Rate‐Sensitive Damage Theory for Brittle Solids

Abstract

A continuous damage theory is presented for the quasi‐static and dynamic behavior of brittle materials. The fact that the strain‐rate effects observed can be mainly attributed to the rate‐sensitivity of the microcracking process makes the damage concept particularly attractive. Considering flat micro‐cracks a vectorial representation is adopted for the damage variable. A free energy function dependent on the coupled invariants of strain and damage is postulated, and the constitutive equations and the damage evolution equations are derived consistently subject to thermodynamic restrictions. The stress‐strain curves for uniaxial tension and compression resulting from the theory are compared with available experimental results for concrete. A decrease in the non‐linearity of the stress‐strain curves is observed as the strain‐rate is increased. A higher strain‐rate sensitivity in tension, as compared to compression, is also predicted. Further results on uniaxial tension illustrate how pre‐existing damage influences the nonlinearity of the stress‐strain curves and results in a rotation of the damage vector.