Issue 45

F. Qui et alii, Frattura ed Integrità Strutturale, 45 (2018) 1-13; DOI: 10.3221/IGF-ESIS.45.01 6 Contact definition and boundary conditions During numerical calculation, the lower rigid plate was clamped and the speed direction of the upper rigid plate was perpendicular to the concrete specimen. There was no friction between the rigid plate and concrete specimen. To keep the element failure contact effective, the single-face automatic contact *CONTACT_AUTOMATIC_SINGLE_SURFACE was adopted for the simulation. M ATERIAL C ONSTITUTIVE M ODEL he reliability of numerical simulation hinges on the feasibility of the numerical simulation model and the accuracy of the material constitutive model. As mentioned before, Liu Haifeng et al. [16-19] simulated the performance of concrete under dynamic load based on the HJC material constitutive model. However, the HJC takes no account of the damage evolution induced by the expansion of concrete volume, and its constitutive relation fails to describe the exact strain rate effect. In this paper, the mortar, aggregate and the ITZ are all illustrated by the concrete material constitutive model proposed by Xu and Wen. The model considers the following factors: the tensile and compressive damage effect, pressure correlation, Lode corner effect and strain rate effect. Since the material properties of the ITZ have not been fully understood, the material attribute of the ITZ was assumed to be the same of the mortar, except that its intensity is 60% of the latter. The relevant features of the material constitutive model are introduced as follows. Pore state equation The mortar, aggregate and the ITZ can be considered as porous materials. The pressure-volume strain relationship can be described by the pore state equation (i.e. p ~  state equation). The volumetric strain of the fully compacted or solid materials can be expressed as [32]:   0 0 0 1 1 1             (3) where  =  /  0 -1 is the volumetric strain;  and  0 are the current density and initial density, respectively;  =  s /  and  0 =  s0 /  0 are the current porosity and initial porosity, respectively;  s and  s0 are the current density and initial density of the solid material, respectively. When   0, the concrete material belongs to the compressive state. The corresponding state equation can be expressed as:   0 0 max 1, min ,1 1 n lock lock crush p p p p                                 (4) 2 3 1 2 3 p K K K       (5) where K 1 , K 2 and K 3 are the bulk modulus of the solid material; p crush is the pore collapse pressure under the load; p lock is the pore densification pressure under the load. When   0, the concrete material belongs to the tensile state. The corresponding state equation can be expressed as: 1 p K   (6) Intensity model Considering the compressive and tensile damage effect of the material, the Lode angle effect, and strain rate effect [28-29, 33], the authors established the material constitutive relation to reveal the main mechanical features of concrete and other quasi-brittle materials based on the tripolar constrained face model. The intensity surface of concrete can be expressed according to the stress level on the material [29]: T