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Ductile void growing in micromorphic GLPD porous plastic solids containing two populations of cavities with different sizes

Roy Burson and Koffi Enakoutsa

Vol. 10 (2022), No. 4, 395–412

Gologanu, Leblond, Perrin, and Devaux (GLPD) developed a constitutive model for ductile fracture for porous metals based on generalized continuum mechanics assumptions. The model predicted with high accuracy ductile fracture process in porous metals subjected to several complex loads. The GLDP model performances over its competitors has attracted the attention of several authors who explored additional capabilities of the model. This paper provides analytical solutions for the problem of a porous hollow sphere subjected to hydrostatic loadings, the matrix of the hollow sphere obeying the GLPD model. The exact solution for the expressions of the stress and the generalized stress the GLPD model involved are illustrated for the case where the matrix material does not contain any voids. The results show that the singularities obtained in the stress distribution with the local Gurson model are smoothed out, as expected with any generalized continuum model. The paper also presents some elements of the analytical solution for the case where the matrix is porous and obeys the full GLPD model at the initial time when the porosity is fixed. The later analytical solution can serve to predict the mechanisms of ductile fracture in porous ductile solids with two populations of cavities with different sizes.

gradient model, analytical solution, plasticity, hollow sphere problem, fracture
Mathematical Subject Classification
Primary: 74A45, 74C05
Received: 20 May 2022
Revised: 11 September 2022
Accepted: 7 November 2022
Published: 30 April 2023

Communicated by Francesco dell'Isola
Roy Burson
Department of Mathematics
California State University
Northridge, CA
United States
Koffi Enakoutsa
Department of Mathematics
California State University
Northridge, CA
United States
Department of Mathematics
University of California Los Angeles
Los Angeles, CA
United States