Stress and Strain - Definition, Stress-Strain Curve, Hooke’s Law, SI Units (2025)

Table of Contents

What is Strain? Types of Strain Stress-Strain Curve Explaining Stress-Strain Graph Hooke’s Law Elastic Moduli of Materials Frequently Asked Questions – FAQs What does the stress-strain curve show? What is the use of the stress-strain diagram? What is the relation between stress and strain? What is the yield point in stress-strain graph? How to make a stress-strain curve? Leave a Comment FAQs

The external force per unit area of the material resulting in the stretch of the material is known as tensile stress.

Compressive Stress

Compressive stress is the force that is responsible for the deformation of the material, such that the volume of the material reduces.

Read More: Compressive Stress

What is Strain?

Strain is the amount of deformation experienced by the body in the direction of force applied, divided by the initial dimensions of the body.

The following equation gives the relation for deformation in terms of the length of a solid:

$\begin{array}{l}\epsilon = \frac{\delta l}{L}\end{array} $

where ε is the strain due to the stress applied, δl is the change in length and L is the original length of the material.

The strain is a dimensionless quantity as it just defines the relative change in shape.

Types of Strain

Strain experienced by a body can be of two types depending on stress application as follows:

Tensile Strain

The deformation or elongation of a solid body due to applying a tensile force or stress is known as Tensile strain. In other words, tensile strain is produced when a body increases in length as applied forces try to stretch it.

Compressive Strain

Compressive strain is the deformation in a solid due to the application of compressive stress. In other words, compressive strain is produced when a body decreases in length when equal and opposite forces try to compress it.

Stress-Strain Curve

When we study solids and their mechanical properties, information regarding their elastic properties is most important. We can learn about the elastic properties of materials by studying the stress-strain relationships, under different loads, in these materials.

The material’s stress-strain curve gives its stress-strain relationship. In a stress-strain curve, the stress and its corresponding strain values are plotted. An example of a stress-strain curve is given below.

Explaining Stress-Strain Graph

The different regions in the stress-strain diagram are:

(i) Proportional Limit

It is the region in the stress-strain curve that obeys Hooke’s Law. In this limit, the stress-strain ratio gives us a proportionality constant known as Young’s modulus. The point OA in the graph represents the proportional limit.

(ii) Elastic Limit

It is the point in the graph up to which the material returns to its original position when the load acting on it is completely removed. Beyond this limit, the material doesn’t return to its original position, and a plastic deformation starts to appear in it.

(iii) Yield Point

The yield point is defined as the point at which the material starts to deform plastically. After the yield point is passed, permanent plastic deformation occurs. There are two yield points (i) upper yield point (ii) lower yield point.

(iv) Ultimate Stress Point

It is a point that represents the maximum stress that a material can endure before failure. Beyond this point, failure occurs.

(v) Fracture or Breaking Point

It is the point in the stress-strain curve at which the failure of the material takes place.

Hooke’s Law

In the 19th-century, while studying springs and elasticity, English scientist Robert Hooke noticed that many materials exhibited a similar property when the stress-strain relationship was studied. There was a linear region where the force required to stretch the material was proportional to the extension of the material, known as Hooke’s Law.

Hooke’s Law states that the strain of the material is proportional to the applied stress within the elastic limit of that material.

Mathematically, Hooke’s law is commonly expressed as:

F = –k.x

Where F is the force, x is the extension in length, and k is the constant of proportionality known as the spring constant in N/m.

Read More: Hooke’s Law

See the video below to learn about the stress-strain curve and Hooke’s law.

Elastic Moduli of Materials

The following table lists Young’s modulus, shear modulus and bulk modulus for common materials.

Material	Young’s modulus (E) in GPa	Shear modulus (G) in GPa	Bulk modulus (K) in GPa
Glass	55	23	37
Steel	200	84	160
Iron	91	70	100
Lead	16	5.6	7.7
Aluminium	70	24	70

Note: GPa is gigapascal and 1 GPa = 1,00,00,00,000 Pa.

