  The classical variational approach to brittle fracture propagation does not
distinguish between strain energy accumulation in tension versus compression
and consequently results in physically unrealistic cracking under compression.
A variety of energy splits have been proposed as a possible remedy. However, a
unique energy split that can describe this asymmetry for general loading
conditions has not been found. The main objective of this paper is to show that
a complete phase-field theory of brittle fracture nucleation and propagation,
one that accounts for the material strength at large, can naturally capture the
tension-compression asymmetry without an energy split. One such theory has been
recently proposed by Kumar et al. (2018). Over the past few years, several
studies have shown that this theory is capable of accurately describing
fracture nucleation and propagation for materials soft and hard under arbitrary
monotonic loading conditions. However, a systematic study of the
tension-compression asymmetry that emerges from this theory has not yet been
reported. This paper does precisely that. In particular, this paper reports a
comprehensive study of crack propagation in two problems, one involving a
symmetric tension-compression state and the other involving larger compressive
stresses at the crack tip. The results are compared with popular energy splits
used in literature. The results show that, remarkably, for the second problem,
only the complete theory is able to produce experimentally consistent results.
