Elastoplastic damage analysis of shells with algebraic derivation of consistent tangent matrix and pseudo-stress

Development of the Galerkin Finite Element Method for Stress-Based Elasticity Problems

This paper proposes a finite element approach to the numerical solution of boundary value problems of linear elasticity theory formulated directly in terms of the stress tensor components. In contrast to the classical finite element formulation, in which displacements are the primary unknowns, the approach considered h...

Stress- and Strain-Based Boundary Value Problems of Elasticity

Boundary value problems in the theory of elasticity are traditionally formulated in terms of displacements, while stresses and strains are calculated from the displacements. Usually, the calculation of stresses and strains is accompanied by approximation errors. In this paper, alternative formulations of elasticity pro...

An augmented mixed finite element method for the Biot problem with nonlinear permeability

In two and three dimensions, we analyze a mixed formulation of the nonlinear Biot equations in terms of the poroelastic stress tensor, the displacement, the pressure, and the rotation tensor. To establish the well-posedness of the problem, we introduce suitable stabilization terms, leading to an augmented mixed formula...

IMPACT OF PRESSURE ON THE DEFORMATION OF BLATZ-KO CYLINDRICAL MATERIAL

This paper examines the finite deformation of hollow cylinders made from compressible Blatz-Ko hyperelastic material under internal, external, and combined pressure loading. It derives parametric closedform solutions for radial displacement and stress using the Cauchy stress tensor and equilibrium equations. Materials...

Elastoplastic inherent strain-based topology optimization for residual stress reduction in metal additive manufacturing

This paper proposes a topology optimization method for reducing the residual stress arising in the building process of metal additive manufacturing. First, a layer-by-layer process analysis model based on an elastoplastic inherent strain method is introduced. In this model, the incremental displacement is solved anew a...

Mechanics of Materials and Structures