Confinement-shear lattice model for concrete damage in tension and compression: I. Theory

The mechanical behavior of the mesostructure of concrete is simulated by a three-dimensional lattice connecting the centers of aggregate particles. The model can describe not only tensile cracking and continuous fracture but also the nonlinear uniaxial, biaxial, and triaxial response in compression, including the postpeak softening and strain localization. The particle centers representing the lattice nodes are generated randomly, according to the given grain size distribution, and Delaunay triangulation is used to determine the lattice connections and their effective cross-section areas. The deformations are characterized by the displacement and rotation vectors at the centers of the particles (lattice nodes). The lattice struts connecting the particles transmit not only axial forces but also shear forces, with the shear stiffness exhibiting friction and cohesion. The connection stiffness in tension and shear also depends on the transversal confining stress. The transmission of shear forces between particles is effected without postulating any flexural resistance of the struts. The shear transmission and the confinement sensitivity of lattice connections are the most distinctive features greatly enhancing the modeling capability. The interfacial transition zone of the matrix (cement mortar or paste) is assumed to act approximately in series coupling with the bulk of the matrix. The formulation of a numerical algorithm, verification by test data, and parameter calibration are postponed for the subsequent companion paper.