TY - JOUR

T1 - Variational regularization of damage models based on the emulated RVE

AU - Schwarz, S.

AU - Junker, Philipp

AU - Hackl, K.

PY - 2021/1

Y1 - 2021/1

N2 - Material models exhibiting softening effects due to damage or localization share the problem of leading to ill-posed boundary value problems that lead to physically meaningless, mesh-dependent finite element results. It is thus necessary to apply regularization techniques that couple local behavior, described, e.g., by internal variables, at a spatial level. The common way to do this is to take into account higher gradients of the field variables, thus introducing an internal length scale. In this paper, we suggest a different approach to regularization that does not make use of any nonlocal enhancement like the inclusion of higher gradients or integration over local sub-domains nor of any classical viscous effects. Instead we perform an appropriate relaxation of the (condensed) free energy in a time-incremental setting which leads to a modified energy that is coercive and satisfies quasiconvexity in an approximate way. Thus, in every time increment a regular boundary value problem is solved. The proposed approach holds the same advantage as other methods, but with less numerical effort. We start with the theoretical derivation, discuss a rate-independent version of the proposed model and present details of the numerical treatment. Finally, we give finite element results that demonstrate the efficiency of this new approach.

AB - Material models exhibiting softening effects due to damage or localization share the problem of leading to ill-posed boundary value problems that lead to physically meaningless, mesh-dependent finite element results. It is thus necessary to apply regularization techniques that couple local behavior, described, e.g., by internal variables, at a spatial level. The common way to do this is to take into account higher gradients of the field variables, thus introducing an internal length scale. In this paper, we suggest a different approach to regularization that does not make use of any nonlocal enhancement like the inclusion of higher gradients or integration over local sub-domains nor of any classical viscous effects. Instead we perform an appropriate relaxation of the (condensed) free energy in a time-incremental setting which leads to a modified energy that is coercive and satisfies quasiconvexity in an approximate way. Thus, in every time increment a regular boundary value problem is solved. The proposed approach holds the same advantage as other methods, but with less numerical effort. We start with the theoretical derivation, discuss a rate-independent version of the proposed model and present details of the numerical treatment. Finally, we give finite element results that demonstrate the efficiency of this new approach.

KW - Damage

KW - Quasiconvex envelope

KW - Relaxation

KW - Variational methods

UR - http://www.scopus.com/inward/record.url?scp=85085307520&partnerID=8YFLogxK

U2 - 10.1007/s00161-020-00886-0

DO - 10.1007/s00161-020-00886-0

M3 - Article

VL - 33

SP - 69

EP - 95

JO - Continuum Mechanics and Thermodynamics

JF - Continuum Mechanics and Thermodynamics

SN - 0935-1175

IS - 1

ER -