ENRICHED GOAL-ORIENTED ERROR ESTIMATION APPLIED TO FRACTURE MECHANICS PROBLEMS SOLVED BY XFEM

Based on the concept of constitutive relation error along with the residual of both origin and dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed in this paper. It leads to high quality local error bounds in the problem of fracture mechanics simulation with extended finite element method （XFEM）, which involves enrichment to solve a stress singularity in the crack. Since goal-oriented error estimation with enriched degrees of freedom gives us a chance to evaluate the XFEM simulation, the stress intensity factor calculated by two kinds of XFEM programs developed by ourselves and by commercial code ABAQUS are compared in this work. By comparing the reliability of the stress intensity factor calculation, the accuracy of two programs in different cases is evaluated and the source of error is discussed. A 2-dimensional XFEM example is given to illustrate the computational procedure.

Morphological stability analysis of vesicles with mechanical-electrical coupling effects

Using a recently established liquid crystal model for vesicles, we present a theoretical method to analyze the morphological stability of liquid crystal vesicles in an electric field. The coupled mechanical-electrical effects associated with elastic bending, osmotic pressure, surface tension, Max- well pressure, as well as flexoelectric and dielectric proper- ties of the membrane are taken into account. The first and second variations of the free energy are derived in a com- pact form by virtue of the surface variational principle. The former leads to the shape equation of a vesicle embedded in an electric field, and the latter allows us to examine the stabil- ity of a given vesicle morphology. As an illustrative exam- ple, we analyze the stability of a spherical vesicle under a uniform electric field. This study is helpful for understanding and revealing the morphological evolution mechanisms of vesicles in electric fields and some associated phenomena of cells.

辐照缺陷装饰位错是否会导致硬化?

纳米尺寸的辐照缺陷常常会在位错线附近聚集,形成装饰效应.研究者通常采用级联诱导源硬化模型描述装饰效应引起的辐照硬化.本研究工作发现不可动辐照缺陷装饰位错会导致辐照硬化,硬化程度与理论模型预测一致.然而,当装饰辐照缺陷可动时,则不发生辐照硬化,甚至发生软化,这种硬化消失是由于位错环始终处于与位错线相互作用力近似为零的区域,并与位错线发生关联运动.该工作带来了对辐照缺陷装饰效应和辐照硬化的新理解.

A hierarchical dislocation-grain boundary interaction model based on 3D discrete dislocation dynamics and molecular dynamics

We develop a new hierarchical dislocation-grain boundary (GB) interaction model to predict the mechanical behavior of polycrystalline metals at micro and submicro scales by coupling 3D Discrete Dislocation Dynamics (DDD) simulation with the Molecular Dynamics (MD) simulation.At the microscales,the DDD simulations are responsible for capturing the evolution of dislocation structures;at the nanoscales,the MD simulations are responsible for obtaining the GB energy and ISF energy which are then transferred hierarchically to the DDD level.In the present model,four kinds of dislocation-GB interactions,i.e.transmission,absorption,re-emission and reflection,are all considered.By this methodology,the compression of a Cu micro-sized bi-crystal pillar is studied.We investigate the characteristic mechanical behavior of the bi-crystal compared with that of the single-crystal.Moreover,the comparison between the present penetrable model of GB and the conventional impenetrable model also shows the accuracy and efficiency of the present model.

XFEM modeling of hydraulic fracture in porous rocks with natural fractures

Hydraulic fracture(HF) in porous rocks is a complex multi-physics coupling process which involves fluid flow, diffusion and solid deformation. In this paper, the extended finite element method(XFEM) coupling with Biot theory is developed to study the HF in permeable rocks with natural fractures(NFs). In the recent XFEM based computational HF models, the fluid flow in fractures and interstitials of the porous media are mostly solved separately, which brings difficulties in dealing with complex fracture morphology. In our new model the fluid flow is solved in a unified framework by considering the fractures as a kind of special porous media and introducing Poiseuille-type flow inside them instead of Darcy-type flow. The most advantage is that it is very convenient to deal with fluid flow inside the complex fracture network, which is important in shale gas extraction. The weak formulation for the new coupled model is derived based on virtual work principle, which includes the XFEM formulation for multiple fractures and fractures intersection in porous media and finite element formulation for the unified fluid flow. Then the plane strain Kristianovic-Geertsma-de Klerk(KGD) model and the fluid flow inside the fracture network are simulated to validate the accuracy and applicability of this method. The numerical results show that large injection rate, low rock permeability and isotropic in-situ stresses tend to lead to a more uniform and productive fracture network.

