A new elasto-plasticity constitutive model for concrete under multiaxial compression based on experimental observations.

This thesis comprises of two different kinds of work. The first part is focussed on existing
experimental data. Investigations and observations of the behaviour of plain
concrete under triaxial and multiaxial compression following cyclic loading and a
variety of stress paths has been presented. The behaviour of concrete with different
constituents was also investigated. The directions of the plastic strain vectors were
identified. Two loading surface were also identified: (i) the Peak Nominal Stress
surface (PNS) which was identified from the peak stresses recorded from stress control
tests and (ii) the Volume Transition Stress surface (VTS) which determines the
onset of the volumetric dilation. The plastic VTS is the surface which was identified
from plastic strain components only. At this surface, the directions of the plastic
strain vectors are purely deviatoric. A proposal for the shapes of the yield surface
for concrete is given. These shapes were identified by the plastic work contours and
also from the directions of the plastic strain vectors assuming the associated flow
rule. This assumption has been verified by examining the normality of the plastic
strain vectors to the PNS surface.
Following the investigation of the experimental data, an examination of various advanced
plasticity models for concrete revealed the need to develop a new constitutive
model with a suitable shape of the loading surfaces and with a better prediction for
the stress-strain response. A new constitutive model for plain concrete has been
developed using the previous work in this field at the University of Sheffield. The
new yield surface was developed as a combination of a reflection of part of the peak
nominal stress surface (PNS) and a quartic function. The continuity, the convexity
and the normality of the yield surfaces were ensured. The model was calibrated
and the optimum values of the thirteen material constants are presented. This is
followed by a sensitivity study with simulations of a wide range of existing experimental
data. Simulations of concrete with different constituents are also presented.
The formulation of the model was simplified and verified by using numerical derivatives.
A comparative study between the analytical and numerical derivatives of the
constitutive model is presented.
The sensitivity study and the simulations of experimental tests showed that the new
constitutive model is: (i) easy to calibrate using only data from uniaxial compression
tests and one triaxial compression test, and (ii) gives very good predictions of stressstrain
response of different types of concrete under triaxial compression stresses and
at different levels of confinement all the way to the peak stress state.