<p>This study aims to use the improved modified extended tanh-function technique (IMETFT) as an analytical approach to investigate the impact of laser pulses on thermoelastic materials with temperature-dependent properties, modeled within the framework of the Lord–Shulman (L-S) theory. Nonlinear thermoelasticity explores scenarios where thermal loading induces significant alterations in both the material characteristics and geometry of a system, which is critical for describing phenomena such as high-rate laser heating and thermal stress generation. Using IMETFT, various families of analytic solutions were derived, involving rational, hyperbolic, and exponential forms. To validate their physical relevance, numerical simulations were conducted for copper with thermoelastic constants (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\lambda _{0}=7.76\times 10^{10}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>λ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>7.76</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>10</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> N/m<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$^{2}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>2</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mu _{0}=3.86\times 10^{10}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>μ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>3.86</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>10</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> N/m<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$^{2}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>2</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\rho _{0}=8954$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>ρ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>8954</mn> </mrow> </math></EquationSource> </InlineEquation> kg/m<InlineEquation ID="IEq6"> <EquationSource Format="TEX">$^{3}$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>3</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$k_{0}=386$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>386</mn> </mrow> </math></EquationSource> </InlineEquation> W/mK) under laser pulse excitation (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">$I_{0}=10^{5}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>I</mi> <mn>0</mn> </msub> <mo>=</mo> <msup> <mn>10</mn> <mn>5</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> J, <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$t_{0}=22$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>22</mn> </mrow> </math></EquationSource> </InlineEquation> ps, <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$r=60~\mu $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>r</mi> <mo>=</mo> <mn>60</mn> <mspace width="3.33333pt" /> <mi>μ</mi> </mrow> </math></EquationSource> </InlineEquation>m). The results reveal a symmetric contractive displacement trough centered at <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$\breve{y}=0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mi>y</mi> <mo>˘</mo> </mover> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, a bell-shaped thermal peak with rapid attenuation, and compressive stresses exceeding <InlineEquation ID="IEq12"> <EquationSource Format="TEX">$-0.58$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mn>0.58</mn> </mrow> </math></EquationSource> </InlineEquation> in normalized units. These findings provide quantitative insight into the interplay between thermal waves and elastic deformation, offering a robust predictive framework for ultrafast laser–material interactions in micro- and nanoscale engineering applications.</p>

Effects of the laser pulses on certain nonlinear thermoelastic media with an efficient analytical technique

期刊论文
发表日期：

2025年10月16日

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Islam Samir,
Hamdy M. Ahmed,
Marin Marin,
Mohamed F. Ismail

摘要

This study aims to use the improved modified extended tanh-function technique (IMETFT) as an analytical approach to investigate the impact of laser pulses on thermoelastic materials with temperature-dependent properties, modeled within the framework of the Lord–Shulman (L-S) theory. Nonlinear thermoelasticity explores scenarios where thermal loading induces significant alterations in both the material characteristics and geometry of a system, which is critical for describing phenomena such as high-rate laser heating and thermal stress generation. Using IMETFT, various families of analytic solutions were derived, involving rational, hyperbolic, and exponential forms. To validate their physical relevance, numerical simulations were conducted for copper with thermoelastic constants ( $\lambda _{0}=7.76\times 10^{10}$ $λ_{0} = 7.76 \times 10^{10}$ N/m $^{2}$ $^{2}$ , $\mu _{0}=3.86\times 10^{10}$ $μ_{0} = 3.86 \times 10^{10}$ N/m $^{2}$ $^{2}$ , $\rho _{0}=8954$ $ρ_{0} = 8954$ kg/m $^{3}$ $^{3}$ , $k_{0}=386$ $k_{0} = 386$ W/mK) under laser pulse excitation ( $I_{0}=10^{5}$ $I_{0} = 10^{5}$ J, $t_{0}=22$ $t_{0} = 22$ ps, $r=60~\mu $ $r = 60 μ$ m). The results reveal a symmetric contractive displacement trough centered at $\breve{y}=0$ $\overset{˘}{y} = 0$ , a bell-shaped thermal peak with rapid attenuation, and compressive stresses exceeding $-0.58$ $- 0.58$ in normalized units. These findings provide quantitative insight into the interplay between thermal waves and elastic deformation, offering a robust predictive framework for ultrafast laser–material interactions in micro- and nanoscale engineering applications.