Abstract

A micropolar peridynamic model for in-plane electro-mechanical behavior of isotropic and orthotropic solids is presented. The analytical implicit formulation of the electrical part of the model is based on the definition of a proper microelectrical energy function and a specific electrical inelastic deformation parameter. A compatibility condition and a constitutive relationship has been derived and thus the electrical stiffness operator has been obtained. The electrical formulation is then coupled with a mechanical micropolar peridynamic formulation that accounts for full orthotropy and isotropy as special case. A distinctive aspect of the formulation is the use of continuous trigonometric functions, for the mechanical and electrical bond properties with respect to the principal material axes. The obtained unified model is capable to predict the mechanical response and the electrical conduction of elastic brittle materials taking into account the influence of cracks and other defects along with mechanical and/or electrical orthotropy. The proposed model has been applied to predict the electric field potential in isotropic and orthotropic square laminae, and to simulate a coupled electromechanical problem.

Abstract

In a number of applications, large size structures subjected to loads that cause highly non-linear behavior need to be analyzed. With the peridynamic theory, proposed by Stewart Silling in 2000 and 2007, elasticity and damage in quasibrittle structures such as plain and reinforced concrete structures can be modeled with the peridynamic theory. To model these structures, lattice models with brittle beam elements are used to model concrete. A shortcoming of lattice and particle models is that they are highly demanding of computational power. Molecular dynamics may be, in some cases an appropriate tool for analyzing microcracks in quasibrittle materials in compression, but molecular dynamics becomes infeasible at scales larger than a few million atoms. For example, in masonry structures, cracks form in the brick mortar joints, and concrete blocks can be assumed to have a uniform displacement field. This allows us to use the peridynamic finite element model, which is an improvement over discrete lattice models. This model assumes a continuous displacement field within each finite element, with displacement discontinuities allowed to develop between finite elements. The objective of this work is to model cracks in quasibrittle structures, with the peridynamic model. The peridynamic finite element model is shown to be much more computer timeand memoryefficient than the similar discrete particle-based models. Results show that this implementation appears to be more computationally efficient than particle or lattice models.