Analysis of stability and bifurcation in nonlinear mechanics with dissipation
type: Item
instance of: scholarly article
title: Analysis of stability and bifurcation in nonlinear mechanics with dissipation
zbMATH Open document ID: 1229.74068
author: C. Stolz
published in: Entropy
publication date: 2012-01-09T00:00:00Z
review text: Summary: The analysis of stability and bifurcation is studied in nonlinear mechanics with dissipative mechanisms: plasticity, damage, fracture. The description is based on introduction of a set of internal variables. This framework allows a systematic description of the material behaviour via two potentials: the free energy and the potential of dissipation. In the framework of standard generalized materials the internal state evolution is governed by a variational inequality which depends on the mechanism of dissipation. This inequality is obtained through energetic considerations in an unified description based upon energy and driving forces associated to the dissipative process. This formulation provides criterion for existence and uniqueness of the system evolution. Examples are presented for plasticity, fracture and for damaged materials.
Mathematics Subject Classification ID: 74H60
Mathematics Subject Classification ID: 37K05
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 74C15
Mathematics Subject Classification ID: 74R10
zbMATH DE Number: 5995931
zbMATH Keywords: stability
zbMATH Keywords: bifurcation
zbMATH Keywords: plasticity
zbMATH Keywords: damage
zbMATH Keywords: fracture
zbMATH Keywords: normality law
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/e13020332
OpenAlex ID: W1979303974
cites work: Q4859467
cites work: A general theory of uniqueness and stability in elastic-plastic solids
cites work: Q5752092
cites work: Mechanical transformations and discontinuities along a moving surface
cites work: Stress-strain relations, uniqueness and variational theorems for elastic-plastic materials with a singular yield surface
cites work: Bifurcation and post-bifurcation analysis in plasticity and brittle fracture
cites work: Continuum Thermodynamics
cites work: Q4019747
cites work: On constitutive inequalities and bifurcation in elastic-plastic solids with a yield-surface vertex
cites work: Elastic-plastic post-buckling from a heterogeneous state
cites work: On the bifurcation and postbifurcation analysis of elastic-plastic solids under general prebifurcation conditions
cites work: On crack propagation in an elastoplastic material: primal and dual approaches to the boundary value problem
cites work: Dual approach in fracture mechanics
cites work: Dual approach in non-linear fracture mechanics
cites work: In-plane perturbation of a system of two coplanar slit-cracks. I: Case of arbitrarily spaced crack fronts
cites work: The nature of configurational forces
cites work: Energy-momentum tensors in elastostatics: Some reflections on the general theory
cites work: On the driving traction acting on a surface of strain discontinuity in a continuum
cites work: Bifurcation of equilibrium solutions and defect nucleation
cites work: Discontinuous equilibrium solutions and cavitation in nonlinear elasticity
DOI: 10.3390/E13020332
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description: scientific article; zbMATH DE number 5995931