Journal of Multiscale Modelling

A multiscale numerical model for the in-plane mechanical behavior of masonry panels is presented. At the microscale, masonry is modeled by rigid blocks interacting through plane, deformable interfaces. These may represent actual mortar joints or virtual preferential fracture surfaces of the blocks (e.g., vertical surfaces crossing a block and connecting vertical joints in the brick rows above and below the considered one). Damage parameters control the interface transitions from a cohesive linear-elastic phase to an elastic-plastic one (modeling frictional sliding and contact) and, eventually, to a completely damaged one. At the panel scale, the material is treated as a finite-element discretized Cauchy continuum, homogenizing the periodic microstructure. The model allows reproducing the main anisotropic nonlinear behaviors of masonry by finite element simulations at a reasonable computational cost. With respect to more traditional phenomenological continuum nonlinear models, a more direct use of experimental data for the quantification of the model parameters is possible. Moreover, these parameters are fewer in number, since part of the complexity of the material is represented by the explicitly modeled microstructural geometry.

We model the mechanical behavior of diatomic crystals in the light of mixture theory. Use is made of an approximation method similar to one proposed by Signorini within the theory of elasticity, by supposing that the relative motion between phases is infinitesimal. The constitutive equations for a mixture of elastic bodies in the absence of diffusion are adapted to the partially linearized case considered here, and the representation theorems for constitutive fields are applied to obtain the final expression of dynamical equations in the form which appears in theories of continua with vectorial microstructure. Comparisons are made with results of lattice theories.

The mathematical modeling of complex biological systems leads to system of coupled nonlinear partial differential equations (PDEs). In this paper, we present a short review on the interaction of the urokinase plasminogen activator (uPA) system with a model for cancer cell in the avascular phase, faced using the moving mesh PDE/(MMPDE) numerical technique. The dynamical evolution of the system as a function of the diffusion properties of cancer cells has been considered, as well as the effect of hypoxia to the cancer evolution, introducing a model equation for the nutrient oxygen. The model parameters have been taken from the data existing in the literature, in particular to gauge the oxygen supply, data determined from in vivo experiments on human tumors have been used. The numerical results obtained simulating a one-dimensional portion of the biological tissue are consistent with the data existing in the literature. Our high-resolution computations show that cancer proliferation begins through highly irregular spatio-temporal pattern, which depends on cancer motility characteristics. In presence of hypoxia, the cancer proliferation patterns are still characterized by an inhomogeneous pattern, but other effects are present which depend on the model parameters, triggered by the oxygen.

The purpose in this paper is to investigate about the behavior of aeronautics composite material subjected to a low energy impact. Low velocity impact in aircraft composite panels is a matter of concern in modern aircraft and can be used either from maintenance accidents tools or in-flight impact with debris. The proposed study considers the dynamics of impact between a small piece of granular material and a large body of composite material. The principal aim is to simulate the impact of runway debris throw-up by the landing gear against an airplane structure. In this simulation, I want to investigate on CFRP composite panels affected by granular particles at low speed in theoretical and experimental tests. The finite element analysis, initially on the macroscale and subsequently on the microscale, shows the damage inside the composite according to the experimental results, but by itself, this classic numerical approach is little suitable to investigate the complete phenomenon. Developing the question, in first step by the classical approach, appears difficult on macro and microscale relationship besides their reciprocal influence over the deformation field. To resolve the last question, I will perform the first step on macroscale FEM analysis and then reduce from the size and effects over an opportune created RVE, such that microscale main effects as local delamination can be reproduced.