Related Reading

Poisson’s ratio
Young’s Modulus
Yield Strength
Plastic Deformation

Frequently Asked Questions – FAQs

What does the stress-strain curve show?

A stress-strain curve is a graphical way to show the reaction of a material when a load is applied. It shows a comparison between stress and strain.

What is the use of the stress-strain diagram?

The stress-strain diagram provides a graphical measurement of the strength and elasticity of the material. Also, the behaviour of the materials can be studied with the help of the stress-strain diagram, which makes it easy to understand the application of these materials.

What is the relation between stress and strain?

The relation between stress and strain is that they are directly proportional to each other up to an elastic limit. Hooke’s law explains the relationship between stress and strain. According to Hooke’s law, the strain in a solid is proportional to the applied stress and this should be within the elastic limit of that solid.

What is the yield point in stress-strain graph?

Yield point is defined as the point at which the material starts to deform plastically. After the yield point is passed, permanent plastic deformation occurs.

How to make a stress-strain curve?

The stress-strain curve is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress and strain can be determined.

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Comments

Lupho Mshumi July 16, 2020 at 3:54 am

Thank you. It is clear, simple and easy to understand

Girish harihar October 19, 2020 at 5:13 pm

Strees and strain difference

sushmitha October 19, 2020 at 7:50 pm

Learn about the difference between stress and strain here.

