A formulation of a Cosserat-like continuum with multiple scale effects

• Published in: Computational materials science Vol. 67; pp. 113 - 122
• Main Authors: Skatulla, S., Sansour, C.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.02.2013; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Generalized continuum; Meshfree methods; Micropolar continuum; Multi-scale approach; Oriented material behaviour; Physics; Scale effects; Solid mechanics; Structural and continuum mechanics; Structural mechanics (beam, string...); Theory and numerical methods; Multi-scale approach; Generalized continuum; Oriented material behaviour; Scale effects; Meshfree methods; Micropolar continuum; Constitutive equation; Human; Freedom degree; Circular plate; Variational methods; Scale effect; Micropolar material; Displacement field; Displacement(deformation); Multiscale method; Continuum mechanics; Bone; Torsion; Cosserat material
• ISSN: 0927-0256; 1879-0801
• DOI: 10.1016/j.commatsci.2012.08.040

► Cosserat-like formulation derived from a unified generalized framework. ► Multiple scale effects and anisotropy associated with micro-structural directions. ► Extra material parameters are purely geometric ones specifying micro-space. ► Projection maps link generalized, macro- and micro-spaces. ► Straightforward and direct application of nonlinear material laws. In this work a generalized continuum formulation is introduced which is based on a theoretical framework of a generalized deformation description proposed by Sansour (1998) [25]. That is the deformation field is composed by macro- and micro-components according to the consideration that the generalized continuum consists of a macro- and micro-continuum. It is demonstrated that by specific definition of the topology of the micro-space this generalized deformation formulation allows for the derivation of a generalized variational principle together with corresponding strain measures and underlying equilibrium equations. The approach makes use of a macroscopic rotation field which is considered to be element of the Lie group SO(3) and independent of the macroscopic displacement field. In that way the formulation incorporates three additional rotational degrees of freedom and is closely related to the Cosserat continuum. In contrast to the conventional Cosserat continuum the proposed generalized formulation allows to describe multiple scale effects associated with multiple micro-structural directions, possibly with a different magnitude for each one. The approach considers a geometrically exact description of finite deformation within the macro-continuum, but as a first step linearises the deformation within the micro-continuum. The constitutive law is defined at the microscopic level and the geometrical specification of the micro-continuum is the only material input which goes beyond that needed in a classical description. Various meshfree computations demonstrate that this model is able to address fundamental physical phenomena which are related to the underlying micro-structure of the material, in particular scale-effects and oriented material behaviour. Clear differences are revealed between a classical and the non-classical formulation.