@article{30656, abstract = {{AbstractOptimized material parameters obtained from parameter identification for verification wrt a certain loading scenario are amenable to two deficiencies: Firstly, they may lack a general validity for different loading scenarios. Secondly, they may be prone to instability, such that a small perturbation of experimental data may ensue a large perturbation for the material parameters. This paper presents a framework for extension of hyperelastic models for rubber-like materials accounting for both deficiencies. To this end, an additive decomposition of the strain energy function is assumed into a sum of weighted strain mode related quantities. We propose a practical guide for model development accounting for the criteria of verification, validation and stability by means of the strain mode-dependent weighting functions and techniques of model reduction. The approach is successfully applied for 13 hyperelastic models with regard to the classical experimental data on vulcanized rubber published by Treloar (Trans Faraday Soc 40:59–70, 1944), showing both excellent fitting capabilties and stable material parameters.}}, author = {{Mahnken, Rolf}}, issn = {{0939-1533}}, journal = {{Archive of Applied Mechanics}}, keywords = {{Mechanical Engineering}}, number = {{3}}, pages = {{713--754}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters}}}, doi = {{10.1007/s00419-021-02069-y}}, volume = {{92}}, year = {{2022}}, } @article{34074, author = {{Mahnken, Rolf and Mirzapour, Jamil}}, issn = {{0939-1533}}, journal = {{Archive of Applied Mechanics}}, keywords = {{Mechanical Engineering}}, number = {{11}}, pages = {{3295--3323}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{A statistically based strain energy function for polymer chains in rubber elasticity}}}, doi = {{10.1007/s00419-022-02237-8}}, volume = {{92}}, year = {{2022}}, } @article{29085, author = {{Cheng, C. and Mahnken, Rolf}}, issn = {{0939-1533}}, journal = {{Archive of Applied Mechanics}}, pages = {{3869--3888}}, title = {{{A modified Zerilli–Armstrong model as the asymmetric visco-plastic part of a multi-mechanism model for cutting simulations}}}, doi = {{10.1007/s00419-021-01982-6}}, year = {{2021}}, } @article{9933, author = {{Mahnken, Rolf and Lenz, Peter and Dammann, Christian}}, issn = {{0939-1533}}, journal = {{Archive of Applied Mechanics}}, pages = {{2081--2099}}, title = {{{"A least squares approach for effective shear properties in an n-layered sphere model"}}}, doi = {{10.1007/s00419-018-1431-5}}, year = {{2018}}, } @article{19426, author = {{Mahnken, Rolf and Lenz, Peter and Dammann, Christian}}, issn = {{0939-1533}}, journal = {{Archive of Applied Mechanics}}, pages = {{2081--2099}}, title = {{{A least squares approach for effective shear properties in an $${{\varvec{n}}}$$ n -layered sphere model}}}, doi = {{10.1007/s00419-018-1431-5}}, year = {{2018}}, } @article{24652, author = {{Düsing, Martin and Mahnken, Rolf}}, issn = {{0939-1533}}, journal = {{Archive of Applied Mechanics}}, pages = {{1947--1964}}, title = {{{A thermodynamic framework for coupled multiphase Ginzburg-Landau/Cahn-Hilliard systems for simulation of lower bainitic transformation}}}, doi = {{10.1007/s00419-016-1161-5}}, year = {{2016}}, } @article{9874, author = {{Hemsel, Tobias and Bornmann, Peter and Morita, Takeshi and Sondermann-Wölke, Christoph and Sextro, Walter}}, issn = {{0939-1533}}, journal = {{Archive of Applied Mechanics}}, keywords = {{Reliability, Ultrasonic power transducers, FMEA}}, pages = {{1--7}}, publisher = {{Springer Berlin Heidelberg}}, title = {{{Reliability analysis of ultrasonic power transducers}}}, doi = {{10.1007/s00419-014-0965-4}}, year = {{2014}}, } @article{9876, abstract = {{Piezoelectric inertia motors use the inertia of a body to drive it by means of a friction contact in a series of small steps. It has been shown previously in theoretical investigations that higher velocities and smoother movements can be obtained if these steps do not contain phases of stiction (''stick-slip`` operation), but use sliding friction only (''slip-slip`` operation). One very promising driving option for such motors is the superposition of multiple sinusoidal signals or harmonics. In this contribution, the theoretical results are validated experimentally. In this context, a quick and reliable identification process for parameters describing the friction contact is proposed. Additionally, the force generation potential of inertia motors is investigated theoretically and experimentally. The experimental results confirm the theoretical result that for a given maximum frequency, a signal with a high fundamental frequency and consisting of two superposed sine waves leads to the highest velocity and the smoothest motion, while the maximum motor force is obtained with signals containing more harmonics. These results are of fundamental importance for the further development of high-velocity piezoelectric inertia motors.}}, author = {{Hunstig, Matthias and Hemsel, Tobias and Sextro, Walter}}, issn = {{0939-1533}}, journal = {{Archive of Applied Mechanics}}, keywords = {{Inertia motor, High velocity, Stick-slip motor, Slip-slip operation, Friction parameter identification}}, pages = {{1--9}}, publisher = {{Springer Berlin Heidelberg}}, title = {{{High-velocity operation of piezoelectric inertia motors: experimental validation}}}, doi = {{10.1007/s00419-014-0940-0}}, year = {{2014}}, } @article{24709, author = {{Mahnken, Rolf and Dammann, Christian}}, issn = {{0939-1533}}, journal = {{Archive of Applied Mechanics}}, pages = {{21--41}}, title = {{{Simulation of strain-induced anisotropy for polymers with weighting functions}}}, doi = {{10.1007/s00419-013-0780-3}}, year = {{2013}}, } @article{24716, author = {{Nörenberg, Nicole and Mahnken, Rolf}}, issn = {{0939-1533}}, journal = {{Archive of Applied Mechanics}}, pages = {{367--378}}, title = {{{A stochastic model for parameter identification of adhesive materials}}}, doi = {{10.1007/s00419-012-0684-7}}, year = {{2012}}, } @article{24713, author = {{Mahnken, Rolf and Shaban, A.}}, issn = {{0939-1533}}, journal = {{Archive of Applied Mechanics}}, pages = {{53--71}}, title = {{{Finite elasto-viscoplastic modeling of polymers including asymmetric effects}}}, doi = {{10.1007/s00419-012-0632-6}}, year = {{2012}}, } @article{25096, author = {{Mahnken, Rolf and Schneidt, Andreas}}, issn = {{0939-1533}}, journal = {{Archive of Applied Mechanics}}, pages = {{229--253}}, title = {{{A thermodynamics framework and numerical aspects for transformation-induced plasticity at large strains}}}, doi = {{10.1007/s00419-009-0308-z}}, year = {{2009}}, }