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')))}):d.click(function(e){e.preventDefault();var a=USER_DETAILS_INPUT_VALIDATORS.phoneValidation(t)&&USER_DETAILS_INPUT_VALIDATORS.nameValiadation(r)&&USER_DETAILS_INPUT_VALIDATORS.emailValidation(i)&&USER_DETAILS_INPUT_VALIDATORS.requiredValidation(o,"","Comment")&&USER_DETAILS_INPUT_VALIDATORS.cityValidation(n,"","City")&&USER_DETAILS_INPUT_VALIDATORS.requiredValidation(s,"","Grade");if(a&&MOBILE_OTP_VALIDATER.isPhoneNumberVerified){jQuery(".cb-error-msg, .cb-success-msg").remove(),jQuery(d).attr("disabled",!0).text("Posting..."),DEFAULT_USER_DETAILS.isUserAlreadyLoggedIn=!0,DEFAULT_USER_DETAILS.isMobileAlreadyVerified=!0,MOBILE_OTP_VALIDATER.verifyToken?DEFAULT_USER_DETAILS.authorization=MOBILE_OTP_VALIDATER.verifyToken:(userFromStorage=JSON.parse(getStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE")),authToken=userFromStorage.authorization,DEFAULT_USER_DETAILS.authorization=authToken),DEFAULT_USER_DETAILS.verifyKey||(userFromStorage=JSON.parse(getStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE")),DEFAULT_USER_DETAILS.verifyKey=userFromStorage.verifyKey),void 0===SESSION_ID&&(DEFAULT_USER_DETAILS.sessionId=generateRandomID()),void 0===SESSION_ID_SECONDARY&&(DEFAULT_USER_DETAILS.sessionIdSecondary=generateRandomID());var l={first_name:r.val(),mobile_number:t.val(),email_address:i.val(),category_type:"COMMENT",session_id:DEFAULT_USER_DETAILS.sessionId,session_id_secondary:DEFAULT_USER_DETAILS.sessionIdSecondary,grade:s.val(),city:n.val(),authorization:DEFAULT_USER_DETAILS.authorization,currentUrl:C_URL,Website_URL:C_URL,Platform:void 0!==navigator.isMobile?navigator.isMobile?"website_mobile":"website_desktop":"",Lead_Magnet_Type:"LEAVE_A_COMMENT_FORM",Device_Details:void 0!==navigator.detectDeviceAgent?navigator.detectDeviceAgent:"",Device_UserAgent:void 0!==navigator.userAgent?navigator.userAgent:""},m=author_submit_form=email_submit_form=captcha_submit_form=!1;u.find('button[name="submit"]').attr("disabled","disabled").val("Posting...").addClass("post-class"),u.find('textarea[name="comment"]').removeClass("cb-error");var _=u.find('textarea[name="comment"]').val().trim(),S=_.replace(/(<([^>]+)>)/gi,"_HTML_").trim(),A=S.split(" ").join("\n");A=A.replace(/^\s*(\[\s*url\s*=\s*)?(https?:\/\/)?(www\.|\S+?\.)(\S+?\.)?\S+\s*$\s*/gm,"_URL_").trim(),""===_||null==_?u.find('textarea[name="comment"]').after('Please enter comment.').addClass("cb-error"):""===S||-1!==S.indexOf("_HTML_")?u.find('textarea[name="comment"]').after('HTML tags are not allowed for comment.').addClass("cb-error"):""===A||-1!==A.indexOf("_URL_")?u.find('textarea[name="comment"]').after('Any external links or urls are not allowed.').addClass("cb-error"):m=!0;var E={},p=jQuery("#data-comment-form"),v=p.serializeArray();if(jQuery.each(v,function(e,a){E[a.name]=a.value,"_wp_unfiltered_html_comment"===a.name&&null!==a.value&&(c=!0)}),!1===c)if(u.find('input[name="author"]').removeClass("cb-error"),u.find('input[name="email"]').removeClass("cb-error"),0!==u.find('textarea[name="g-recaptcha-response"]').length){var I=u.find('textarea[name="g-recaptcha-response"]').val().trim();""===I||null==I?u.find(".g-recaptcha").append('Please check the captcha form.'):captcha_submit_form=!0}else captcha_submit_form=!0;else author_submit_form=!0,email_submit_form=!0,captcha_submit_form=!0;m&&captcha_submit_form?(MOBILE_OTP_VALIDATER.verifyToken?E.authorization=MOBILE_OTP_VALIDATER.verifyToken:(userFromStorage=JSON.parse(getStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE")),authToken=userFromStorage.authorization,E.authorization=authToken),E.comment=S,E.author=r.val(),E.email=i.val(),E.mobileNumber=l.mobile_number,delete E.city,delete E.grade,E.ajax_comment_request=1,jQuery.post(BASE_URL+"wp-comments-post.php",E,function(e){if(u.find('button[name="submit"]').attr("disabled",!1).val("Post Comment").removeClass("post-class"),null!=e){var a=JSON.parse(e);"success"===a.status&&a.response?(c?addGAEvent(USER_DETAILS_CONFIG.isUserAlreadyExist,"created Successfully"):(o.val(""),addGAEvent(USER_DETAILS_CONFIG.isUserAlreadyExist,"created Successfully"),0!==u.find('textarea[name="g-recaptcha-response"]').length&&grecaptcha.reset(),jQuery(d).attr("disabled",!1).text("Post Comment"),jQuery("#cancel-comment-reply-link").click(),jQuery(".form-submit").after('Thanks! 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Validate your Mobile Number

