Mathematical modeling of the nonlinear triaxial behavior and damage of such a complexmaterial as concrete has been a long-standing\udchallenge in which progress has been made only in gradual increments. The goal of this study is a realistic and robust material model for explicit\udfinite-element programs for concrete structures that computes the stress tensor from the given strain tensor and some history variables. Themicroplanemodels,\udwhich use a constitutive equation in a vectorial rather than tensorial form and are semimultiscale by virtue of capturing interactions\udamong phenomena of different orientation, can serve this goal effectively. This paper presents a new concrete microplane model, M7, which\udachieves this goal much better than the previous versions M1–M6 developed at Northwestern University since 1985. The basic mathematical\udstructure of M7 is logically correlated to thermodynamic potentials for the elastic regime, the tensile and compressive damage regimes, and the\udfrictional slip regime.Given that the volumetric-deviatoric (V-D) split of strains is inevitable for distinguishing between compression failures at low\udand high confinement, the key idea is to apply the V-Dsplit only to the microplane compressive stress-strain boundaries (or strain-dependent yield\udlimits), the sumof which is compared with the total normal stress from the microplane constitutive relation. This avoids the use of the V-D split of\udthe elastic strains and of the tensile stress-strain boundary, which caused various troubles in M3–M6 such as excessive lateral strains and stress\udlocking in far postpeak uniaxial extension, poor representation of unloading and loading cycles, and inability to represent high dilatancy under\udpostpeak compression in lower-strength concretes. Moreover, the differences between high hydrostatic compression and compressive uniaxial\udstrain are accurately captured by considering the compressive volumetric boundary as dependent on the principal strain difference. The model is\udverified extensively in the companion paper.
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