No abstract

Highly anisotropic materials like wood and unidirectional polymer composite structures are sensitive to shear deformations, in particular close to fixed joints. Large wooden structures in buildings and, e.g. wind-turbine blades, are designed to last for decades, and hence are susceptible to unwanted creep deformations. For improved structural design, the shear-creep properties of the material are needed. These are rarely available in the literature, possibly because of technical difficulties to achieve a well-defined shear-stress state in test specimens. For cost-efficient testing, this goal of a pure stress state necessarily needs to be compromised. In the present study, we propose a simple test method based on uniaxial compression on wooden cubes, but is equally applicable for fibre composites. The viscoelastic shear properties of Norway spruce (Picea abies) under off-axis creep compression tests have been characterised in all three directions. The tests are performed in a controlled climate chamber and the creep strains are captured using digital-image correlation.

No abstract

No abstract

The literature in the field of higher-order homogenization is mainly focused on 2-D models aimed at composite materials, while it lacks a comprehensive model targeting 3-D lattice materials (with void being the inclusion) with complex cell topologies. For that, a computational homogenization scheme based on Mindlin (type II) strain gradient elasticity theory is developed here. The model is based on variational formulation with periodic boundary conditions, implemented in the open-source software FreeFEM to fully characterize the effective classical elastic, coupling, and gradient elastic matrices in lattice materials. Rigorous mathematical derivations based on equilibrium equations and Hill–Mandel lemma are provided, resulting in the introduction of macroscopic body forces and modifications in gradient elasticity tensors which eliminate the spurious gradient effects in the homogeneous material. The obtained homogenized classical and strain gradient elasticity matrices are positive definite, leading to a positive macroscopic strain energy density value—an important criterion that sometimes is overlooked. The model is employed to study the size effects in 2-D square and 3-D cubic lattice materials. For the case of 3-D cubic material, the model is verified using full-field simulations, isogeometric analysis, and experimental three-point bending tests. The results of computational homogenization scheme implemented through isogeometric simulations show a good agreement with full-field simulations and mechanical tests. The developed model is generic and can be used to derive the effective second-grade continuum for any 3-D architectured material with arbitrary geometry. However, the identification of the proper type of generalized continua for the mechanical analysis of different cell architectures is yet an open question.