We investigate rate-independent stress paths under constant rate of strain within the hypoplasticity theory of Kolymbas type. For a particular simplified hypoplastic constitutive model, the exact solution of the corresponding system of nonlinear ordinary differential equations is obtained in analytical form. On its basis, the behaviour of stress paths is examined in dependence of the direction of the proportional strain paths and material parameters of the model.

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We study stress paths that are obtained under proportional deformations within the rate-independent hypoplasticity theory of Kolymbas type describing granular materials like soil and broken rock. For a particular simplified hypoplastic constitutive model by Bauer, a closedform solution of the corresponding system of non-linear ordinary differential equations is available. Since only negative principal stresses are relevant for the granular body, the feasibility of the solution consistent with physics is investigated in dependence of the direction of a proportional strain path and constitutive parameters of the model.

We consider the topology optimization of a rotating electric machine in magnetoquasistatic operation in two space dimensions. This amounts to a topology optimization problem subject to a parabolic PDE constraint on a moving domain which we intend to solve by means of the topological derivative concept. For that purpose, we consider a topological perturbation of the materials in the space‐time cylinder along a trajectory given by the rotation of the machine. Using a Lagrangian approach, we derive the topological derivative formula, which depends on the solution of an exterior problem that is bounded in time and unbounded in the space directions. We use this sensitivity information for the design optimization of an electric motor by means of a level set method.