A semi-analytical integration method for the numerical simulation of nonlinear visco-elasto-plastic materials

Thermo-viscoelastic homogenization of 3D woven composites with time-dependent expansion coefficients

“…The numerical implementation of the integral form of viscoelasticity is largely simplified if the relaxation modulus can be written in terms of a Prony series [Zocher et al, 1997;Sawant and Muliana, 2008;Hirsekorn et al, 2010Hirsekorn et al, , 2011, i.e.,…”

“…For numerical integration of the constitutive equations in a FE code, we assume that the evolution of strain, CTE, and CCS over a given time step is linear. With this approximation, the evolution equations of the internal variables can be solved analytically to obtain their increments over the time step [Zocher et al, 1997;Hirsekorn et al, 2011]. More details on the incremental procedure are given in Appendix A.…”

Formulation of non-linear viscoelastic–viscoplastic constitutive equation for polyamide 6 resin

“…In some studies, the viscoelastic behavior is neglected and thus the numerical implementation into commercial software applied to a finite element analysis, such as ABA-QUS, is relatively easy; however, this might be unsuitable for cases discussing long-term durability [13,20,21,22,23,24,25,26]. Many studies have employed non-linear viscoelastic-viscoplastic constitutive equations to express the time-dependent stress-strain relationships of matrix resins [27,28,29,30,31,32,33,34,35,36]. For example, there have been studies on applying damage as a factor in a non-linear viscoelastic-viscoplastic constitutive equation [37,38,39,40,41].…”

An Eigenexpansion Method in 2D Viscoelastic Materials

“…The Laplace transform is an effective method since the problems can be discussed in the phase domain [11][12][13][14][15]. However, this method present some difficulties due to its inverses transform can not be purchased by analytical techniques [16][17][18][19][20][21][22][23]. Thus numerical approaches are often used [24][25][26][27][28][29][30][31].…”