On determination of the damping factor of linear viscoelastic materials using dynamic indentation:a theoretical study

In this study,we theoretically investigate the dynamic indentation for measuring the loss (damping) factor of a linear viscoelastic material from its indentation response.A rigid indenter with arbitrary tip profile is assumed to indent into a viscoelastic substrate with arbitrary shape.We perform a theoretical analysis and identify the conditions under which the loss factor of the material can be determined from the phase angle between the applied harmonic indentation load and the corresponding harmonic displacement,a directly measurable quantity in a dynamic indentation test.To validate the conclusion drawn from our theoretical analysis,a series of numerical experiments are performed,including the spherical indentation of a soft layer with irregular surface morphology bonded to a rigid substrate,a conical indenter with tip defects indenting into a half-spherical particle,and the indentation of porous materials.This study may facilitate the use of the dynamic indentation technique to evaluate the damping properties of linear viscoelastic materials,including some advanced polymers and biological soft tissues.

Damage evaluation of reinforced concrete frame based on a combined fiber beam model

In order to analyze and simulate the impact collapse or seismic response of the reinforced concrete(RC)structures,a combined fiber beam model is proposed by dividing the cross section of RC beam into concrete fiber and steel fiber.The stress-strain relationship of concrete fiber is based on a model proposed by concrete codes for concrete structures.The stress-strain behavior of steel fiber is based on a model suggested by others.These constitutive models are implemented into a general finite element program ABAQUS through the user defined subroutines to provide effective computational tools for the inelastic analysis of RC frame structures.The fiber model proposed in this paper is validated by comparing with experiment data of the RC column under cyclical lateral loading.The damage evolution of a three-dimension frame subjected to impact loading is also investigated.

Fundamental problem in optimizing the biaxial testing specimen

Most of the elements in structural design are subjected to the complex loading conditions that need to be predicted in advance for a reliable design. The failure prediction of these structural elements is based on the failure theories that employ the experimental data of the uniaxial, the biaxial and the shear tests. Among these tests, the biaxial testing is used to model the behavior of the structure loaded in more than one direction. In this study, we discover an interesting fact for the biaxial tension specimen that the thickness reduction of the measuring region cannot increase the stress to a high level. This behavior of the biaxial testing is different from the uniaxial testing where the thickness reduction of the measuring region always increases its stress to a higher level. Therefore, we further investigate the biaxial testing specimen via related fundamental problem, i.e., an axisymmetric plate with varying thickness under axisymmetric tension. We perform the shape optimization based on our analytical solution and the FEM results. For an infinite axisymmetric disk, the optimized design should include a low slope diverging section connecting the inner to outer region. On the contrary, the larger inner measuring region for finite axisymmetric disk would result in higher corresponding stress. These conclusions can be used as a guideline for the design of a biaxial testing specimen.

软材料薄层-刚性基底系统在椭圆柱压痕中的表面效应

表面效应对软材料(如水凝胶和生物组织)的力学性能有重要影响.本文研究了软材料薄层-刚性基底系统在椭圆柱压头下的平面应变压痕问题,理论分析了表面效应对压痕过程的影响,考虑了不同椭圆轴比参数下的压痕行为的差异.采用具有表面张力影响的弹性层的Kerr模型,获得了压痕响应中力和位移的解析表达式,并通过有限元模拟验证了理论解.基于该理论解,分析了椭圆压头横截面的长轴与短轴之比对表面效应的影响规律.研究结果不仅有助于理解尺寸效应对软材料压痕行为的影响,而且对相关的力学性能测试具有指导价值.

A Crystal Plasticity Model with Irradiation Effect for the Mechanical Behavior of FCC Metals

In this paper,a crystal plasticity model considering the irradiation effect based on the thermal activation theory is established.The evolutions of screw dislocations,edge dislocations,and stacking fault tetrahedrals(SFTs)(induced by irradiation)are included into the model.The interactions between dislocations and irradiation-induced SFTs are also considered.The constitutive model is numerically implemented on the ABAQUS platform through UMAT subroutine and applied to study the irradiation effect on the mechanical behavior of pure copper.The mechanical properties of single and polycrystalline copper are studied,and the simulation results show that the constitutive model can properly predict the mechanical behavior of irradiated pure copper.Especially for polycrystalline copper,the simulation results are in good agreement with the experimental data.