'))})),getInputAccordingSessionID(e,t,l,m,r,i,n,s),t.on("input",function(){USER_DETAILS_INPUT_VALIDATORS.phoneValidation(this)}),o.on("input",function(){USER_DETAILS_INPUT_VALIDATORS.requiredValidation(this,"","Comment ")}),r.on("input",function(){USER_DETAILS_INPUT_VALIDATORS.nameValiadation(this)}),i.on("input",function(){USER_DETAILS_INPUT_VALIDATORS.emailValidation(this)}),s.on("input",function(){USER_DETAILS_INPUT_VALIDATORS.requiredValidation(this,"","Grade")}),n.on("input",function(){this.isValidInput=USER_DETAILS_INPUT_VALIDATORS.cityValidation,this.requiredName="City";var e=jQuery(this);USER_DETAILS_INPUT_VALIDATORS.cityValidation(e,"","City")}),n.on("change",function(){this.isValidInput=USER_DETAILS_INPUT_VALIDATORS.cityValidation,this.requiredName="City";var e=jQuery(this);USER_DETAILS_INPUT_VALIDATORS.cityValidation(e,"","City")})}}function addGAEvent(e,a){e?GA_FLAG&&ga("send","event","Post Comment Successful","Post Comment activity "+a+" By Existed User","URL: "+C_URL):GA_FLAG&&ga("send","event","Post Comment Successful","Post Comment activity "+a+" By New User","URL: "+C_URL)}function getInputAccordingSessionID(e,a,t,r,i,s,n,o){var d,l;if(null!==getStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE")&&(d=JSON.parse(getStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE")),l=d.sessionId,sessionIDSec=d.sessionIdSecondary,void 0!==l&&"undefined"!=typeof sessionIDSec)){var m={session_id:l,session_id_secondary:sessionIDSec};jQuery.ajax({type:"POST",url:USER_DETAILS_CONFIG.apis.userChecBySessionIDUrl,data:m,success:function(e){e.success&&(a.val(e.data.mobile).attr("disabled",!0),t.addClass("hidden"),r.removeClass("hidden"),i.val(e.data.name).attr("disabled",!1).parent().removeClass("hidden"),s.val(e.data.email).attr("disabled",!1).parent().removeClass("hidden"),n.val(e.data.city).attr("disabled",!1).parent().removeClass("hidden"),o.val(e.data.grade).attr("disabled",!1).parent().removeClass("hidden"),MOBILE_OTP_VALIDATER.isPhoneNumberVerified=d.isMobileAlreadyVerified,USER_DETAILS_CONFIG.isUserAlreadyExist=!0,USER_DETAILS_CONFIG.userDetails=e.data)},error:function(e){console.log(e)}})}}var SESSION_ID,SESSION_ID_SECONDARY,DEFAULT_USER_DETAILS={author:"",email:"",mobile:"",isUserAlreadyLoggedIn:!1,isMobileAlreadyVerified:!1,sessionId:"",sessionIdSecondary:"",authorization:"",verifyKey:""},USER_DETAILS_CONFIG={isUserAlreadyExist:!1,apis:{userChecBySessionIDUrl:BASE_URL+"wp-json/spidy/v1/get_user_by_session_id_api/",userCheckUrl:BASE_URL+"wp-json/spidy/v1/user_check_api/?wp-json_allow",userCreateUpdateUrl:BASE_URL+"wp-json/spidy/v1/user_create_update_api/?wp-json_allow",city:{url:BCAP_API_BASE_URL+"api/geo_dimensions/india_state_city_list/?limit="+INDIA_STATE_CITY_LIST_LIMIT_VAL,method:"GET"}},userDetails:""},USER_DETAILS_INPUT_VALIDATORS={getParameterByName:function(e,a){a=a?"?"+a:window.location.search;var t=new RegExp("[?&]"+e.replace(/\[/g,"\\[").replace(/\]/g,"\\]")+"(?:=([^]*))?(?:[]|$)").exec(a);return t?t[1]?decodeURIComponent(t[1].replace(/\+/g," ")):"":null},requiredValidation:function(e,a,t){var r=jQuery(e),i=r.val(),s="";return r.siblings(".input-error-msg").remove(),i&&null!==i||(s=t+" is required."),s?(r.addClass("input-error").removeClass("input-valid"),r.after('

'+s+"

"),!1):(r.removeClass("input-error"),r.addClass("input-valid"),!0)},emailValidation:function(e,a){var t=jQuery(e),r=t.val(),i="",s=/^(([^<>()[\]\\.,;:\s@\"]+(\.[^<>()[\]\\.,;:\s@\"]+)*)|(\".+\"))@((\[[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}\])|(([a-zA-Z\-0-9]+\.)+[a-zA-Z]{2,13}))$/;return t.siblings(".input-error-msg").remove(),r&&null!==r?r.match(s)||(i="Email-id is not valid."):i="Email-id is required.",i?(t.addClass("input-error").removeClass("input-valid"),t.after('

