Owing to the absence of proper analytical solution of cantilever beams for couple stress/strain gradient elasto-plastic theory, experimental studies of the cantilever beam in the micro-scale are not suitable for the d...Owing to the absence of proper analytical solution of cantilever beams for couple stress/strain gradient elasto-plastic theory, experimental studies of the cantilever beam in the micro-scale are not suitable for the determination of material length-scale. Based on the couple stress elasto-plasticity, an analytical solution of thin cantilever beams is firstly presented, and the solution can be regarded as an extension of the elastic and rigid-plastic solutions of pure bending beam. A comparison with numerical results shows that the current analytical solution is reliable for the case of σ0 〈〈 H 〈〈 E, where σ0 is the initial yield strength, H is the hardening modulus and E is the elastic modulus. Fortunately, the above mentioned condition can be satisfied for many metal materials, and thus the solution can be used to determine the material length-scale of micro-structures in conjunction with the experiment of cantilever beams in the micro-scale.展开更多
The phase field method for fracture integrates the Griffith theory and damage mechanics approach to predict crack initiation and propagation within one framework.It replaced the discrete representation of crack by dif...The phase field method for fracture integrates the Griffith theory and damage mechanics approach to predict crack initiation and propagation within one framework.It replaced the discrete representation of crack by diffusive damage and solved it based on a minimization of the global energy storage functional.As a result,no crack tracking topology is needed,and complex crack shapes can be captures without user intervention.However,it is also reported to have an inconsistency between the predicted fracture toughness and the material strength.Recently,a novel energetic degradation function was proposed in literature to handle this issue.This research does some further modifications to the global energy storage functional so that Newton's method can be directly used to solve the energy minimization.With the new energy form,direct implementation of the length-scale independent phase field method into finite element packages like LS-DYNA becomes possible.This paper presents the framework and details of implementing the length-scale independent phase field method into LS-DYNA through a user-defined element and material subroutine.Several numerical examples are presented to compare with the experiment crack shape.Most importantly,this paper is one of the first ones to quantitatively predict accurate force response compared to experiments.These examples verify the accuracy of the new energy form and implementation.展开更多
This study uses iso-geometric investigation,which is based on the non-uniform rational B-splines(NURBS)basis function,to investigate natural oscillation of bi-directional functionally graded porous(BFGP)doublycurved s...This study uses iso-geometric investigation,which is based on the non-uniform rational B-splines(NURBS)basis function,to investigate natural oscillation of bi-directional functionally graded porous(BFGP)doublycurved shallow microshells placed on Pasternak foundations with any boundary conditions.The characteristics of the present material vary in both thickness and axial directions along the x-axis.To be more specific,a material length-scale coefficient of the microshell varies in both thickness and length directions as the material's mechanical properties.One is able to develop a differential equation system with varying coefficients that regulate the motion of BFGP double-curved shallow microshells by using Hamilton principle,Kirchhoff-Love hypothesis,and modified couple stress theory.The numerical findings are reported for thin microshells that are spherical,cylindrical,and hyperbolic paraboloidal,with a variety of planforms,including rectangles and circles.The validity and effectiveness of the established model are shown by comparing the numerical results given by the proposed formulations with previously published findings in many specific circumstances.In addition,influences of length scale parameters,power-law indexes,thickness-to-side ratio,and radius ratio on natural oscillation responses of BFGP microshells are investigated in detail.展开更多
基金the National Natural Science Foundation of China (50479058, 10672032)
文摘Owing to the absence of proper analytical solution of cantilever beams for couple stress/strain gradient elasto-plastic theory, experimental studies of the cantilever beam in the micro-scale are not suitable for the determination of material length-scale. Based on the couple stress elasto-plasticity, an analytical solution of thin cantilever beams is firstly presented, and the solution can be regarded as an extension of the elastic and rigid-plastic solutions of pure bending beam. A comparison with numerical results shows that the current analytical solution is reliable for the case of σ0 〈〈 H 〈〈 E, where σ0 is the initial yield strength, H is the hardening modulus and E is the elastic modulus. Fortunately, the above mentioned condition can be satisfied for many metal materials, and thus the solution can be used to determine the material length-scale of micro-structures in conjunction with the experiment of cantilever beams in the micro-scale.
文摘The phase field method for fracture integrates the Griffith theory and damage mechanics approach to predict crack initiation and propagation within one framework.It replaced the discrete representation of crack by diffusive damage and solved it based on a minimization of the global energy storage functional.As a result,no crack tracking topology is needed,and complex crack shapes can be captures without user intervention.However,it is also reported to have an inconsistency between the predicted fracture toughness and the material strength.Recently,a novel energetic degradation function was proposed in literature to handle this issue.This research does some further modifications to the global energy storage functional so that Newton's method can be directly used to solve the energy minimization.With the new energy form,direct implementation of the length-scale independent phase field method into finite element packages like LS-DYNA becomes possible.This paper presents the framework and details of implementing the length-scale independent phase field method into LS-DYNA through a user-defined element and material subroutine.Several numerical examples are presented to compare with the experiment crack shape.Most importantly,this paper is one of the first ones to quantitatively predict accurate force response compared to experiments.These examples verify the accuracy of the new energy form and implementation.
文摘This study uses iso-geometric investigation,which is based on the non-uniform rational B-splines(NURBS)basis function,to investigate natural oscillation of bi-directional functionally graded porous(BFGP)doublycurved shallow microshells placed on Pasternak foundations with any boundary conditions.The characteristics of the present material vary in both thickness and axial directions along the x-axis.To be more specific,a material length-scale coefficient of the microshell varies in both thickness and length directions as the material's mechanical properties.One is able to develop a differential equation system with varying coefficients that regulate the motion of BFGP double-curved shallow microshells by using Hamilton principle,Kirchhoff-Love hypothesis,and modified couple stress theory.The numerical findings are reported for thin microshells that are spherical,cylindrical,and hyperbolic paraboloidal,with a variety of planforms,including rectangles and circles.The validity and effectiveness of the established model are shown by comparing the numerical results given by the proposed formulations with previously published findings in many specific circumstances.In addition,influences of length scale parameters,power-law indexes,thickness-to-side ratio,and radius ratio on natural oscillation responses of BFGP microshells are investigated in detail.
