. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of orthotropic plates are discussed in detail.