'+i+"

"),!1):(t.removeClass("input-error"),t.addClass("input-valid"),!0)},nameValiadation:function(e,a,t){var r=jQuery(e),i=r.val(),s=t||"Name",n="",o=/^[a-zA-Z][a-zA-Z\-\ \.]{2,}$/i;return r.siblings(".input-error-msg").remove(),n=i&&null!==i?i.length<=2?"Name should be minimum 3 characters.":i.match(o)?"":"Accepts alphabets only.":s+" is required.",n?(r.addClass("input-error").removeClass("input-valid"),r.after('

'+n+"

"),!1):(r.removeClass("input-error"),r.addClass("input-valid"),!0)},phoneValidation:function(e,a){var t=jQuery(e),r=t.val(),i="",s=/^\d{10}$/,n=/^\d{1,10}$/;if(t.siblings(".input-error-msg").remove(),r&&null!==r)if(r.match(n))r.match(s)||(i="Mobile No. should be 10 digits.");else{let e=t.val().replace(/[^0-9]+/g,"");t.val(e),i=t.val()?"Mobile No. should be 10 digits.":"Mobile No. is required."}else i="Mobile No. is required.";return i?(t.addClass("input-error").removeClass("input-valid"),t.after('

'+i+"

"),!1):(t.removeClass("input-error"),t.addClass("input-valid"),!0)},ajaxCall:function(e,a,t,r){jQuery.ajax({type:e,url:a,crossDomain:!0,data:t,headers:{"content-type":"application/x-www-form-urlencoded"},success:function(e){r&&r(e)},error:function(e){r&&r(e)}})},cities:[],cityAutoSuggestions:function(e){var a;USER_DETAILS_INPUT_VALIDATORS.ajaxCall(USER_DETAILS_CONFIG.apis.city.method,USER_DETAILS_CONFIG.apis.city.url,"",function(e){e.results.length&&(a=e.results,USER_DETAILS_INPUT_VALIDATORS.cities=e.results)});var t=jQuery("["+e+"]"),r=t.find("input");r.on("input",function(){0;var e=jQuery(this).val().toLowerCase(),i="";if(t.find("ul").remove(),e.length>=1){var s=jQuery.grep(a,function(a,t){return 0===a.city.toLowerCase().indexOf(e)});s.length&&(s.every(function(a,t){return i+='

'+a.city.toLowerCase().replace(e,""+e+"")+"

",6!==t}),t.append("

"+i+"

"))}t.find("ul>li>a").on("click",function(e){e.stopPropagation(),r.val(jQuery(this).text()),t.find("ul").remove(),0,r[0].isValidInput(r)})}),jQuery("body").on("click",function(){t.find("ul").remove(),0})},cityValidation:function(e,a,t){if(USER_DETAILS_INPUT_VALIDATORS.requiredValidation(e,a,t)){if(!USER_DETAILS_INPUT_VALIDATORS.cities.length)return!0;if(USER_DETAILS_INPUT_VALIDATORS.cities.filter(function(a){return a.city.toLocaleLowerCase()==e.val()}).length)return e.siblings(".input-error-msg").remove(),e.removeClass("input-error"),e.addClass("input-valid"),!0;e.addClass("input-error").removeClass("input-valid"),e.after('

