A new fast method for solving contact plasticity and its application in analyzing elasto-plastic partial slip

This paper presents a new method of contact plasticity analysis, based on Galerkin vectors, to solve the stresses caused by eigenstrain or plastic strain. The plastic strain region below the contact surface is divided into a number of elementary cuboids, where the plastic strains are assumed to be constant in every cuboidal element. The influence coefficients, relating plastic strains to residual displacements or residual stresses, can be divided into four terms: one due to the plastic strains in the full space, and others due to the image plastic strains in the virtual half space. Each term can be solved quickly and efficiently by using the three-dimensional discrete convolution and fast Fourier transform or the three-dimensional combined discrete convolution and correlation and fast Fourier transform. This new method is used to analyze the contact plastic residual displacements and residual stresses for several contact cases to reveal its efficiency. Partial slip contact involving an elasto-plastic body is investigated. Results show that the stick–slip behavior is affected by the plastic strains, and the surface stresses exhibit more complex behavior than those from a pure elastic partial slip contact.

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► We develop a 3D-FFT based computational method for solving contact plasticity.
► Partial slip contact involving an elasto-plastic body is investigated.
► The stick–slip behavior is affected by the plastic flow.
► Yield maps are drawn for the contact of similar and dissimilar materials.