Many rubber-toughened epoxies are thought to derive the bulk of their toughness through the processes of rubber cavitation and plastic shear-yielding in the epoxy matrix. Constraint relief has been considered to be a key mechanism which allows extra plastic shear deformation to occur. The present work attempts to provide direct experimental evidence of the constraint relief effect by combining testing geometries that vary the degree of constraint with microscopic observations. The results show that the success of a rubber as a toughening agent for epoxies is closely related to its ability to cavitate. Evidence for local constraint relief is presented. Upon cavitation of the rubber, the stress state in a specimen with initial constraint is found to change to a plane stress state. The constraint relief circumvents or delays the crack initiation in the matrix, which allows more plastic deformation to occur.
In this paper, the improved complex variable moving least-squares (ICVMLS) approximation is presented. The ICVMLS approximation has an explicit physics meaning. Compared with the complex variable moving least-squares (CVMLS) approximations presented by Cheng and Ren, the ICVMLS approximation has a great computational precision and efficiency. Based on the element-free Galerkin (EFG) method and the ICVMLS approximation, the improved complex variable element-free Galerkin (ICVEFG) method is presented for two-dimensional elasticity problems, and the corresponding formulae are obtained. Compared with the conventional EFG method, the ICVEFG method has a great computational accuracy and efficiency. For the purpose of demonstration, three selected numerical examples are solved using the ICVEFG method.
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