Comparison of evolving gradient damage formulations with different activity functions

Adam Wosatko

doi:10.1007/s00419-021-01889-2

Abstract

In the paper, two existing upgrades of the gradient damage model for the simulations of cracking in concrete are compared. The damage theory is made nonlocal via a gradient enhancement to overcome the mesh dependence of simulation results. The implicit gradient model with an averaging equation, where the internal length parameter is assumed as constant during the strain softening analysis, gives unrealistically broadened damage zones. The gradient enhancement of the scalar damage model can be improved via a function of an internal length scale, so an evolution of the gradient activity is postulated during the localization process. Two different modifications of the averaging equation and respective evolving gradient damage formulations are presented. Different activity functions are tested to see whether the formation of a too wide damage zone still occurs. Activating or localizing character of the gradient influence can be introduced and the impact of both approaches on the numerical results is shown in the paper. The aforementioned variants are implemented and examined using the benchmarks of tension in a bar and bending of a cantilever beam.

Highlights

In the paper, continuum damage mechanics [24] is employed to simulate cracking in concrete
A portion of the results is made for the SVS gradient damage (SVSGD) model, but the PS gradient damage (PSGD) model, where function φ1( ̃) is used, is presented here for one case
The computations are performed mainly using function φ2(ω) and the PS gradient damage (PSGD) model, but other available options are taken into account in order to show the outcome of employment of different functions and models

Summary

Introduction

Continuum damage mechanics [24] is employed to simulate cracking in concrete. The application of the model in a local version leads to material softening. It has been known for years, see, for example, [7], that ill-posedness of the boundary value problem (BVP) and spuriously mesh-sensitive results occur for local models. Concrete cracking is simulated as strain localization by means of the narrowest band of finite elements allowed for the discretization, so a suitable localization limiter is needed, cf [9]. A gradient operator [2,11,18,30] can be employed in order to ensure objectivity in numerical modelling of localization phenomena

Results

Discussion

Conclusion