Exponential stability for a plate equation with p‐Laplacian and memory terms

This paper is concerned with the energy decay for a class of plate equations with memory and lower order perturbation of p‐Laplacian type, with simply supported boundary condition, where Ω is a bounded domain of , g > 0 is a memory kernel that decays exponentially and f(u) is a nonlinear perturbation. This kind of problem without the memory term models elastoplastic flows. Copyright © 2012 John Wiley & Sons, Ltd.     

各向异性介质中周期性界面裂纹的弹塑性问题

应用富里叶积分变换方法将裂纹边值问题化为对偶积分方程组,再用定积分变换法将问题进一步化为奇异积分方程组,求得了双材料各向异性弹塑性介质中周期性界面裂纹反平面问题的封闭形式解,并作为特例讨论了各向同性双材料问题、各向异性单一材料问题及各向同性—各向异性双材料问题.结果表明:裂纹尖端前沿的塑性区尺寸、裂纹的张开位移(COD)均决定于两种材料流动极限中的较小者及裂纹的长度和相邻两裂纹的间距,此外,COD还与材料模量有关.     

弹塑性变形油藏中多相渗流的数值模拟

基于流固耦合力学理论,建立了弹性变形油藏中多相渗流的数学模型,该模型考虑了渗流与变形的耦合作用,以及注采交变载荷作下油藏多孔介质的弹性变形特征,给出了耦合数值模拟方法和算例。     

三维脆弹塑性断裂损伤模型在裂隙岩体工程中的应用

根据Ｂｅｔｔｉ能量互易定理,修正自洽法理论和节理裂隙断裂扩展过程中的能量转换与能量耗散建立了岩体的能量损伤演化方程,在此基础上通过有效应力体现损伤与塑变殂的耦合效应。     

多相固体弹塑性本构方程的同类性

本文以复合材料为背景,讨论多相固体即混合物的等效弹塑性本构方程.按照所提出的等效本构方程的定义,文章证明,由服从广义正交法则的多种均匀的弹塑性介质组成的混合物具有与它的组分介质同类的、也服从广义正交法则的等效本构方程.     

An effective boundary method for the analysis of elastoplastic problems

In this paper, a series of effective formulae of the boundary element method is presented. In these formulae, by using a new variable two kernels are only of the weaker singularity of Lnr (where r is the distance between a source point and a field point). Hence, the singularities in the conventional displacement formulation and stress formulation at internal points are reduced respectively so that the "boundary-layer" effect which strongly degenerates the accuracy of stress calculation by using original formulae is eliminated. Also the direct evaluation of coefficients C (boundary tensor), which are difficult to calculate, is avoided. This method is used in elastoplastic analysis. The results of the numerical investigation demonstrate the potential advantages of this method.     

一种有效的分析弹塑性问题的边界元法

本文提出了一组有效的边界元公式.该公式通过利用一个新的变量,使核函数仅具有lnr(r为源点和场点的距离)的较低阶奇异性,从而,在积分点的传统位移和应力公式的奇异性得到降低,且原公式中影响应力计算精度的边界层效应得到消除.同时,也避免了难于计算的参数C.将该方法应用到弹塑性分析中,数值分析结果表明该公式具有明显的优势.     

Numerical Simulation of Hydraulic Fractures Intersecting Natural Fractures in Shale With Plastic Deformation北大核心CSCD

The plastic deformation and numerous natural joints of shale pose a great challenge for the predic⁃ tion of the hydraulic fracture geometry extension. Based on the finite element method, a fully coupled numeri⁃ cal model for elastoplastic hydraulic fractures was established with natural fractures and bedding planes consid⁃ ered. The numerical model was validated with the KGD analytical solution and Blanton’s curve. The numerical results show that, compared with the numerical model solution of linear elasticity, the hydraulic fractures are prone to enter the natural weak interface due to the rock plastic deformation. The rock plastic deformation area mainly lies in the reservoir layer during the fracture propagation. In the case of rock ductile damage, the hy⁃ draulic fracture is more likely to penetrate the bedding plane. Hydraulic fractures can directly penetrate natural fractures and bedding planes at high injection rates due to large driving forces. The study provides new insights in terms of hydraulic fracture extension in elastoplastic formations. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.