Browsing by Author "Mergheim, J."

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Open Access
Aspects of computational homogenization in magneto-mechanics: Boundary conditions, RVE size and microstructure composition
(Elsevier, 2018-01) Zabihyan, R.; Mergheim, J.; Javili, Ali; Steinmann, P.
In the present work, the behavior of heterogeneous magnetorheological composites subjected to large deformations and external magnetic fields is studied. Computational homogenization is used to derive the macroscopic material response from the averaged response of the underlying microstructure. The microstructure consists of two materials and is far smaller than the characteristic length of the macroscopic problem. Different types of boundary conditions based on the primary variables of the magneto-elastic enthalpy and internal energy functionals are applied to solve the problem at the micro-scale. The overall responses of the RVEs with different sizes and particle distributions are studied under different loads and magnetic fields. The results indicate that the application of each set of boundary conditions presents different macroscopic responses. However, increasing the size of the RVE, solutions from different boundary conditions get closer to each other and converge to the response obtained from periodic boundary conditions.
Open Access
Towards elasto-plastic continuum-kinematics-inspired peridynamics
(Elsevier BV, 2021-07-01) Javili, Ali; McBride, A. T.; Mergheim, J.; Steinmann, P.
The main objective of this contribution is to develop a dissipation-consistent elasto-plastic peridynamic (PD) formulation that is also geometrically exact. We distinguish between one-neighbour, two-neighbour and three-neighbour interactions. One-neighbour interactions are equivalent to the bond-based interactions of the original PD formalism. However, two- and three-neighbour interactions are fundamentally different to state-based interactions, as the basic elements of continuum kinematics are preserved exactly. We investigate the consequences of the angular momentum balance and provide a set of appropriate arguments for the interaction potentials accordingly. Furthermore, we elaborate on restrictions on the interaction energies and derive dissipation-consistent constitutive laws through a Coleman–Noll-like procedure. Although the framework is suitable for finite deformations, an additive decomposition of the kinematic quantities into elastic and plastic parts is rigorously proven to be a correct choice. Crucially, in our proposed scheme, the elasto-plastic framework resembles standard one-dimensional plasticity, for all interactions. Finally, we demonstrate the capability of our proposed framework via a series of numerical examples.