Selected Concrete Models Studied Using Willam’s Test

Abstract

Willam’s test is a quick numerical benchmark in tension–shear regime, which can be used to verify inelastic (quasi-brittle) material models at the point level. Its sequence consists of two separate steps: uniaxial tension accompanied with contraction—until the tensile strength is attained; and next for softening (cracking) of the material—tension in two directions together with shear. A rotation of axes of principal strains and principal stresses is provoked in the second stage. That kind of process occurs during the analysis of real concrete structures, so a correct response of the material model at the point level is needed. Some familiar concrete models are selected to perform Willam’s test in the paper: concrete damaged plasticity and concrete smeared cracking—distributed in the commercial ABAQUS software, scalar damage with coupling to plasticity and isotropic damage—both implemented in the FEAP package. After a brief review of the theory, computations for each model are discussed. Passing or failing Willam’s test by the above models is concluded based on their results, indicating restrictions of their use for finite element computations of concrete structures with predominant mixed-mode fracture.

Numerically Efficient Three-Dimensional Model for Non-Linear Finite Element Analysis of Reinforced Concrete Structures

“…In order to assess different concepts of including the cracking phenomenon into FE models, the Willam’s test was proposed [ 61 ]. The results of this test for material models available in the Diana code can be found in Reference [ 47 ], whereas comprehensive study on among others models available in the Abaqus code is summarised in Reference [ 62 ]. The test consists of two phases: phase 1—uniaxial tension up to the crack formation, components of the strain increments vector in the Cartesian coordinate system have the following ratio: ; phase 2—biaxial tension and shear, components of the strain increments vector in the Cartesian coordinate system have the following ratio: .…”

A Numerical Study on 3D Printed Cementitious Composites Mixes Subjected to Axial Compression

“…The yield function is defined primarily in terms of the von mises equivalent stress, the hydrostatic pressure stress, and the maximum principal effective stress amidst other dimensionless ratios. More details can be found here [52][53][54][55][56][57][58]. Figure 2g shows the yield surface in the deviatoric plane governed by K c , which is the ratio of the second stress invariant on the tensile meridian, i.e., (the distance between the hydrostatic axis and the tensile meridian) to that on the compressive median, i.e., (the distance between the hydrostatic axis and the compressive meridian) at initial yield.…”