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A platform for research: civil engineering, architecture and urbanism
Modelling masonry structures using gradient elasticity
Masonry is a heterogeneous and anisotropic composite material susceptible to microcracks due to the different mechanical properties of its constituents parts; the brick units and mortar joints. Several homogenisation techniques have been proposed to simplify the complex nature of masonry and models accounting for the anisotropies have been developed (Anthoine, 1997; Milani, Lourenço, & Tralli, 2006). The fundamental idea behind the homogenisation theory is to represent masonry by an isotropic continuum with average properties introducing macroscopic stresses and strains (Zucchini & Lourenço, 2009). The elastic properties of the homogenised masonry can be captured applying these models and moreover, the elastic domain boundaries can be defined. Several phenomena occurring in the micro-scale such as microcracking, size effect etc. are not taken into consideration in these homogenised masonry models. Microcracking, is an inevitable part of the mortar hydration process, but it also appears as static loads are gradually applied due to the different mechanical behaviour of the materials. Other external loads such as inertial loading due to ground shaking can cause extended extensive cracking visible in naked eye. Crack lines are formed at the boundaries of brick units and propagate through the surrounding mortar as mortar cracks. In severe loading or weak bricks cracks can also propagate through brick units. Cracks and discontinuities at interfaces cannot be captured by classical elastic theory and moreover, strain softening cannot be represented in the stress-strain law. The common modeling approach is the application of finite element method using classical linear or non-linear constitutive laws in deriving the element stiffness matrix, albeit not considering the microstructural or, scale effects. Micro models have been proposed but their use is limited to only small dimensions models such as wallettes or parts of structures. Gradient elasticity theory developed by Aifantis (Aifantis, 2009; Altan & Aifantis, 2011) is a phenomenological theory where the effect of microstructure is taken into account by modifying the classical Hooke’s law through the introduction of an extra gradient term in the form of a Laplacian of strain. This gradient-dependent elastic constitutive equation is then used in conjunction with the standard equilibrium equation and non-standard boundary conditions (associated with higher order terms) in order to determine the scale (or microstructure) dependent stress and strain fields. This paper explores the application of gradient elasticity in analysing masonry structures using finite elements (FE).
Modelling masonry structures using gradient elasticity
Masonry is a heterogeneous and anisotropic composite material susceptible to microcracks due to the different mechanical properties of its constituents parts; the brick units and mortar joints. Several homogenisation techniques have been proposed to simplify the complex nature of masonry and models accounting for the anisotropies have been developed (Anthoine, 1997; Milani, Lourenço, & Tralli, 2006). The fundamental idea behind the homogenisation theory is to represent masonry by an isotropic continuum with average properties introducing macroscopic stresses and strains (Zucchini & Lourenço, 2009). The elastic properties of the homogenised masonry can be captured applying these models and moreover, the elastic domain boundaries can be defined. Several phenomena occurring in the micro-scale such as microcracking, size effect etc. are not taken into consideration in these homogenised masonry models. Microcracking, is an inevitable part of the mortar hydration process, but it also appears as static loads are gradually applied due to the different mechanical behaviour of the materials. Other external loads such as inertial loading due to ground shaking can cause extended extensive cracking visible in naked eye. Crack lines are formed at the boundaries of brick units and propagate through the surrounding mortar as mortar cracks. In severe loading or weak bricks cracks can also propagate through brick units. Cracks and discontinuities at interfaces cannot be captured by classical elastic theory and moreover, strain softening cannot be represented in the stress-strain law. The common modeling approach is the application of finite element method using classical linear or non-linear constitutive laws in deriving the element stiffness matrix, albeit not considering the microstructural or, scale effects. Micro models have been proposed but their use is limited to only small dimensions models such as wallettes or parts of structures. Gradient elasticity theory developed by Aifantis (Aifantis, 2009; Altan & Aifantis, 2011) is a phenomenological theory where the effect of microstructure is taken into account by modifying the classical Hooke’s law through the introduction of an extra gradient term in the form of a Laplacian of strain. This gradient-dependent elastic constitutive equation is then used in conjunction with the standard equilibrium equation and non-standard boundary conditions (associated with higher order terms) in order to determine the scale (or microstructure) dependent stress and strain fields. This paper explores the application of gradient elasticity in analysing masonry structures using finite elements (FE).
Modelling masonry structures using gradient elasticity
Kouris, LAS (author) / Bournas, D (author) / Demosthenis, Vl. (author) / Kouris, EG (author) / Aifantis, EC (author)
2019-09-16
Conference paper
Electronic Resource
English
DDC:
690
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