Skip to Main content Skip to Navigation
Journal articles

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Abstract : The construction of regularization operators presented in this work is based on the introduction of strain or damage micromorphic degrees of freedom in addition to the displacement vector and of their gradients into the Helmholtz free energy function of the constitutive material model. The combination of a new balance equation for generalized stresses and of the micromorphic constitutive equations generates the regularization operator. Within the small strain framework, the choice of a quadratic potential w.r.t. the gradient term provides the widely used Helmholtz operator whose regularization properties are well known: smoothing of discontinuities at interfaces and boundary layers in hardening materials, and finite width localization bands in softening materials. The objective is to review and propose nonlinear extensions of micromorphic and strain/damage gradient models along two lines: the first one introducing nonlinear relations between generalized stresses and strains; the second one envisaging several classes of finite deformation model formulations. The generic approach is applicable to a large class of elastoviscoplastic and damage models including anisothermal and multiphysics coupling. Two standard procedures of extension of classical constitutive laws to large strains are combined with the micromorphic approach: additive split of some Lagrangian strain measure or choice of a local objective rotating frame. Three distinct operators are finally derived using the multiplicative decomposition of the deformation gradient. A new feature is that a free energy function depending solely on variables defined in the intermediate isoclinic configuration leads to the existence of additional kinematic hardening induced by the gradient of a scalar micromorphic variable.
Complete list of metadata

https://hal-mines-paristech.archives-ouvertes.fr/hal-01337863
Contributor : Bibliothèque Umr7633 <>
Submitted on : Monday, June 27, 2016 - 3:38:04 PM
Last modification on : Wednesday, October 14, 2020 - 4:01:35 AM

Links full text

Identifiers

Citation

Samuel Forest. Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2016, 472 (2188), 20150755, 27 p. ⟨10.1098/rspa.2015.0755⟩. ⟨hal-01337863⟩

Share

Metrics

Record views

357