Analytical stress solutions of a closed deformation path with stretching and shearing using the hypoelastic formulations

DOI10.1016/S0997-7538(03)00031-7zbMath1032.74516MaRDI QIDQ1418717

D. Massart

Publication date: 14 January 2004

Published in: European Journal of Mechanics. A. Solids (Search for Journal in Brave)

zbMATH Keywords

rateCorotational coordinate frameHypoelasticityObjective stressSpin tensor

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics (74G10)

Related Items

Modeling of finite strain viscoplasticity based on the logarithmic corotational description ⋮ On the consequences of the adoption of the Zaremba-Jaumann objective stress rate in FEM codes ⋮ Logarithmic rate implementation in constitutive relations of finite elastoplasticity with kinematic hardening ⋮ Large deformation plasticity. From basic relations to finite deformation ⋮ Finite-amplitude shear wave in pre-stressed thin elastomers ⋮ The Prandtl‐Reuss equations revisited ⋮ Objective stress rates, path-dependence properties and non-integrability problems ⋮ Finite element study of the energy dissipation and residual stresses in the closed elastic deformation path ⋮ Is an additive decomposition of a rate of deformation and objective stress rates passé?

Cites Work

• Unnamed Item
• Unnamed Item
• Remarks on rate constitutive equations for finite deformation problems: Computational implications
• On the analysis of rotation and stress rate in deforming bodies
• Hypo-elasticity and elasticity
• A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations
• On objective corotational rates and their defining spin tensors
• Strain rates and material spins
• Hypo-elasticity model based upon the logarithmic stress rate
• Logarithmic strain, logarithmic spin and logarithmic rate
• Existence and uniqueness of the exactly integrable hypoelastic equation \(\overset\circ\tau^*=\lambda(\text{tr }D)I+2\mu \)D and its significance to finite inelasticity
• Numerical integration of rate constitutive equations in finite deformation analysis
• Eulerian strain-rate as a rate of logarithmic strain
• Studies of finite element procedures—Stress solution of a closed elastic strain path with stretching and shearing using the updated Lagrangian Jaumann formulation
• Numerical study of consistency of rate constitutive equations with elasticity at finite deformation
• Formulation of implicit finite element methods for multiplicative finite deformation plasticity
• [https://portal.mardi4nfdi.de/wiki/Publication:5652282 Einige Bemerkungen zu einer allgemeinen Klasse von Stoffgesetzen f�r gro�e elasto-plastische Form�nderungen]