Applications of tensor functions to the formulation of yield criteria for anisotropic materials
type: Item
instance of: scholarly article
title: Applications of tensor functions to the formulation of yield criteria for anisotropic materials
zbMATH Open document ID: 0629.73021
DOI: 10.1016/0749-6419(88)90003-4
author: Josef Betten
published in: International Journal of Plasticity
publication date: 1988-01-01T00:00:00Z
review text: Yielding of anisotropic materials can be characterized by yield criteria which are scalar-valued functions of the stress tensor and of material tensors, for instance, of rank two or four, characterizing the anisotropic properties of the material. Because of the requirement of invariance, a yield criterion can be expressed as a single-valued function of the integrity basis. In finding an integrity basis involving the stress tensor and material tensors, the constitutive equations are first formulated based on the tensor function theory. Since the plastic work characterizes the yield process, we read from this scalar expression the essential invariants to formulate a yield criterion. Some examples for practical use are discussed in detail.
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 53A45
zbMATH DE Number: 4024880
zbMATH Keywords: system of invariants
zbMATH Keywords: coefficients of characteristic polynomial for fourth-order tensor
zbMATH Keywords: eigenvalue problem
zbMATH Keywords: Lagrange multiplier method
zbMATH Keywords: yield criteria
zbMATH Keywords: scalar-valued functions
zbMATH Keywords: stress tensor
zbMATH Keywords: material tensors
zbMATH Keywords: rank two
zbMATH Keywords: anisotropic properties
zbMATH Keywords: single-valued function
zbMATH Keywords: integrity basis
MaRDI profile type: Publication
full work available at URL: 0749-6419(88)90003-4
OpenAlex ID: W2048529690
description: scientific article; zbMATH DE number 4024880