A new finite strain elastoplastic J2-flow model is established with an explicit formulation of work-hardening and softening effects up to eventual failure,in which both a new flow rule free of yielding and an asymptotically vanishing stress limit are incorporated.The novelties of this new model are as follows:(i)Fatigue failure effects under repeated loading conditions with either constant or varying amplitudes are automatically characterized as inherent response features;(ii)neither additional damage-like variables nor failure criteria need to be involved;and(iii)both high-and low-cycle fatigue effects may be simultaneously treated.A fast and efficient algorithm of high accuracy is proposed for directly simulating high-and medium-high-cycle fatigue failure effects under repeated loading conditions.Toward this goal,a direct and explicit relationship between the fatigue life and the stress amplitude is obtained by means of explicit and direct procedures of integrating the coupled elastoplastic rate equations for any given number of loading-unloading cycles with varying stress amplitudes.Numerical examples suggest that the new algorithm is much more fast and efficient than usual tedious and very time-consuming integration procedures.
According to the well-known models for rubberlike elasticity with strainstiffening effects, the unbounded strain energy is generated with the unlimitedly growing stress when the stretch approaches certain limits. Toward a solution to this issue, an explicit approach is proposed to derive the multi-axial elastic potentials directly from the uniaxial potentials. Then, a new multi-axial potential is presented to characterize the strain-stiffening effect by prescribing suitable forms of uniaxial potentials so that the strain energy is always bounded as the stress grows to infinity. Numerical examples show good agreement with a number of test data.
A new finite strain elatoplastic J2-flow model with coupling effects of both isotropic and anisotropic hardening is proposed with the co-rotational logarithmic rate.In terms of certain single-variable shape functions representing uniaxial loading and unloading curves,explicit multi-axial expressions for the three hardening quantities incorporated in the new model proposed are derived in unified forms for the purpose of automatically and accurately simulating complex pseudoelastic-to-plastic transition effects of shape memory alloys(SMAs)under multiple loading-unloading cycles.Numerical examples show that with only a single parameter of direct physical meaning for each cycle,accurate and explicit simulations may be achieved for extensive data from multiple cycle tests.
1 Uniqueness concerning exact linearization Most recently[1–2],the Schr¨odinger equation governing the quantum effects has been shown to be derivable as exact linearization from the following nonlinear field equations governing the dynamic responses of the newly discovered quantum-continua[1–2].
A new approach is proposed to characterize the work-hardening behavior of metals based on the stress-strain data from uniaxial extension testing.With this new approach,the yield strength as a function of the plastic work can be determined by directly fitting a wellchosen single-variable shape function to any given uniaxial data from the initial yielding up to the strength limit,in an explicit sense with no need to carry out the usual tedious trial-and-error procedures in treating nonlinear elastoplastic rate equations toward identifying numerous unknown parameters.Numerical examples show that the simulation results with the new approach are in accurate agreement with the test data.
Deformable micro-continua of highly localized nature are found to exactly exhibit all quantum effects commonly known for quantum entities at microscopic scale.At every instant,the spatial configuration of each such micro-continuum is prescribed by four spatial distributions of the mass,the velocity,the internal stress,and the intrinsic angular momentum.The deformability features of such micro-continua in response to all configuration changes are identified with a constitutive equation that specifies how the internal stress responds to the mass density field.It is shown that these microcontinua are endowed with the following unique response features:(i)the coupled system of the nonlinear field equations governing their dynamic responses to any given force and torque fields is exactly reducible to a linear dynamic equation governing a complex field variable;(ii)this fundamental dynamic equation and this complex field variable are just the Schrodinger equation and the complex wave function in quantum theory;and,accordingly,(iii)the latter two and all quantum effects known for quantum entities are in a natural and unified manner incorporated as the inherent response features of the micro-continua discovered,thus following objective and deterministic response patterns for quantum entities,in which the physical origins and meanings of the wave function and the Schrodinger equation become self-evident and,in particular,any probabilistic indeterminacy becomes irrelevant.
