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中文摘要：
对于密实砂土峰值后应变软化特性引起的材料强非线性问题,利用常规有限元所采用的隐式算法很难求解,而动态松弛法在求解这类非线性问题方面却具有独特的优势。针对砂土应变软化强非线性问题,将动态松弛法与有限单元法相结合,提出了一种新的动态松弛有限元法。该方法根据动态松弛法的显式特性,由中心差分法导出了动态松弛有限元法的基本控制方程,并实现了对应力-应变空间中整个平衡路径的追踪。将动态松弛法嵌入到非线性有限元程序中,即可对砂土材料应变软化引起的强非线性问题进行有限元数值计算。该有限元程序中,应力更新采用回归映射算法。最后通过对砂土平面应变压缩试验进行有限元模拟,验证了动态松弛有限元法在求解材料强非线性问题方面的优越性。
英文摘要：
In the presence of the strong material nonlinearity caused by post-peak strain softening of dense sandy soils,the solution of traditional finite element method（FEM） with implicit algorithm often becomes intractable.The dynamic relaxation（DR） method has a great reputation in solving highly nonlinear equations.A new dynamic relaxation-finite element method（DR-FEM） for strong nonlinearity caused by post-peak strain softening of sands is proposed,which takes into account the advantages of DR and FEM together.According to the explicit nature of DR and the central difference technique,the general governing equations of DR-FEM has been derived.The way of tracing the whole equilibrium curve in the stress-strain space has also been presented;and then the DR method is implemented into a general nonlinear finite element codes.The return mapping algorithm is used for stress updating,which is a first-order approximated Euler backward integration.Therefore,the strong material nonlinearity caused by post-peak strain softening of sandy soils can be simulated by the proposed DR-FEM combined with the corresponding material model.The DR-FEM is validated by simulating the result of physical plane strain compression test performed on sands.It is shown that the DR method has a superiority to solve the material nonlinearity.
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