Should be selected from the list

')}return!1}};(function(){if(jQuery("#data-comment-form").length>0){commentForm("COMMENT");var e=jQuery("[data-name-field]"),a=jQuery("[data-email-field]"),t=jQuery("[data-grade-fg]"),r=jQuery("[data-city-fg]");e.length>0&&a.length>0&&phoneNumberValidation("#data-comment-form",e,a,t,r,"COMMENT"),USER_DETAILS_INPUT_VALIDATORS.cityAutoSuggestions("data-city-auto-suggestions-comment")}})(),window.onbeforeunload=function(){null!==getStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE")&&clearLocalStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE"),null!==getStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE_expiresIn")&&clearLocalStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE_expiresIn")};

FAQs

Stress and Strain - Definition, Stress-Strain Curve, Hooke’s Law, SI Units? ›

Hooke's Law states that the strain of the material is proportional to the applied stress within the elastic limit of that material. Mathematically, Hooke's law is commonly expressed as: F = –k.x.

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What is the SI unit of stress and strain? ›

Answer and Explanation:

Since the S.I units of Force and Area are Newton (N), and meter squared ( ) respectively, the S.I unit of Stress is: N / m 2 , or pascal (Pa). The strain is defined as the ratio fo the change in the length/volume of the object, to the original length of the object.

What is the stress-strain curve answer? ›

A stress-strain curve is a graphical depiction of a material's behavior when subjected to increasing loads. Stress is defined as the ratio of force to cross-sectional area, while strain is defined as the ratio of the change in length of a dimension to the dimension's original length.

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What are the units for stress-strain curve? ›

Engineering stress and strain

Subscript 0 denotes the original dimensions of the sample. The SI derived unit for stress is newtons per square metre, or pascals (1 pascal = 1 Pa = 1 N/m²), and strain is unitless.

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What does Hooke's law essentially defines stress or strain? ›

EXPLANATION: Hooke's law states that within the elastic limit the stress applied on a body is directly proportional to strain produced. So the Hooke's law defines the elastic limit.

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What unit is stress? ›

Stress is the measure of an external force acting over the cross sectional area of an object. Stress has units of force per area: N/m² (SI) or lb/in² (US). The SI units are commonly referred to as Pascals, abbreviated Pa.

What is the SI base unit for strain? ›

Strain has dimension of a length ratio, with SI base units of meter per meter (m/m). Hence strains are dimensionless and are usually expressed as a decimal fraction or a percentage.

What is the Hooke's law of stress-strain curve? ›

Hooke's law shows that the force needed to the material to expand or compress by some distance. The stress and strain diagram shows that the behaviour of the material under the gradual increase of the load. The stress and diagram can be drawn for all the material, to know its behaviour under different load conditions.

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How to describe a stress-strain curve? ›

Stress strain curves visually display the material's deformation in response to a tensile, compressive, or torsional load. Depending on the material being tested, a stress strain curve can indicate key properties of the material including its elastic region, plastic region, yield point, and ultimate tensile strength.

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What is the formula for the stress-strain curve? ›

stress = (elastic modulus) × strain. stress = (elastic modulus) × strain. As we can see from dimensional analysis of this relation, the elastic modulus has the same physical unit as stress because strain is dimensionless.

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What is the stress curve explained? ›

The Stress curve is a graphical representation of how stress can affect someone. It uses a curved line to show how our performance level can rise, peak and fall as demands increase. It shows how some stress can help us work at our best but also what happens when demands become too much.

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What is strain units? ›

The change in length, compared to the original length, is strain. Although it has no dimensions, strain is usually expressed in units represented as ε, which is in/in or mm/mm. Since the magnitude of the measured strain is small, the standard practice is to use units of microstrain (µε), which is [ε x 10^-6].

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What is the true stress-strain curve? ›

The true stress – true strain curve gives an accurate view of the stress-strain relationship, one where the stress is not dropping after exceeding the tensile strength stress level. True stress is determined by dividing the tensile load by the instantaneous area.

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What is the proportional limit in a stress-strain curve? ›

The proportional limit is the point on a stress-strain curve where the linear, elastic deformation region transitions into a non-linear, plastic deformation region. In other words, the proportional limit determines the greatest stress that is directly proportional to strain.