https://sam.ensam.eu:443 The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material. Sun, 08 Mar 2026 09:55:50 GMT 2026-03-08T09:55:50Z http://hdl.handle.net/10985/16599 Dissipation in hysteretic rubber mount models PENAS, Rafael; GAUDIN, Arnaud; KREIS, Adrien; BALMES, Etienne Rubber mounts are elements of extreme importance in automotive suspension, and accurate modeling is crucial for comfort design. While mount characterization is typically done using cycles, actual performance is often associated with transients. The paper thus focuses on the impact of power dissipation on suspension models during transients. For scalar or 0D hysteretic models that respect Madelung rules and Masing’s law, a method is introduced to compute instant dissipation even for models where it is not explicitly available. It is shown that stiffness and dissipation depend only on the last turning point and this dependence should be the core aspect for identifying and modeling hysteretic dissipation. The second section introduces two different 0D models having the same full cycle dissipation and force amplitude, thus the same storage and loss moduli in a first harmonic approximation of the mount behavior, though having different instantaneous dissipation. The case of a transient starting torque soliciting a suspended powertrain is finally considered. The different suspension models are shown to have different instant dissipation which might deeply modify the conclusions drawn from the dynamic simulation. Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/10985/16599 2019-01-01T00:00:00Z PENAS, Rafael GAUDIN, Arnaud KREIS, Adrien BALMES, Etienne Rubber mounts are elements of extreme importance in automotive suspension, and accurate modeling is crucial for comfort design. While mount characterization is typically done using cycles, actual performance is often associated with transients. The paper thus focuses on the impact of power dissipation on suspension models during transients. For scalar or 0D hysteretic models that respect Madelung rules and Masing’s law, a method is introduced to compute instant dissipation even for models where it is not explicitly available. It is shown that stiffness and dissipation depend only on the last turning point and this dependence should be the core aspect for identifying and modeling hysteretic dissipation. The second section introduces two different 0D models having the same full cycle dissipation and force amplitude, thus the same storage and loss moduli in a first harmonic approximation of the mount behavior, though having different instantaneous dissipation. The case of a transient starting torque soliciting a suspended powertrain is finally considered. The different suspension models are shown to have different instant dissipation which might deeply modify the conclusions drawn from the dynamic simulation. http://hdl.handle.net/10985/22300 A unified non-linear system model view of hyperelasticity, viscoelasticity and hysteresis exhibited by rubber PENAS, Rafael; BALMES, Etienne; GAUDIN, Arnaud Rubber modeling is an old subject and so many models exist that it is difficult to have a clear vision of what exists and is more appropriate. Rather than attempting a standard review, this paper proposes classification using the traditional system modeling strategy, where raw measurements are either processed to obtain non-parametric models, or used to identify parametric models, whose accuracy can be controlled by order selection or by numerical implementation considerations. A full test campaign, including multi-step relaxation, low speed triangular and sine tests, on a large deformation compression sample is used to illustrate the need to model and combine the base behaviors known as hyperelasticity, viscoelasticity, and rate independent hysteresis. The equivalence between linear viscoelasticity and linear time invariant systems is used to clarify the link between order selection and accuracy of a generalized Maxwell model. Rate independent hysteresis is analyzed using a convolution product like the one used for viscoelastic transients by introducing a relaxation modulus. Measurements of the hysteretic relaxation modulus are used to propose strategies to measure the asymptotic hyperelastic modulus and discriminate between different hysteretic model forms. A parallel between Iwan and Maxwell models is detailed, and non-parametric models are used to show that the two overlap in the low frequency small deformation regime. Regularized rate independent hysteresis and non-linear viscoelasticity are finally shown to lead to a similar view allowing a transition between the rate independent and linear relaxation models. The instantaneous ratio analytic force and displacement signals, or instant complex modulus, is introduced as novel non-parametric estimation of sine measurements and shown to be a powerful tool to analyze and validate the fact that a force rate relaxation with non-linear relaxation frequencies is most appropriate to represent the non-linear coupling of all three effects. Sun, 01 May 2022 00:00:00 GMT http://hdl.handle.net/10985/22300 2022-05-01T00:00:00Z PENAS, Rafael BALMES, Etienne GAUDIN, Arnaud Rubber modeling is an old subject and so many models exist that it is difficult to have a clear vision of what exists and is more appropriate. Rather than attempting a standard review, this paper proposes classification using the traditional system modeling strategy, where raw measurements are either processed to obtain non-parametric models, or used to identify parametric models, whose accuracy can be controlled by order selection or by numerical implementation considerations. A full test campaign, including multi-step relaxation, low speed triangular and sine tests, on a large deformation compression sample is used to illustrate the need to model and combine the base behaviors known as hyperelasticity, viscoelasticity, and rate independent hysteresis. The equivalence between linear viscoelasticity and linear time invariant systems is used to clarify the link between order selection and accuracy of a generalized Maxwell model. Rate independent hysteresis is analyzed using a convolution product like the one used for viscoelastic transients by introducing a relaxation modulus. Measurements of the hysteretic relaxation modulus are used to propose strategies to measure the asymptotic hyperelastic modulus and discriminate between different hysteretic model forms. A parallel between Iwan and Maxwell models is detailed, and non-parametric models are used to show that the two overlap in the low frequency small deformation regime. Regularized rate independent hysteresis and non-linear viscoelasticity are finally shown to lead to a similar view allowing a transition between the rate independent and linear relaxation models. The instantaneous ratio analytic force and displacement signals, or instant complex modulus, is introduced as novel non-parametric estimation of sine measurements and shown to be a powerful tool to analyze and validate the fact that a force rate relaxation with non-linear relaxation frequencies is most appropriate to represent the non-linear coupling of all three effects. http://hdl.handle.net/10985/23311 Hyper-reduced models of hyperelastic dissipative elastomer bushings PENAS, Rafael; GAUDIN, Arnaud; BALMES, Etienne Rubber mount modeling in multibody simulation is crucial for accuracy in this type of calculation, and despite its importance, they are often underestimated in terms of modeling. The present work aims to develop and implement a finite element model suited for rubber behavior in large deformations, and apply hyperreduction techniques to evaluate the possibility of a direct implementation into a multibody simulation, or to generate a novel family of joint models. The article begins with the development and implementation of the material behavior, then a brief explanation on the implemented finite elements routine along with the hyper-reduction method used. An analysis of the results and an insight of future developments closes the article. Tue, 01 Sep 2020 00:00:00 GMT http://hdl.handle.net/10985/23311 2020-09-01T00:00:00Z PENAS, Rafael GAUDIN, Arnaud BALMES, Etienne Rubber mount modeling in multibody simulation is crucial for accuracy in this type of calculation, and despite its importance, they are often underestimated in terms of modeling. The present work aims to develop and implement a finite element model suited for rubber behavior in large deformations, and apply hyperreduction techniques to evaluate the possibility of a direct implementation into a multibody simulation, or to generate a novel family of joint models. The article begins with the development and implementation of the material behavior, then a brief explanation on the implemented finite elements routine along with the hyper-reduction method used. An analysis of the results and an insight of future developments closes the article.