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The material properties of green wood in the shaft of vital trees differ significantly from the generally known material properties of technically processed, dried wood. Furthermore, completely different residual stresses and fracture mechanisms are present in the natural full cross‐section [1]. The properties also depend on the tree species. Our work focuses on green wood from european beech (Fagus...
In this work we discuss the relaxed micromorphic model and implementation details for a full three‐dimensional formulation entailing a quadratic Lagrangian‐Nédélec finite element and appropriate boundary conditions in the discrete setting.
The relaxed micromorphic model is a generalized continuum theory with the capacity to capture more complex kinematical behaviour than in the classical Cauchy continua...
Tree engineering is a young discipline utilizing trees as structural elements, where the determination of limit loads in tree trunks is of great importance. Simple numerical models underestimate the load‐bearing capacity of green wood in contrast to experimental bending tests. A well‐known reason for this is the residual stress state of the living tree lowering compressive stress towards the trunks...
We use an extended balance of linear momentum derived from stress field analysis of higher order terms in power series expansion. Thus, the balance equation accounts for higher gradients of stress in the contiguity of continuum points. Interestingly, it does not coincide with the balance of linear momentum from strain gradient elasticity. As shown in [1], it exhibits an inverse sign for the extended...
The composition of fibers and matrix is of great importance in several fields of engineering, such as steel reinforcement in concrete for civil engineering or lightweight applications in the automotive and aviation industry, as it allows combining the advantages of both materials. If the bond between fibers and matrix is ideally strong enough, the mechanical deformation can be assumed to be equal...
We use a Phase Field Model (PFM) for the evolution of load‐bearing structures on base of the equivalent stress criterion. Similar to Evolutionary Structural Optimization, the equivalent stress from all integration points is collected to evaluate a threshold. The approach couples density and stiffness to the phase field variable. The topology evolves from homogeneously filled regions by nucleation...
The comprehensive optimization of truss and frame structures considers all three kinds of optimization aspects: topology, shape, and sizing of members. However, the simultaneous solution of the problem increases the complexity of the problem and leads to high demands for the used optimization algorithm. We propose to split the process into two tasks using specialized algorithms for each stage. First,...
The present contribution compares the solution of a phase field problem by the finite element method (FEM) with isogeometric analysis (IGA). For the sake of simplicity, the coupling to additional fields is neglected. Thus, the phase field variable appears as the only unknown in the boundary value problem. The numerical solutions are compared to the analytical solution, elaborated by Falk, of the Allen‐Cahn...
Energy harvesting based on the transformation of mechanical into electrical energy is under investigation. Mechanical deformations from ambient parasitic vibrations serve as energy source for our nanogenerator concept with barium titanate as ferroelectric material. The energy harvesting process is enabled by the designed polarization domain topology. Due to the deformation in the ferroelectric film,...
Comprehensive optimization of truss and frame structures is intended to optimize all aspects of a structure: the topology, shape and size of members. However, simultaneous optimization of all mentioned aspects increases the complexity of the problem and leads to high demands for the used optimization algorithm. We propose to decompose the optimization task and to use specialized algorithms for each...
A phase field model is used to evolve structures with almost homogeneous equivalent stress σv. The model combines the sensitivity of a stress‐based and a couple‐stress‐based objective function. Since couple‐stress typically increases at stress‐singularities, it is an efficient parameter to influence the topology of load‐bearing structures facing that problem. Further, it will be shown that this combination...
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